THEORETICAL AND APPLIED MECHANICS

H. AREF, Head
J. W. PHILLIPS, Associate Head
212 Talbot Laboratory, 104 S. Wright St.,
Urbana, IL 61801-2935 - 217-333-2322


The Department of Theoretical and Applied Mechanics is the academic and intellectual home of the science of mechanics. The mission of the department is both to nurture mechanics as a scientific discipline in its own right and to serve as an interface between basic work and applications in the many engineering disciplines that use mechanics. Because of the interdisciplinary nature of work in mechanics, the department strives to strengthen ties with programs in related fields, such as physics, applied mathematics, geology, materials science, and scientific computing.

Founded in 1890 to provide instruction in mechanics for all College of Engineering students a duty that the department still fulfills Theoretical and Applied Mechanics (TAM) has evolved into a broad, interdisciplinary group of faculty and students tackling problems in applied and computational mathematics, dynamics, solid mechanics, fluid mechanics, and mechanics of materials. Work in applied and computational mathematics focuses on asymptotic analysis, mathematical modeling, stochastic estimation, and advanced algorithms for large-scale computing. In dynamics, there are projects on elastic waves, the role of heterogeneity on acoustic signatures, and aspects of modern dynamical systems theory including chaos. The emphasis in solid mechanics is on characterizing, understanding, and modeling the behavior of modern materials, such as composites and shape-memory alloys, and on basic mechanisms, such as localization, embrittlement, and phase transformations. The main activity in fluid mechanics is the problem of turbulent flow and approaches range from advanced experimental techniques, such as holographic particle image velocimetry, to very large-scale numerical simulations that also address problems in convection and combustion.

Graduate research is an integral part of the educational program in TAM. Most of the research projects involve master's and doctoral students engaged in thesis research. The department is an active participant in the college-wide Computational Science and Engineering Program.

Several laboratories, both for research and instruction, are maintained in TAM and service a large number of students each year. TAM is building up a considerable presence on the World Wide Web for on-campus instruction, distance learning, and general information about activities in mechanics.

An active program of visitors, seminars, and short courses hosted by the department helps further the science of mechanics within the college and across the university.



APPLIED MATHEMATICS


Stagnation Points in Vortex Flows
H. Aref,* M. Brøns (Technical Univ. of Denmark)
National Science Foundation, CTS 93-11545
We consider the problem of locating stagnation points in the flow produced by a system of N interacting point vortices in 2-D. There is a general solution, due to a theorem by Siebeck (1864), that the stagnation points are the foci of a certain plane curve of class N - 1 that has all lines connecting vortices pairwise as tangents. The theorem uses ideas from algebraic geometry. We have considered in detail the case N = 3, for which Siebeck's curve is a conic. The issue of invariance of the topology of streamlines during the motion is being explored.

The Plane Problem of Linearized Elastostatics
D. E. Carlson,* E. I. Pourmal
University of Illinois
All of the conventional approaches to the plane problem of linearized elastostatics (i.e., plane strain, plane stress, and generalized plane stress) rest on approximations that go beyond those inherent in the underlying linearized theory of elasticity. Here, we use some new results due to D. Gregory concerning the form of the exact three- dimensional solution to the plane problem to investigate these approximations.

Consequences of the Heat Conduction Inequality and Material Symmetry in Nonlinear Thermoelasticity
D. E. Carlson,* D. R. Anderson
University of Illinois
In nonlinear thermoelasticity, the heat conduction inequality is a familiar implication of the second law of thermodynamics. It has long been known that the heat conduction inequality has certain consequences such as the vanishing of the heat flux when the temperature gradient vanishes. A new consequence recently uncovered by M. E. Gurtin and P. W. Voorhees supplies the form of the constitutive equation for the heat flux vector. Here, we investigate this new structure in the presence of various material symmetries.

Propagation and Scattering of Coupled Surface Waves in Curver Elastic Structures
J. G. Harris,* A. Folguera
National Science Foundation, DMS 95-00723; Petroleum Research Fund, ACS-PRF 29555-AC9; U.S. Air Force, F49620-96-1-0190
This research investigates mathematically the propagation of a surface wave over a curved elastic shell and demonstrates that it will couple from the exterior surface to the interior one, propagate along it, and ultimately return to the exterior. Thus, it can sense damage to an interior surface and carry that information to the exterior. Curved structures must be nondestructively inspected for damage at their interior surface while in service. Ultrasonic inspection using this wave provides one way to carry this out. To date we have succeeded in exhibiting the coupling in plates whose thicknesses change slowly. Also, work on the in-plane equations in the curved coordinate system has begun.

Diffraction from Wave-bearing Strips
J. G. Harris,* S. Asghar (Quaid-i-Azam Univ.)
National Science Foundation, INT 95-11686
Diffraction from a strip when the strip is rigid has many approximate solutions of varying degrees of accuracy. One method is the Wiener- Hopf technique, which yields uniform asymptotic expressions for wide strips. The present research extends this technique to problems where the strip is elastic and therefore capable of interacting with the incident sound wave in a way that makes the interaction quite nonlocal. The problem has been formulated as a set of integral equations. Solutions are sought in the form of asymptotic expansions using the thickness of the strip as the small parameter. We are at work on solving the remaining integral equations. This work is part of a U.S.-Pakistan scientific exchange.

Development of Spline-based Numerical Methods for Turbulence Simulation
R. D. Moser,* K. Shariff (NASA Ames Res. Center)
University of Illinois
Numerical simulation of turbulence has generally relied on highly accurate numerical methods known as spectral methods. However, spectral methods are extremely limited in the geometries in which they can be used and this (among other things) has limited the application of turbulence simulation. A new class of numerical methods is being developed that retains much of the high accuracy of spectral methods, but which is considerably more flexible. The methods are similar to finite-element methods, but use spline expansions, which are more accurate than finite elements, but less flexible. They can be viewed as a compromise between the extreme accuracy of spectral methods and the great flexibility of finite-element methods.

Theory of Detonation Instability
D. S. Stewart,* M. Short
U.S. Air Force Office of Scientific Research, F49620-96-1-0260
Continuation of the project exploits relevant asymptotic limits for the standard detonation model to construct a wholly analytic theory of detonation stability. Recent new results for highly overdriven detonation are obtained. New insights on cellular detonation dynamics are obtained. Work has started on application of detonation shock dynamics to explosive systems such as flux compressors and thin-film detonation.



BEHAVIOR OF ENGINEERING MATERIALS


Phase-Field-based Modeling of Damage in Solids
E. Fried*
U.S. Office of Naval Research (SBC), ONR-TPSU-UIUC-0461-1323
This project is part of a large-scale effort in integrated predictive diagnostics. It entails the development of a theory that can be used to analyze the relationship between the physical processes underlying damage progression and the estimation from data of damage observables and predictive models. Two main types of modeling efforts can currently be identified in the literature: those that focus on modeling physical phenomena at the macroscopic level and those that are concerned with the application of perturbation and/or estimation theory to systems with parameter drift. The goal is to find model problems of intermediate complexity that bridge the gap between these two approaches.

Dislocation Mobility Controlled Brittle-to-Ductile Transition
K. J. Hsia,* B. D. Ferney
National Science Foundation, CMS 95-22661; NSF Fellowship
This study aims at developing a mechanistic model capable of predicting brittle-to-ductile transition behavior for some simple material systems. Of particular interest are those materials in which the brittle-to-ductile transition is dislocation-mobility controlled. The interactions between dislocations and the crack tip are investigated to evaluate the effect of shielding. Both the stationary crack and the propagating crack are studied to determine the effects of strain rate as well as crack velocity on brittle-to-ductile transition.

Experimental Study of Brittle-to-Ductile Transition in Cleavage Fracture
K. J. Hsia,* B. D. Ferney, M. R. DeVary, J. Gutzmer
National Science Foundation, CMS 95-22661; NSF Fellowship
Brittle-to-ductile transition is the result of the competition between two atomistic processes at sharp crack tips, namely, separation of atoms and generation of dislocations. An experimental technique is developed to reveal the key parameters of brittle-to- ductile transition, including temperature, strain rate, and critical dislocation structure at the crack tip. An atomically sharp crack is propagated with various crack velocities against a temperature gradient, from the low-temperature brittle side toward the high- temperature ductile end. Crack-arrest temperature is determined as a function of crack velocity. Dislocation structure at the arrested crack front is studied with microanalysis techniques.

Effects of Surface Microstructure on Strength
K. J. Hsia,* A. Pearlstein* (Mech. & Indus. Engr.),
U.S. Department of Energy, DE-FG02-96ER45607
The program is supported by a U.S. Department of Energy initiative to develop scientific understanding of surface preparation processes to enhance adhesive bond strength and durability for lightweight vehicles. Metal surfaces (e.g., aluminum) are usually chemically treated before being adhesively bonded together to form a structural component. The chemical treatment produces an oxide film with complicated microstructures. This project aims at providing a mechanistic understanding of the relationship between the microstructure of the oxide film and the interfacial failure strength of adhesive joints.

Experimental Study of Dislocation Nucleation Conditions
K. J. Hsia,* T. J. Lagger
National Science Foundation, CMS 95-22661
The dislocation nucleation condition at a crack tip often determines whether the fracture process is brittle or ductile. Experimental evidence shows that such nucleation occurs only at discrete sites along the crack front. However, the condition for activating these nucleation sources is not known. This project aims at providing a mechanistic understanding of the dislocation nucleation process by fundamental experiments. The crack tip condition as well as the dislocation structure will be studied, and the data will be used to develop mechanistic models.

Fatigue of Welds and Adhesive Joints
H. Sehitoglu* (Mech. & Indus. Engr.), F. V. Lawrence, Jr.* (Civil & Environ. Engr.), D. F. Socie* (Mech. & Indus. Engr.), J. E. Stubbins* (Nucl. Engr.), K. J. Hsia* (Theoret. & Appl. Mech.), N. Chen, H. Hsieh, S. Andrews, T. McGreevy
Fracture Control Program
Factors that control the fatigue behavior of welded components are currently being studied. Analytical methods for estimating the total fatigue life of butt and fillet welds subjected to variable-amplitude loading histories are evaluated. Surface treatments, such as shot peening and laser dressing of the weld toe, are investigated as possible methods for improving the fatigue strength. A new model for estimating the fatigue life of weldments has been proposed for butt, T-joint, and cruciform weldments using the concepts of "crack closure" for cracks emanating from a notch. Results compare favorably with experimental data in the UIUC fatigue data bank and with experimental work in the literature.

Fatigue Crack Growth and Crack Closure
H. Sehitoglu* (Mech. & Indus. Engr.), F. V. Lawrence, Jr.* (Civil & Environ. Engr.), D. F. Socie* (Mech. & Indus. Engr.), J. E. Stubbins* (Nucl. Engr.), K. J. Hsia* (Theoret. & Appl. Mech.), N. Chen, H. Hsieh, S. Andrews,
Fracture Control Program
The aim of this study is to develop a life prediction methodology for fatigue crack growth based on the changes in crack opening levels with maximum stress level, crack length, geometry, mean stress, and microstructure. The primary tool for the determination of opening stress is an elastic-plastic finite-element simulation of fatigue crack growth. Stress-strain behavior in the model accounts for slip at the microlevel as well as elastic anisotrophy. Fatigue crack growth data obtained under conditions of intermediate- and large-scale yielding, including low-cycle fatigue and biaxial loading, are successfully correlated only when closure-modified parameters are employed.

Life Prediction Methods for Notched Members under Nonproportional Multiaxial Fatigue
H. Sehitoglu* (Mech. & Indus. Engr.), F. V. Lawrence, Jr.* (Civil & Environ. Engr.), D. F. Socie* (Mech. & Indus. Engr.), J. E. Stubbins* (Nucl. Engr.), K. J. Hsia* (Theoret. & Appl. Mech.), N. Chen, H. Hsieh, S. Andrews,
Fracture Control Program
To develop fatigue life prediction methods for notched components subjected to nonproportional multiaxial fatigue, the local stresses and strains must be related to the global stresses and strains by some approximation procedure, such as Neuber's rule. Experimental tests on notched shafts subjected to proportional and nonproportional loading in tension and torsion are being performed. The results are being used to develop and verify the approximation procedure. Fatigue life estimates will then be made using an appropriate damage model that is based upon observations made during the tests. A life prediction scheme will be developed from the approximation procedure and the appropriate damage model and will be verified from the results of the tests.

Fatigue Life Prediction of Composites
H. Sehitoglu* (Mech. & Indus. Engr.), F. V. Lawrence, Jr.* (Civil & Environ. Engr.), D. F. Socie* (Mech. & Indus. Engr.), J. E. Stubbins* (Nucl. Engr.), K. J. Hsia* (Theoret. & Appl. Mech.), N. Chen, H. Hsieh, S. Andrews,
Fracture Control Program
Fiber-reinforced sheet molding compound is an attractive material used in ground-vehicle structural applications. It experiences cyclic loading in service, therefore, understanding the fatigue behavior as a function of processing conditions, chemistry of constituents, and loading conditions is important. The purpose of this work is to analyze some of the available fatigue data on these materials and to conduct experiments to identify the nature of damage mechanisms and to study cumulative fatigue damage. Tension-compression testing will be considered to gain insight into mean stress effects. In all these cases the fiber orientation of the molded part affects the progression of damage.

Durability of Advanced Materials
H. Sehitoglu* (Mech. & Indus. Engr.), F. V. Lawrence, Jr.* (Civil & Environ. Engr.), D. F. Socie* (Mech. & Indus. Engr.), J. E. Stubbins* (Nucl. Engr.), K. J. Hsia* (Theoret. & Appl. Mech.), N. Chen, H. Hsieh, S. Andrews,
Fracture Control Program
Recent developments in processing technology have resulted in advanced materials with lower fabrication costs and improvements in microstructural uniformity. To utilize the full potential of these materials, new design tools have to be developed in collaboration with industry. Examples of such materials include metal matrix composites and short reinforcement fibers in epoxy matrices. The metal matrix composites with higher elastic modulus, higher temperature capabilities, and lower weight compared to their counterparts represent excellent opportunities for engine, brake, and rotating components in the ground vehicle industry.

Probabilistic Methods
H. Sehitoglu* (Mech. & Indus. Engr.), F. V. Lawrence, Jr.* (Civil & Environ. Engr.), D. F. Socie* (Mech. & Indus. Engr.), J. E. Stubbins* (Nucl. Engr.), K. J. Hsia* (Theoret. & Appl. Mech.), N. Chen, H. Hsieh, S. Andrews,
Fracture Control Program
A comprehensive fatigue damage model is being developed to address the following issues: What governs the nucleation of a microcrack within a single grain or other suitable microstructural unit cell? What governs the growth of this microcrack into adjacent microstructural unit cells? When does the microcrack develop enough plasticity to sustain its growth? These elements will be combined into a model for the entire fatigue damage process.

Processing Existing Materials to Enhance Performance and Reduce Cost
H. Sehitoglu* (Mech. & Indus. Engr.), F. V. Lawrence, Jr.* (Civil & Environ. Engr.), D. F. Socie* (Mech. & Indus. Engr.), J. E. Stubbins* (Nucl. Engr.), K. J. Hsia* (Theoret. & Appl. Mech.), N. Chen, H. Hsieh, S. Andrews,
Fracture Control Program
It is no longer possible to specify a material without first considering its processing. In some applications, the so-called old materials processed in new ways are often more cost effective than some of the new advanced materials. Surface treatments such as carburizing and nitriding have been used for many years. Flexible manufacturing processes, such as those using lasers, now offer the potential to modify surfaces selectively to produce superior mechanical properties of traditional lower cost materials.

High-Temperature Static and Cyclic Fatigue Failure in Ceramic Materials
D. F. Socie* (Mech. & Indus. Engr.), K. J. Hsia,* Z. Zhao
U.S. Department of Energy, DE-FG02-96ER45439
Ceramic materials often contain a thin layer of intergranular glassy phase that becomes a viscous fluid at elevated temperatures. Failures of ceramics under static and cyclic loadings at high temperatures are strongly dependent on the behavior of the viscous phase. The current project studies in detail the response of the intergranular glassy phase for different grain geometries, a range of volume fraction of the intergranular phase, and magnitude of viscosity. Failure processes under static and cyclic loading due to accumulation of intergranular damage in the form of grain-boundary cavities are also investigated.

Constitutive Response and Failure Behavior of Energetic Materials
P. Sofronis*
DOE Center for Simulation of Advanced Rockets
A numerical simulation approach is used to understand the major issues of deformation and fracture in solid propellants. The methodology of Hill for polycrystalline aggregates is used to assess the constitutive interactions of the propellant constituents (binder, fuel, oxidizer) by the finite-element method. The adverse effect of tiny voids around the crystalline oxidizer, which form during fabrication or by long- term chemical reactions, is investigated. In this context, the effect of the propellant hardening rates on the localization of the material deformation into bands of intense shear is analyzed. A central goal of this research is to devise a criterion for the onset of unstable crack advance on the basis of local material damage.

Creep Resistance of Composite Materials
P. Sofronis,* P. B. R. Nimmagadda
University of Illinois; National Science Foundation, MSS 92-10686
Reinforcements are known to increase the creep resistance of metal and intermetallic matrix composite materials. However, at temperatures higher than approximately half the melting temperature of the matrix, the composite strength is limited and sometimes the strengthening imparted by the reinforcements is lost. The composite behavior is investigated by studying the degradation effects of stress-driven diffusion and slip along the reinforcement-matrix interface. The finite-element method is used to solve the relevant boundary-value problems, and asymptotic solutions at the sharp fiber corners are sought to study the corner singularity effects on the numerical calculations.

The Mechanics of Hydrogen Embrittlement
P. Sofronis,* H. K. Birnbaum (Mater. Sci. & Engr.),
U.S. Department of Energy, DE-FG02-96ER45439
Hydrogen embrittlement is a severe environmental type of failure and the mechanisms involved are not well understood. Recent numerical results on the effect of hydrogen on dislocation--defect interactions are used to study the hydrogen-induced localization of plastic deformation into bands of intense shear and the hydrogen effect on crack tip blunting. In hydride-forming systems, the finite-element method is used to predict the size of the hydrides accommodated by plastic deformation in the neighborhood of a crack tip. The results are used to establish criteria for the onset of crack propagation in engineering materials in the presence of hydrogen.

Mechanics of Powder Consolidation
P. Sofronis,* R. S. Averback (Mater. Sci. & Engr.),
U.S. Department of Energy, DE-FG02-96ER45439
Powder densification is used to manufacture advanced structural materials and the promising class of nanocrystalline materials. The finite-element method is used to predict the deformation of a powder under general loading conditions. Scaling laws are detected for the macroscopic strain rate as a function of the macroscopic stress in the numerical results. The mechanisms considered include linear and nonlinear deformation effects, diffusion (grain boundary and surface), and grain-boundary slip. The coupling of these mechanisms is accounted for in the models, which are tested against experimental measurements from the densification of nanophase TiO powder compacts.

Hydrogen-induced Cracking in Pressure Tubes
P. Sofronis*
Atomic Energy Control Board of Canada
The purpose of this research is to understand the phenomenology of hydride formation and fracture of the zirconium alloys used in the CANDU reactor pressure tubes. The primary focus is on modeling the stress-induced hydrogen transport and elastoplastically accommodated hydride formation and cracking resulting from tensile stresses. The thermodynamics of the accommodation is being assessed and the concept of terminal solid solubility of hydrogen as affected by the elastoplasticity stresses is thoroughly defined. The finite-element results are used to identify the temperature, strain rate, and initial concentration regimes in which hydrogen-induced failure is possible.

Numerical Modeling of Plastic Deformation and Fracture at a Blunt Notch in the Presence of Hydrogen
P. Sofronis,* A. Taha
Westinghouse Electric Corp.
The purpose of this work is to determine the critical fracture criterion for hydrogen-enhanced cracking in nickel-base alloys, including temperature and strain-rate sensitivities using finite- element calculations for stress, strain, and hydrogen distributions ahead of notched and cracked geometries. This investigation is also expected to lead to an increased understanding of the behavior of notched geometries as compared with precracked geometries.

Application of Debond Length Measurements to Examine the Mechanics of Fiber Pushout
N. R. Sottos,* V. T. Bechel
U.S. Office of Naval Research, N00014-92-J-1620
The interface failure sequence was observed during fiber pushout tests on several model composites. Composites with varying fiber-to-matrix moduli ratios, sample lengths, interface bond strength, and processing residual stresses were tested to determine which composites would debond from the top and which from the bottom. The debond length as a function of force and displacement was measured in a polariscope for two model composites. The pushout data were fit to an analytical shear-lag solution as well as a finite-element simulation of the fiber pushout problem to obtain the model II toughness of the fiber-matrix interface.

Dimensional Stability of Woven Glass/Epoxy Laminates for Circuit-Board Applications
N. R. Sottos,* P. Shrotriya
Motorola Inc.
Micromechanical structure-property relationships are developed for woven glass/epoxy laminates for circuit-board applications. Residual stresses and warpage of the laminates caused by processing and thermal cycling are investigated as a function of the microstructure of the woven material. In particular, the effects of the number of threads, crimp, and the amount of twist are studied. The influence of the two- dimensional nature of the weave on the deformation behavior is investigated also. Overall, optimization of the microstructure for dimensionally stable structures is desired.

Micromechanical Behavior of Shape-Memory-Alloy Composites
N. R. Sottos,* K. D. Jonnalagadda
U.S. Office of Naval Research, N00014-92-J-1620
Shape-memory-alloy (SMA) wires have been successfully embedded in polymer matrix composite materials to provide active vibration and structural control. Experimental and analytical methods are developed to investigate the micromechanical behavior of such SMA composites. Interferometric methods are applied to measure in situ local deformations of embedded SMA wires, while photoelastic techniques are used to examine local stresses induced during actuation. Investigations focus on the influence of interfacial surface properties on the efficiency and repeatability of actuation. Theoretical models for predicting shape-memory behavior are developed and compared with experimental observations.

Interfacial Design of Composites for Improved Damage Tolerance
N. R. Sottos,* T. J. Mackin, V. Damljanovic
U.S. Air Force Office of Scientific Research, F4962-98-1-0084
The relationship between interfacial properties and damage tolerance in high-temperature composites is investigated. A range of micro- and macro-level experimental techniques are utilized to characterize local damage and stress concentrations in a composite and to correlate the damage with interfacial properties. Model composite systems with controlled changes in the interfacial properties are used to elucidate the relationships between micromechanical properties and damage tolerance. The research should result in a detailed picture of damage evolution based upon micromechanical models that rationalize the evolution of damage in terms of interfacial properties and relate the evolution of damage to the macroscopic stress redistribution.

Characterization of Electronics Packaging Materials
N. R. Sottos,* E. A. Stout
Motorola Inc.
Trends toward smaller packages and higher circuit densities have made electronics packaging increasingly complex. Understanding the thermal and mechanical response of these various components is critical for optimizing manufacturing processes to yield maximum performance and reliability. The current work has resulted in the development of a unique capability to test small-scale electronic components using interferometric methods. This experimental setup enables in situ measurement of thermomechanical properties and constitutive response of various electronic components. Creep of electronics packaging components at elevated temperature, thermomechanical properties of thin films, and solder strains induced by thermomechanical loading of a package are investigated.

Influence of Fiber Surface Chemistry on E-Glass Bundle Strength
N. R. Sottos,* K. D. Jonnalagadda, E. N. Brown
Owens-Corning Fiberglas
An extensive experimental test program is being carried out to measure the breaking strength of glass fiber bundles with different surface chemistries when systematically subjected to different relative-humidity levels. An acoustic-emission technique is used to correlate individual fiber breaks with load--displacement data during the test. The influence of the surface chemistry on bundle strength in each of the different environments, as well as the reversibility of the effect in a dry environment, is of primary importance.

Characterization of Active Materials for Microactuators and Sensors
N. R. Sottos,* L. Lian
National Science Foundation, CMS 95-32038
As active materials are developed on smaller and smaller scales for the next generation of smart materials systems, and as the applications of these materials in micro-electro-mechanical systems (MEMS) require finer resolutions, the need to understand and predict material response becomes critical. An extensive experimental investigation is carried out to characterize the response of active materials in the form of thin films, fibers, and particulates embedded in a passive matrix or deposited on a substrate. Experimental data will be used to evaluate models reported in the literature for their ability to predict the response of active materials and provide guidelines for the development of improved models when necessary.

Mechanical Ignition of Condensed Phase Energetic Materials
D. S. Stewart,* G. A. Ruderman, E. Fried
USAF Wright Laboratory Armament Directorate; Eglin AFB, F08630-95-1- 0004; AFOSR F49620-96-1-0260
An effort continues to model the mechanical ignition of a condensed phase energetic material that is subjected to mild impact. The explosive crystal HMX has been the initial focus. A complete continuum, thermomechanical model of HMX has been formulated that models the phase changes from solid to liquid to vapor to reacted products. Calculations have been carried out for a constant-volume thermal explosion. One-dimensional time-dependent wave propagation and simulation are being developed for shear bands and longitudinal wave propagation.

Smart Tagged Composite Materials
S. R. White,* F. Browers, J. A. Hommema
U.S. Army Construction Engineering Research Laboratories, DACA88-97-K- 0001
Knowledge of the health of a material or structure is critical for timely maintenance and repair of components. This issue is especially difficult for composites because subsurface flaws are hidden from visual inspection. By incorporating smart material tags into the matrix of a polymer composite and then interrogating these tags, the state of health of a composite structure can be qualified throughout its processing and service life. Tagging materials investigated include piezoelectrics, shape-memory alloys, electrostrictives, ferromagnetics, and magnetostrictive materials.

Mechanics of Processing--Fabrication of Thick Composite Materials
S. R. White,* R. A. Lindberg
University of Illinois
Thick polymer composites are difficult to process. They are prone to thermal spiking, excessive processing time, nonuniform curing and consolidation, and high residual stresses. In this research, new manufacturing techniques are being developed to solve these problems. The underlying processing science is being investigated using a combined analytical and experimental approach. Processing models are formulated to explain and predict the behavior of thermosetting composites during cure, and experiments are conducted to validate these models. The research is multidisciplinary, drawing from principles in solid and fluid mechanics, thermodynamics, polymer chemistry, and heat transfer.

Self-repairing Polymeric Composites
S. R. White,* N. R. Sottos*, P. Geubelle,* M. R. Kessler,
U.S. Army Corps of Engineers Construction Engineering Research Laboratories, DACA88-95-D-0004-2
When a plant or animal is injured, its systems secrete certain substances to cause filling, healing, or regeneration at the site of the injury. Can structural composite materials be designed to mimic this type of healing behavior? Our research is focused on the development of self-healing concepts for polymeric composite materials. One such concept is the incorporation of hollow polymer microspheres filled with a repair agent. Once a crack occurs in the material, the repair agent would release and fill the cracks, rebonding the crack surfaces together.

The Potential Use of Corn and Its By-Products for Structural Composite Materials
S. R. White,* N. R. Sottos, T. J. Mackin
University of Illinois
About 9% of the total corn crop grown in the U.S. is currently used for nonfood, industrial applications. In most of these applications, corn and its by-products are used as a low-grade filler material. The current investigation seeks to identify the feasibility of using corn for low-cost structural composite materials. Several corn parts, including the husk, the cob, the kernel, and the silk, as well as the starch and meal, are evaluated for effectiveness as a reinforcement in a polymer matrix. Extensive characterization of the corn reinforcement, fabrication, and testing of the resulting corn composites will be carried out.



COMPUTATIONAL MECHANICS


Computational Aeroacoustics
S. Balachandar,* S. J. Parker
UIUC Air Conditioning and Refrigeration Center; University of Illinois
Computational aeroacoustics is a relatively new and rapidly growing field of research that combines the disciplines of acoustics and computational fluid mechanics. The principal goals of this project are to understand better the complex wake flow behind such objects as propeller fans and heat exchangers and to develop efficient predictive methodologies for evaluating radiated and scattered noise. Various computational approaches to aeroacoustics will be explored and the optimal methodology for the present problem will be identified.

Simulation of Mantle Convection
S. Balachandar,* D. A. Yuen,* T. A. Cortese
National Science Foundation, DMS 96-22889; Minnesota Supercomputer Institute; U.S. Army High-Performance Computing and Research Center
The strongly chaotic convective flow in the Earth's mantle is well evident through its surface manifestations of mountain formation, continental break-up, and volcanic activity. Here we model mantle convection with an anelastic-liquid approximation, which accounts for depth-dependent thermodynamic and transport properties. Internal heat generation and multiple phase transitions are included in this formalism. The resulting complex variable-coefficient PDEs are solved efficiently using spectral-method techniques. Massively parallel computing and large-scale graphics are an integral part of this ongoing program.

Simulation of Turbulent Mixing in Stirred-Tank Reactors
S. Balachandar,* M. Y. Ha,* K. Kar
Dow Chemical Co.
Stirred-tank reactors are commonly used in the chemical industry for mixing and chemical reaction. Their design and scale-up process typically relies heavily on a series of expensive laboratory-scale experiments and pilot plants. On the other hand, the predictive capability of conventional Reynolds-averaged Navier-Stokes simulations has been observed by the industry to be less than adequate in accurately accounting for the large-scale dynamics and their effect on stirring and mixing. Here we will develop and perform large-eddy simulation of flow in a simple stirred-tank reactor. The results will be compared with those obtained from particle-image velocimetry and laser-Doppler velocimetry measurements.

Phase-Field Elasticity as Applied to Phase Transitions and Fracture
E. Fried,* M. E. Gartin (Carnegie Mellon Univ.)
U.S. Department of Energy, 96-DOE-F-1682
This project focuses on the development of phase-field models that regularize conventional theories for solid-state phase transitions and dynamical fracture along with associated numerical methods. The goal is to apply these models to study nucleation and the development of fine structure during phase transitions and also to the initiation, branching, splitting, crossing, and coalescence of cracks during dynamical fracture processes.

Process Modeling and Optimization for Crashworthiness of Extruded Aluminum Components
R. B. Haber,* D. A. Tortorelli* (Mech. & Indus. Engr.),
National Science Foundation, DMI-9700460; Alcoa Corp.
The objective of this project is to improve the crashworthiness of extruded aluminum automotive components by simultaneously optimizing the process and product designs. To achieve this goal, researchers at UIUC will develop improved numerical models for extrusion and quenching processes that predict product shape and microstructure. An experimental program at Alcoa will calibrate and verify the process models, which will be integrated with existing crashworthiness models at Alcoa. Nonlinear programming strategies will be used to optimize the processing conditions and extrusion die geometry to achieve the desired performance. In particular, the quench process parameters will be optimized to obtain favorable precipitate distributions in order to limit microcracking under crash loads.

Interface between Solid Mechanics and Combustion/Turbulence
R. B. Haber,* D. A. Tortorelli* (Mech. & Indus. Engr.)
DOE Center for Simulation of Advanced Rockets
This project is part of the center's effort to develop computational technologies for large-scale, multiphysics simulations of solid-fuel rocket engines. In particular, the project addresses the problem of interfacing solid mechanics simulations of propellant and casing structures with simulations of combustion and turbulent flow within a rocket engine. Both normal and abnormal burn scenarios are of interest. Some of the computational challenges include grid generation and adaptive analysis, variable domain geometries, bridging disparate length and time scales, exchanging large data sets between simulations with diverse grid structures, and strategies for parallel execution of multiphysics codes.

Mesoscale Fracture
R. B. Haber,* P. H. Geubelle* (Aero. & Astro. Engr.)
DOE Center for Simulation of Advanced Rockets
The focus of this research is on mesoscale (i.e., pertaining to length scales associated with the propellant grain structure) simulations of fracture in solid-fuel engines. Simulations will be based on cohesive fracture models implemented in adaptive finite-element codes. Large- scale, parallel computing methods will be developed to enable three- dimensional fracture simulations. Existing cohesive failure models will be extended to model the viscoelastic fracture processes observed in solid rocket fuels. Simulation of the interactions between fracture and combustion processes is a long-term objective.

A Computational Testbed for Crack Propagation Problems in Aerospace Structures
R. B. Haber,* F. L . Carranza, J. Telesman (NASA Lewis Res. Center)
National Aeronautics and Space Administration, NGT 70374, University of Illinois
Control of creep and fatigue crack growth in high-temperature engine components is a key enabling technology for the next generation of high-performance aircraft. This project involves numerical studies of oxidation-driven crack growth at elevated temperatures. An adaptive space-time finite-element formulation models transient and steady- state crack growth, including stress-enhanced grain-boundary diffusion of oxygen. A moving cohesive interface model provides a criterion for intergranular fracture. Results include new stability criteria for cohesive fracture models and extensive studies of intergranular fracture in a viscoplastic material under various load programs, with and without oxygen embrittlement.

Motion of Propellant Combustion Interface
D. S. Stewart,*
DOE Center for Simulation of Advanced Rockets
A model for the motion of the propellant combustion interface inside a solid rocket motor is being developed. The initial model will be based on the propagation of a normal surface; hence the combustion layer will be modeled as a surface of discontinuity. The jump states will be provided by an analysis of a solid-flame reactive zone based on collaboration with Professor Quinn Brewster of Mechanical and Industrial Engineering.

Program-Burn and Level-Set Technology
D. S. Stewart,* B. S. Okhuysen, J. Bdzil (LANL)
Los Alamos National Laboratory, 673M0014-9
This project has formalized the concept of program burn, which is a numerical strategy used in detonation hydrocodes to replace the detonation reaction zone with a discrete heat-releasing algorithm on a pointwise mesh of the underlying code. New singular partial differential equations have been formulated to serve as a model for the new system. The properties of the discrete recursions that result are being studied.



DYNAMICS, VIBRATIONS, AND WAVES


Diffuse Ultrasonics and Materials Characterization
R. L. Weaver*
National Science Foundation, CMS 97-01142
The diffuse ultrasonics of polycrystalline materials is studied with a view toward ultimate applications in robust ultrasonic characterization of microstructures and flaw detection in the midst of grain noise. The main focus is on the validation of ultrasonic radiative transfer formulations of multiple diffuse scattering in polycrystals. Of particular interest is the transition from the simple single-scattering limit model used by many, through the complicated regime in which typical rays have scattered a few times, to the once again simple diffusion limit in which typical rays have scattered many times. Theoretical and numerical work is complemented by experimental work done elsewhere.

Diffuse Reverberant Ultrasonics in Time-varying Media
R. L. Weaver*
National Science Foundation, CMS 97-01142
Reverberant ultrasound in low-damping materials survives long after the pulse has terminated. Typical rays can survive for periods of the order of 105 cycles in, for example, aluminum, and therefore explore the sample thoroughly. Such fields are complex random interference patterns whose phase and amplitude are, because of the long ray path lengths, strong functions of such parameters as temperature, strain, and geometry (e.g. crack opening). This project seeks to ascertain to what extent the variation of these fields with sundry quasi-static parameters can be modeled and understood, and then perhaps used for materials characterization.

Diffuse Ultrasonics in Strongly Scattering Media
R. L. Weaver*
National Science Foundation, CMS 97-01142
Ultrasound in materials with extremely strong scattering microstructures, with mean free paths of the order of wavelengths, is studied. Examples include solid foams, slurries, and polycrystalline aggregates of crystallites of strong anisotropy. The particular focus is on energy-density fluctuations and energy transport as one approaches the Anderson localization transition.

Flow Diagnostics and Noise Generation in a Fan-Coil Assembly
R. L. Weaver,* S. Balachandar,* J. C. Dutton* (Mech. & Indus. Engr.), D. K. Ford, A. M. Jacobi
UIUC Air Conditioning and Refrigeration Center
In the air-conditioning and refrigeration industries, acoustic noise strongly influences human comfort, customer satisfaction, and general system quality. Unfortunately, the underlying noise source and the responsible components are not always well understood. This pilot project brings together researchers in fluid dynamics and acoustics in an attempt to understand the flow features responsible for the generation of objectionable noise in an axial fan and coil heat- exchanger unit. We will make measurements of flow, of radiated acoustic noise, and of near-field dynamic pressure, in an attempt to locate and characterize the actual sources of the noise.



MECHANICS OF FLUIDS


Conditional Eddies in Wall Turbulence
R. J. Adrian,* S. Balachandar, J. Zhou
U.S. Office of Naval Research, N00014-93-I-0552
The evolution of hairpin conditional eddies is being studied by direct numerical simulation. It is found that eddies of sufficient strength are capable of autogeneration--creating replicas of themselves which can eventually form long packets of hairpins that fill the wall layer.

Structure of Turbulence in Wall Layers
R. J. Adrian,* T. J. Hanratty (Chem. Engr.), Z.-C. Liu,
U.S. Office of Naval Research, N00014-82-K-0324, N00014-93-1-0552
A pulsed laser instrument is being used to measure instantaneous velocity fields in low and moderate Reynolds number turbulent flow in channels, pipes, and boundary layers. The structure in these flows is being studied as a function of Reynolds number, and the two-point spatial correlation is being measured. High-resolution techniques are being employed to examine the mechanisms that create the logarithmic layer and the outer wake region.

Turbulent Thermal Convection
R. J. Adrian,* R. L. Fernandes, S. E. Hommema,
National Science Foundation, ATM 95-22662
The structure of thermal convection is being studied by particle- image velocimetry techniques in which two-dimensional velocity vector fields in a planar "slice" of the flow are measured. Of particular interest are the structure at high Rayleigh number and measurement of two-point spatial correlations in convection between hot and cold horizontal plates, convection under a stably stratified layer, and convection over nonuniformly heated horizontal surfaces.

Holographic Particle-Image Velocimeter System
R. J. Adrian,* K. T. Christensen
Ford Research Foundation
A pulsed Nd:YAG system has been developed to record holographically sequential images of fine particles in air for the purpose of measuring three-dimensional vector fields in a volume. The system is being applied to studies of the structure of turbulence in pipe flow and in internal combustion.

Development of Particle-Image Velocimeter Instrumentation
R. J. Adrian,* Z.-C. Liu, S. M. Soloff
TSI, Inc.; National Science Foundation, ATM 95-22662
The particle-image velocimeter (PIV) technique makes simultaneous measurements of fluid velocity vectors at several thousand points in a fluid flow and provides instantaneous flow patterns. New methods of interrogation and image analysis are being investigated. Systems under development include a new interrogation approach that yields superresolution and a stereo method for 3-D vectors.

PIV Study of a Complex Flow inside a Plenum
R. J. Adrian,* S. T. Thoroddsen, C. D. Tomkins
Caterpillar Inc./Solar Turbines
Particle-image velocimetry (PIV) is applied to the study of a turbulent velocity field inside a plenum of complex geometry. A water- model fed by a 65-ft stand-pipe can generate high-volume flow rates at very large Reynolds numbers. The PIV measurements are concentrated on planar regions of particular interest to the functionality of the plenum.

Topological Fluid Dynamics of Stirring
H. Aref,* P. Boyland, M. A. Stremler
National Science Foundation, CTS 93-11545
A new approach to fluid advection is presented which utilizes the Thurston-Nielsen classification theorem. The prototypical problem of stirring of fluid confined to a disk by a finite number of stirrers is considered. A key role is played by the representation of a given stirring action as a braid in a (2 + 1)-dimensional space-time made up of the flow plane and a time axis. An experiment using a viscous fluid stirred by three rods is performed to illustrate the practical applicability of the theoretical developments.

Discrete Vortex Models of Turbulent Flows
H. Aref,* M. A. Stremler, D. L. Vainchtein, D. O. Pouchkin
National Science Foundation, CTS 93-11545; U.S. Office of Naval Research Fellowship
We are exploring various vortex systems in which the vorticity is concentrated in well-defined "coherent structures" as models of turbulent flow situations. These include forced shear layers and wakes, both in two and three dimensions. We are also exploring certain families of analytical solutions that may provide benchmarks for computer simulation codes. The hope is that these models will provide insight into turbulent flows not easily obtained by conventional Reynolds stress models.

Particle Dispersion in Large-Eddy Simulation
S. Balachandar*
DOE Center for Advanced Rocket Simulation
A next-generation large-eddy simulation (LES) formulation will be used to evaluate the deterministic predictabilty of advection and dispersion of aluminum droplets and aluminum-oxide soot. Existing subgrid-scale advection and dispersion models will be tested for their performance. Corresponding direct numerical simulations will be performed to guide development of improved subgrid models. Particular attention will be paid to the development of accurate methodologies for tracking particle size and number density spectra within the context of LES. Agglomeration of soot particles will also be considered.

Stability of Corner Flow
S. Balachandar,* S. J. Parker
NASA Langley Research Center, NAG 1-1583
Flow along a corner formed by the intersection of two solid surfaces, such as a wing-body junction, has been experimentally observed to be more unstable than the corresponding flow over a single flat surface. In this study, a self-similar mean flow in the corner region is obtained through the boundary-layer approximation. The stability of this mean flow is investigated through linear stability analysis for both inviscid and viscous modes. The resulting eigenvalue problems are very large, and efficient computational algorithms involving Arnoldi iteration and polynomial filtering are currently under investigation. Nonlinear evolution of these linearly unstable disturbances will be investigated through direct numerical simulations.

Large-Eddy Simulaton of Wake Flows
S. Balachandar,* J. W. Wu
U.S. Air Force Office of Scientific Research; National Science Foundation, CTS-9616219
One concept that looks particularly promising in the simulation of turbulent flows is large-eddy simulation (LES). However, LES is not yet a reliable predictive tool, because there are several limiting factors that still remain to be addressed. There is a concentrated effort within the Theoretical and Applied Mechanics Department directed toward the development of optimal formulations of LES using stochastic and dynamical systems concepts that address these issues. Within this larger effort, we will perform a very large-scale direct numerical simulation (DNS) of flow over a circular cylinder at a Reynolds number on the order of 3000. The DNS results will be used to guide the development of LES filters and models.

Separated Flow over an Elliptic Cylinder
S. Balachandar,* J. W. Wu
University of Illinois
Here we focus on the instability mechanisms responsible for the complex nature of flow behind two-dimensional cylinders at moderate Reynolds numbers. Using linear and weakly nonlinear stability analysis, we investigate the Hopf bifurcation and onset of periodic shedding behind circular and elliptic cylinders. A Floquet stability analysis will be used to study the secondary instability and associated onset of three-dimensionality in the wake. Direct numerical simulations of the cylinder wake have provided a detailed picture of the self-sustained autogeneration of three-dimensional streamwise vortices. Subsequent spanwise subharmonic instability and associated period-doubling mechanisms are currently under investigation.

Simulation of Aluminum Droplet Combustion
S. Balachandar,* D. S. Stewart,* H. Krier,* M. Q. Brewster*
DOE Center for Simulation of Advanced Rockets
Detailed 3-D microsimulations of aluminum droplet combustion will be performed. Effects of droplet Reynolds number and critical parameters describing the surrounding medium, such as temperature, species concentration, and local flow gradient will be investigated. A low- Reynolds-number assumption will be made to evaluate flow within the droplet; surface-tension effects of temperature and concentration gradient within the droplet can also be accounted for. Deviation from sphericity can be significant for larger droplets and this effect will be investigated by considering prolate spheroidal droplets. The effect of radiative heat transfer on droplet temperature distribution and hence on combustion rate will also be included in the analysis. The present investigation will begin with simple semiempirical chemistry.

Segregation during Flows of Granular Media
E. Fried*
University of Illinois
Applications in which granular media are encountered occur in many industries, including those that involve the processing of minerals, chemicals, pharmaceuticals, and foodstuffs. Quite often the media encountered in such settings are heterogeneous mixtures composed of particles that differ in size, shape, and other characteristics. Segregation, by particle type, commonly occurs during flows of such mixtures, with the influence of particle size believed to be the most significant. Whereas segregation is essential and desirable in mineral processing, it is highly undesirable in chemical and pharmaceutical processing, where the goal is to achieve uniform mixing. The aim of this research is to increase our understanding of the coupled influences exerted by diffusion and convection during segregation by particle size.

Turbulence Simulation for Solid Rocket Applications
R. Moser,* R. Adrian, S. Balachandar, S. Volker
DOE Center for Simulation of Advanced Rockets
New large-eddy simulation (LES) model and simulation techniques are being developed for use in the simulation of solid rocket motors. Solid rocket flows present interesting challenges to turbulence simulation, including large transpiration, combustion, large temperature and density variations, and burning particles. These complications will be treated using the optimum LES modeling technique based on stochastic estimation.

A New Approach to the Large-Eddy Simulation of Turbulence
R. D. Moser,* S. Balachandar, R. J. Adrian, J. A. Langford, S. Volker, J. W. Wu
National Science Foundation, CTS 96-16219; National Aeronautics and Space Administration, NGT 2-52229
Large-eddy simulation (LES) is a promising technique for turbulence prediction in which the largest, most energetic turbulent eddies are simulated while the effects of smaller-scale turbulence is modeled. New techniques for performing such simulations are being developed based on the formalism of stochastic estimation and on concepts from chaotic dynamical systems. In this new approach, it is possible to optimize both the subgrid model and the filtering operation by which the large scales are defined. Further, one can determine how accurate an LES can be. This new approach should allow LES to fulfill its great promise as an accurate and reliable engineering prediction tool.

Modeling Compressibility Effects in Turbulence
R. D. Moser,* S. G. Borodai, W.-Y. Kwok
U.S. Air Force Office of Scientific Research, F49620-97-1-0089
Most fundamental work in the modeling of turbulence has been done for incompressible turbulence. In this research, we extend these incompressible models to the compressible case using low-Mach-number asymptotics. Such approximations can be valid even in quite large Mach-number flows because the turbulence in these flows is generally at much lower Mach numbers. Thus, an approximation valid to very large Mach numbers can be obtained. The validity of the analysis is being confirmed by appeal to direct numerical simulations of compressible turbulent flows. This asymptotic analysis will be used to develop a rational technique for applying ideas from incompressible turbulence modeling to compressible flows.

Direct Numerical Simulation of Compressible Turbulent Boundary Layers
R. D. Moser,* S. Guarini (Stanford Univ.), N. Mansour (NASA Ames)
NASA Ames Research Center
Despite the importance of compressibility in engineering applications, compressible turbulence is not as well understood as its incompressible counterpart. In particular, there are uncertainties as to exactly what the effects of compressibility on turbulence are. Direct numerical simulation provides an opportunity to address these uncertainties because it allows us to use diagnostics that are not possible in experiments. The simulations performed here will be used to distinguish between compressibility and variable property (i.e., density and viscosity) effects, including fluctuating properties.

Turbulent Plume Convection
D. N. Riahi*
University of Illinois
Models of axisymmetric cylindrical plumes are being developed for turbulent thermal convection using asymptotic and scaling analyses. These models are based on the restrictions of infinite Prandtl number and steady-state conditions. The models will be extended to arbitrary Prandtl number, unsteady cases, and to nonaxisymmetric flow conditions and will be compared with the available experimental observations.

Renormalization Group Theory and Modeling for Turbulence
D. N. Riahi*
University of Illinois
Renormalization group theory and other modeling techniques are being developed for nonhomogeneous turbulence. The goal is to develop reliable and rational turbulence models that can be used for large- eddy simulations of complex nonhomogeneous turbulence problems.

Roughness Effects on Thermal and Shear Flows
D. N. Riahi*
University of Illinois
Effects of roughness elements of arbitrary shape, placed on the boundary of a layer of fluid, on the flow structures and instabilities are studied by analytical and computational methods. Certain conditions are determined under which the preferred flow structure is controlled and the heat flux is enhanced by the surface corrugation effects.

Instabilities in Turbulent Shear Flows
D. N. Riahi*
University of Illinois
This research concerns instabilities that exist in wall-bounded turbulent shear flows and their roles and origins in relation to streaks and large structures in such flows. Studies are based on both analytical and computational methods.

Convection during Alloy Solidification
D. N. Riahi,* C. F. Baker
University of Illinois
Effects of crystallization on nonlinear convection in a normal or high-gravity binary-alloy melt are investigated. Emphasis is given to examination of the mushy layer near the solidification front. Finite- amplitude effects are studied under certain controlling processes by analytical and computational techniques. The models include the basic physical conditions that are of interest in the field of materials processing.

Advanced Solid Rocket System Integration
D. S. Stewart*
DOE Center for Simulation of Advanced Rockets
The new 5-year, $20 million Center for Simulation of Advanced Rockets is one of the DOE Academic Alliances Level I centers in the Accelerated Strategic Computing Initiative (ASCI) Program. The goal of the center is to carry out whole-system simulations of advanced rockets on tera-scale computater platforms. A system simulation code is being developed based on constituent codes for components and interfaces. The task of system integration consists of designing system simulation models that are well-posed, can be validated against experiments, and can be successfully mapped to parallel computing architectures.

Intermittent Turbulence in a Taylor-Couette Device
S. T. Thoroddsen,* J. M. Bauer
University of Illinois
For a narrow range of parameters, the transition inside a Taylor- Couette apparatus is characterized by intermittent turbulent spots that grow and decay. The closed circular geometry of this configuration allows the whole life-cycle of these turbulent features to be observed. The transition from these spots to spiral turbulence is also being studied.

Effects of Buoyancy on Vortex Dynamics and Turbulence
S. T. Thoroddsen,* J. Parsons
University of Illinois
An experimental apparatus is being devised to study the effects of buoyancy forces on the vortical structures in a stably stratified fluid. A stably stratified, three-layer water channel will be constructed and instrumented with video particle-image velocimetry. Laser-induced fluorescence will also be used to study the baroclinic generation of vorticity in two parallel shear layers. The inhibition of mixing will be quantified in relation to the stratification strength and shear rates. A uniformly stratified shear channel will also be constructed, based on a new design, employing a real-time mixing manifold.

Coating Flows Inside a Partially Filled Rotating Cylinder
S. T. Thoroddsen*
University of Illinois
A partially filled circular cylinder is rotated about its horizontal axis of symmetry. The fluid is pulled up the sides of the cylinder, as in the rotomolding manufacturing process. A complicated interplay between gravity, inertial, and viscous forces, characterized by the cylinder rotation rate, volume filling ratio, and viscosity of the fluid, leads to a number of different flow regimes, some exhibiting instabilities. Experiments performed over a wide range of parameter space are aimed at mapping out stable and unstable regimes to help with the design of manufacturing protocols leading to a uniform coating on the inside of the cylinder. Special attention is being paid to the hysteresis in the process.

Studies of Drop Impacts on Fluid and Solid Surfaces
S. T. Thoroddsen,* D. N. Riahi, E. N. Tan
University of Illinois
The fluid dynamics of the rapid distortion of a fluid drop impacting either a solid wall or a thin layer of fluid is studied. High-speed flash photography demonstrates the formation of a thin jet of fluid being ejected from the drop along the surface. The speed of this jet and its breakup into a fingering pattern is being studied systematically. The inertia of the fluid, its viscosity, the surface tension, and the wettability of the surface all have important effects and make theoretical analysis very difficult. The theoretical approach is based on perturbation, similarity, asymptotic, and characteristic methods.

Two-Phase Flow in a Hele-Shaw Cell
S. T. Thoroddsen,* E. N. Tan
University of Illinois
The gravity-driven flow of a bubbly liquid between two closely spaced glass plates is studied. Multiple video cameras are used to follow the motion of thousands of bubbles and their interactions. The effective forces of buoyancy, viscosity, surface tension, and inertia depend strongly on bubble size. This dependence leads to the segregation of the different bubble sizes.

Modeling Semiconductor Crystal Growth in Space with Magnetic Fields
J. S. Walker*
National Aeronautics and Space Administration, NCC 8-90
Computer chips, other integrated circuits, and optical devices are produced on polished wafers sliced from single crystals of semiconductors such as silicon and gallium-arsenide. Methods to improve crystal quality are being developed by growing crystals in space where most of the deleterious buoyant convection is eliminated. However, residual accelerations and thermocapillary convections continue to create crystal defects. NASA is planning to use a magnetic field to stabilize and control the melt motion in order to eliminate crystal defects. Asymptotic methods are being used to develop models to guide the optimization of the NASA process, and these models are being validated by comparison with experimental measurements.



MECHANICS OF SOLIDS


Nucleation and Refinement of Microstructure
E. Fried*
National Science Foundation, CMS 97-96177
Martensitic alloys exhibit metastable equilibria involving microstructures consisting of different phases and their variants. Particular microstructural features may, depending on context, enhance or inhibit performance of such alloys. This research is intended to increase understanding of the manner in which various microstructures are created and altered during the course of phase transitions in martensitic alloys.

Experimental, Analytical, and Computational Study of Nematic Optical Elastomers
E. Fried,* D. E. Carlson, R. D. James (Univ. of Minnesota)
National Science Foundation, CMS 96-10286
Optical elastomers are a novel class of materials formed by the cross- linking of polymeric liquid crystals. These materials possess properties of both scientific and technological importance, with observed phenomena including stress-induced optical switching, stress- induced shifts in phase-transition temperatures, piezoelectricity, spontaneous macroscopic shape changes accompanying phase transitions, and nonmonotonic (or discontinuous) stress-strain relations. This research combines experiment, theory, and computation with the aim of developing an understanding of the optomechanical response of nematic optical elastomers under biaxial loading conditions.

Wire Rope Path Independence
G. A. Costello,* J. M. Hardin
University of Illinois
The dependence of the loading path of a wire rope is investigated. The existing load-deformation theory is slightly path-dependent. This path dependence is believed to be caused by the approximations introduced by the relationships between the stress couples and the curvature and twist. Plots are shown depicting this discrepancy.

Cord-reinforced Cylindrical Shells
G. A. Costello,* A. J. Paris
University of Illinois
Methods for determining the load-deformation behavior of cord- reinforced cylindrical shells were developed. The matrix was modeled as linear elastic. The cords were modeled using the theory developed by Costello. The cord-reinforced shell was modeled following the theory of bending of cylindrical shells by Flügge. Two shell geometries were considered: first, the cords were parallel to the axis of the shell and on the middle surface, and second, the cords were at an angle to the axis of the shell and off the middle surface. In each case, the response due to uniformly distributed axisymmetric axial load, edge moment, transverse edge shear, in-plane shear, and uniform internal pressure has been found for both semi-infinite and finite cylinders.

A Generalized Formulation of Linearized Elastodynamics
D. A. Tortorelli* (Mech. & Indus. Engr.), D. E. Carlson
University of Illinois
The conventional theory of linearized elastodynamics addresses the case of motions that have small displacement gradients with respect to a reference configuration of the elastic body that is unstressed and at rest. Here, we develop a theory of much wider applicability in which the linearization is with respect to a reference configuration that is loaded and in rigid motion.

On the Theory of Thermoelasticity in the Presence of Internal Constraints
D. A. Tortorelli* (Mech. & Indus. Engr.), D. E. Carlson
University of Illinois
Generally, in internally constrained nonlinear thermoelasticity, it is hypothesized that the dependent fields are given by constitutive functions of appropriate independent fields to within indeterminate reaction fields. The assumption that the reactions do not contribute to the rate of entropy production in processes that satisfy the internal constraints leads to the form of the reactions. Here, we show that by a slight reorganization of the conventional development, it is possible to infer the existence of the reaction fields (except for the one corresponding to the heat flux). Furthermore, the forms of the reactions are obtained, as are the usual results for the constitutive functions.



JOURNALS AND BOOKS


Applied Mathematics
RIAHI, D. N. Renormalization group analysis for thermal turbulence. Int. J. Math. Math. Sci., 20, 305-310 (1997).
RIAHI, D. N. Weakly and strongly nonlinear stability analysis for convection systems: nonlinear instability analysis. Advances in Fluid Mechanics (Dabnath and Choudhary, eds.; Computational Mechanics Publications, UK) 186-219 (1997).
SHORT, M. and D. S. STEWART. Low-frequency, two-dimensional, linear instability of plane detonation. J. Fluid Mech., 340, 249-295 (1997).

Behavior of Materials
CASAGRANDA, A. and P. SOFRONIS. Numerical observations of scaling laws in the consolidation of powder compacts. Acta Met. Mater., 45, 4835-4845 (1997).
DEY, N., K. J. HSIA, and D. F. SOCIE. The effects of grain size distribution on cavity nucleation and creep deformation in ceramics containing viscous grain boundary phase. Acta Met. Mater., 45, 4117-4129 (1997).
FRIED, E. Correspondence between a phase-field theory and a sharp-interface theory for crystal growth. Continuum Mech. Thermodyn., 9, 33-60 (1997).
FRIED, E. and G. GRACH. An order-parameter based theory as a regularization of a sharp-interface theory for solid-solid phase transitions. Arch. Rational Mech. Anal., 138, 355-404 (1997).
HSIA, K. J. and Y.-B. XIN. Discussion on the comment on the simulation of the brittle-ductile transition in silicon single crystals using dislocation mechanics. Scr. Mater., 37:12, 1905-1907 (1997).
JONNALAGADDA, K., G. E. KLINE, and N. R. SOTTOS. Local displacements and load transfer in shape memory alloy composites. Exp. Mech., 37:1, 82-90 (1997).
XIN, Y.-B. and K. J. HSIA. Simulation of the brittle-to-ductile transition in silicon single crystals using dislocation mechanics. Acta Met. Mater., 45, 1747-1759 (1997).

Computational Mechanics
CARRANZA, F. L., B. FANG, and R. B. HABER. A moving cohesive interface model for fracture in creeping materials. Computat. Mech., 19, 517-521 (1997).
FANG, B., F. L. CARRANZA, and R. B. HABER. An adaptive discontinuous Galerkin method for viscoplastic analysis. Computer Methods Applications Mechanics and Engineering, 150, 191-198 (1997).
XU, S., T. ASLAM, and D. S. STEWART. High resolution numerical simulation of ideal and non-ideal compressible reaction flow with embedded internal boundaries. Combust. Theory Modeling, 1:1, 113-142 (1997).

Dynamics, Vibrations, and Waves
HARRIS, J. G., D. A. REBINSKY, and G. WICKHAM. Interrogating a thin layer of heterogeneity with confocal transducers. Review of Progress in Quantitative NDE (Thompson and Chimenti, eds.; Plenum) vol. 15A, 1027-1033 (1997).
LEGRAND, O., F. MORTESSAGNE, and R. L. WEAVER. Semiclassical analysis of spectral correlations in regular billiards with point scatterers. Phys. Rev. E, 55, 7741-7744 (1997).
TI, B. W., W. D. O'BRIEN, and J. G. HARRIS. Measurement of coupled wave propagation in an elastic plate. J. Acoust. Soc. Amer., 102, 1528-1531 (1997).
WEAVER, R. L. Mean and mean square responses of a prototypical master/fuzzy system. J. Acoust. Soc. Amer., 101, 1441-1449 (1997).
WEAVER, R. L. Multiple scattering theory for a plate with sprung masses, mean responses. J. Acoust. Soc. Amer., 101, 3466-3474 (1997).

Mechanics of Fluids
ADRIAN, R. J. Dynamic ranges of velocity and spatial resolution of particle image velocimetry. Meas. Sci. Technol., 8, 1393-1398 (1997).
ADRIAN, R. J. Particle-based flow visualization. J. Flow Vis. Soc. Japan, 17, Suppl. 1, 3-12 (1997).
ADRIAN, R. J., D. F. G. DURAO, F. DURST, M. V. HEITOR, M. MAEDA, and J. H. WHITELAW (eds.). Developments in Laser Techniques and Fluid Mechanics (Springer-Verlag) 477 pp. (1997).
BAKER, C. F. and D. N. RIAHI. Chimney formation and flow instabilities in a mushy layer with deformed boundaries. Centrifugal Materials Processing (Regel and Wilcox, eds.; Plenum) 163-168 (1997).
FUJISAWA, N. and R. J. ADRIAN. Three-dimensional temperature measurement by liquid crystal thermometry and its application to the study of turbulent thermal convection. Trans. Jap. Soc. Mech. Engr., 607, 63-77 (1997).
HILL, R. J. and S. T. THORODDSEN. Experimental evaluation of acceleration correlations for locally isotropic turbulence. Phys. Rev. E, 55:2, 1600-1606 (1997).
KING, S. D., S. BALACHANDAR, and J. J. ITA. Using eigenfunctions of the two-point correlation function to study convection with multiple phase transformations. Geophys. Res. Lett., 24, 703-706 (1997).
LIU, Z. C., R. J. ADRIAN, C. D. MEINHART, and W. LAI. Structure of a turbulent boundary layer using a stereoscopic, large format video-PIV. Developments in Laser Techniques and Fluid Mechanics (Adrian, et al., eds.; Springer-Verlag) 259-273 (1997).
MEI, R., R. J. ADRIAN, and T. J. HANRATTY. Turbulent dispersion of heavy particles with nonlinear drag. J. Fluids Engr., 119, 170-179 (1997).
OAKLEY, T. R., E. LOTH, and R. J. ADRIAN. A two-phase cinematic PIV method for bubbly flows. J. Fluids Engr., 119, 707-712 (1997).
RIAHI, D. N. Roughness effects on convection in a rectangular cubic box. Bulletin APS, 42, 2258 (1997).
RIAHI, D. N. Effects of high gravity on freckles formation and convection in a mushy layer. Centrifugal Materials Processing (Regel and Wilcox, eds.; Plenum Press) 169-176 (1997).
RIAHI, D. N. Effects of centrifugal and coriolis forces on chimney convection during alloy solidification. J. Cryst. Growth, 179, 287-296 (1997).
RIAHI, D. N. Effects of roughness on nonlinear stationary vortices in rotating disk flaws. Math. Comput. Modeling, 25, 71-82 (1997).
RIAHI, D. N. Finite bandwidth, long wavelength convection with boundary imperfections: near-resonant wavelength excitation. J. Math. Phys. Sci., 21, 171-182 (1997).
RIAHI, D. N. Weakly nonlinear instability of non-parallel shear-flows. Int. J. Nonlinear Mech., 32, 277-283 (1997).
SAYRE, T. L. and D. N. RIAHI. Oscillatory instabilities of the liquid and mushy regions during solidification of alloys under rotational constraint. Acta Mech., 121, 143-152 (1997).
SOLOFF, S. M., R. J. ADRIAN, and Z. C. LIU. Distortion compensation to improve the accuracy of monoscopic and stereoscopic particle image velocimetry. Meas. Sci. Technol., 8, 1393-1398 (1997).
THORODDSEN, S. T. and L. MAHADEVAN. Experimental study of coating flows in a partially-filled horizontally rotating cylinder. Exp. Fluids, 23:1, 1-13 (1997).
XU, S. and D. S. STEWART. Deflagration to detonation transition in porous energetic materials: a comparative model study. J. Engr. Math., 31, 143-172 (1997).
ZHANG, L. W., S. BALACHANDAR, and D. K. TAFTI. Effects of intrinsic three-dimensionality on heat transfer and friction in a periodic array of parallel plates. Numer. Heat Transfer, A31, 327-353 (1997).
ZHANG, L. W., S. BALACHANDAR, D. K. TAFTI, and F. M. NAJJAR. Heat-transfer enhancement in inline and staggered parallel-plate fin heat exchangers. Int. J. Heat Mass Transfer, 40, 2307-2325 (1997).
ZHOU, J., C. D. MEINHART, S. BALACHANDAR, and R. J. ADRIAN. Formation of hairpin packets in wall turbulence. Self-Sustaining Mechanisms in Wall Turbulence (Panton, ed.) 109-134 (1997).

Mechanics of Solids
CERMELLI, P. and E. FRIED. The influence of inertia on the configurational forces in a deformable solid. Proc. R. Soc. Lond., A 453, 1915-1927 (1997).
CHERUKURI, H. P. and T. G. SHAWKI. On shear band nucleation and the finite propagation speed of thermal disturbances. Int. J. Solids Struct., 34:4, 435-450 (1997).
XU, Z. and K. J. HSIA. A numerical solution of a surface crack under cyclic hydraulic pressure loading. ASME J. Tribol., 637-645 (1997).



PAPERS PRESENTED AT CONFERENCES AND SYMPOSIA


Applied Mathematics
STEWART, D. S. and J. YAO. On the evolution of detonation cells. Proc. 26th Int. Symp. on Combust., 2981-2989 (1997).

Behavior of Materials
CASAGRANDA, A. and P. SOFRONIS. Scaling laws in the consolidation of powder compacts. Proc. IUTAM Symp. on Mech. of Granular and Porous Mater. (Cambridge Univ., 1997) (Fleck and Cocks, eds.; Kluwer Academic) 105-116 (1997).
HSIA, K. J., N. DEY, and D. F. SOCIE. Static and cyclic fatigue failure at high temperatures in ceramics containing grain boundary phase: experiments. Cleavage Fracture: George R. Irwin Symp. (Chan, ed.) TMS Fall Mtg (Indianapolis, Ind.) 367-376 (1997).
JONNALAGADDA, K. D., N. R. SOTTOS, M. A. QIDWAI, and D. C. LAGOUDAS. Analysis of phase transformation fronts in embedded shape memory alloy composites. Smart Struct. and Mater. 1997: Math. and Control in Smart Struct. ( Varadan and Chandra, eds.) SPIE 3039 (San Diego, Calif.) 242-253 (1997).
JUNG, D., A. HEGEMAN, N. R. SOTTOS, P. H. GEUBELLE, and S. R. WHITE. Self-healing composites using embedded microspheres. ASME vol. MD-80, 265-275 (1997).
LUFRANO, J., P. SOFRONIS, and H. K. BIRNBAUM. The mechanics of hydride formation and embrittlement. Recent Adv. in Solids/Struct. and Appl. of Metallic Mater. ASME Int. Mech. Engr. Congr. and Expo. (Dallas, Tex., 1997) vol.PVP-369, 261-271 (1997).

Dynamics, Vibrations, and Waves
FRIED, E., A. SHEN, and S. T. THORODDSEN. Wave patters in a thin layer of sand in a rotating horizontal cylinder. Proc. 50th Ann. Mtg., Div. of Fluid Dyn. (San Francisco, Calif., 1997) Bull. Amer. Phys. Soc., 42, 2123 (1997).
SHEN, A., E. FRIED, and S. T. THORODDSEN. Fingering at the front of a granular layer within a cylinder rotating about its horizontal axis. Proc. 50th Ann. Mtg., Div. of Fluid Dyn. (San Francisco, Calif., 1997) Bull. Amer. Phys. Soc., 42, 2271 (1997).

Engineering Education
SHAWKI, T. G., H. AREF, and J. W. PHILLIPS. Mechanics on the Web. Proc. Int. Conf. on Engr. Educ.: Progress through Partnerships, 12 pp. (Chicago, Ill., 1997).

Mechanics of Fluids
ADRIAN, R. J. New methodologies for experimental flow engineering. Proc. JSME Centennial Grand Congr. (Tokyo, Japan, 1997) JSME no. 97-203, 23-30 (1997).
ADRIAN, R. J., S. M. SOLOFF, Z-C. LIU, C. D. MEINHART, and W. LAI. Stereoscopic PIV applications to the study of turbulence. Proc. Wkshp. on PIV (Fukui, Japan, 1997) 75-84 (1997).
GUARINI, S., R. MOSER, K. SHARIFF, and A. WRAY. Direct numerical simulation of supersonic turbulent boundary layers using mixed Fourier-spectral B-spline method. SIAM 45th Anniv. Mtg. (Stanford, Calif., 1997).
MITTAL, R. and S. BALACHANDAR. On the inclusion of three-dimensional effects in simulations of two-dimensional bluff-body wake flows. FED Summer Mtg., ASME (Vancouver, B.C., Canada) 1-8 (1997).
RIAHI, D. N. Roughness effects on thermal and shear flow instabilities. Int. Conf. on Math Today and Tomorrow (Orlando, Fla., 1997).
SAKAKIBARA, J. and R. J. ADRIAN. Measurement of whole field temperature using two-color LIF. Proc. 34th Nat. Heat Transfer Conf. (Japan) 421-422 (1997).
THORODDSEN, S. T. and J. SAKAKIBARA. Evolution of the fingering pattern of an impacting drop. Proc. 50th Ann. Mtg., Div. of Fluid Dyn. (San Francisco, Calif., 1997) Bull. Amer. Phys. Soc., 42, 2179 (1997).
ZHOU, J., C. D. MEINHART, S. BALACHANDAR, and R. J. ADRIAN. Formation of coherent hairpin packets in wall turbulence. Self-Sustaining Mechanisms in Wall Turbulence (Panton, ed.; Computational Mechanics Publ.) 109-134 (1997).
ZHOU, J., C. D. MEINHART, S. BALACHANDAR, and R. J. ADRIAN. Coherent hairpin packets in near-wall turbulence. 7th Asian Congr. of Fluid Mech. (Madras, India) (1997).

Mechanics of Solids
HSIA, K. J., T.-L. ZHANG, and D. F. SOCIE. Effects of crack surface morphology on fracture behavior under mixed mode I/III loading. Fatigue and Fracture Mech.: 27, ASTM STP 1296, 152-174 (1997).



THESES


Behavior of Materials
BECHEL, V. T. The application of debond length measurements to examine the accuracy of composite interface properties derived from fiber pushout testing. Ph.D. thesis, N. R. Sottos, adviser (1997).
BOGUSH, L. L. Experimental analysis of void growth in an epoxy resin. M.S. thesis, S. R. White, adviser (1997).
JONNALAGADDA, K. D. Local displacements and load transfer of shape-memory alloy composites in polymeric matrices. Ph.D. thesis, N. R. Sottos, adviser (1997).
ZHU, H. Coupled thermo-mechanical fixed-grid finite element model with application to initial solidification. Ph.D. thesis, B. G. Thomas and T. G. Shawki, advisers (1997).

Computational Mechanics
CARRANZA, F. L. A numerical study of integranular and oxidation-driven fracture in an elastic-viscoplastic material. Ph.D. thesis, R. B. Haber, adviser (1997).

Mechanics of Fluids
FORD, D. K. Hilbert space projections and the Navier-Stokes equation. Ph.D. thesis, D. S. Stewart, adviser (1997).
ZHOU, J. Self-sustaining formation of packets of hairpin vortices in a turbulent wall layer. Ph.D. thesis, R. J. Adrian, adviser (1997).



AWARDS AND HONORS


Ronald J. Adrian
Member, National Academy of Engineering
Fellow, American Physical Society
Associate Fellow, American Institute of Aeronautics and Astronautics
Honorary Doctorate, Technical University, Libson
Tau Beta Pi Daniel C. Drucker Eminent Faculty Award, College of Engineering, UIUC, 1988
Colwell Merit Award, Society of Automotive Engineers, 1989, 1991
Arnold O. Beckman Research Award, UIUC, 1990
Editor, Experiments in Fluids Journal, 1990-
Institute of Physics Best Paper, 1995
Leonard C. and Mary Lou Hoeft Endowed Chair in Engineering, 1997

Hassan Aref
NSF Presidential Young Investigator Award, 1985
Foreign Member, Danish Centre for Applied Mathematics and Mechanics
Fellow, American Physical Society
Stanley Corrsin Lectureship, Johns Hopkins University, 1988
Westinghouse Distinguished Lectureship, University of Michigan, 1991

S. Balachandar
Francois N. Frenkiel Award, American Physical Society, 1996

Donald E. Carlson
Fellow, American Academy of Mechanics
Editor-in-Chief, Journal of Elasticity, 1982-98

Herbert T. Corten, Emeritus
Nadai Award, American Society of Mechanical Engineers, 1988

George A. Costello, Emeritus
Fellow, American Society of Mechanical Engineers

Eliot Fried
National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship, 1992-95
National Science Foundation Research Initiation Award, 1993

Robert B. Haber
Beckman Associate, Center for Advanced Study, UIUC, 1982
Cray University Research Affiliate, 1985-93

K. Jimmy Hsia
National Science Foundation Research Initiation Award, 1992

Robert E. Miller, Emeritus
Honorary Knight of St. Pat, College of Engineering, UIUC, 1988
Distinguished Educator Award, American Society for Engineering Education, Mechanics Division, 1991

Robert D. Moser, Jr.
NASA Medal for Exceptional Scientific Achievement, 1995

James W. Phillips
Experimental Techniques Award, Society for Experimental Mechanics, 1987

Tarek G. Shawki
NSF Presidential Young Investigator Award, 1989
Andersen Consulting Award for Excellence in Advising, College of Engineering, UIUC, 1989

Petros Sofronis
National Science Foundation Research Initiation Award, 1992

Nancy R. Sottos
Office of Naval Research Young Investigator Award, 1992

D. Scott Stewart
Editor, SIAM Journal of Applied Mathematics, 1995-

Richard L. Weaver
Fellow, Acoustical Society of America