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.

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.

On the Domain of Validity of Linearlized Elasticity
D. E. Carlson*
University of Illinois

It is widely recognized that the validity of the linearized theory of elasticity rests on the assumption that the deformation be 'small' in some appropriate sense. More careful elasticians know that the basic equations of the linearized theory are implied by the nonlinear theory under the assumption that the displacement gradient be small. Here, we note that justification of the substitution of the linearized constitutive equation into the stress equations of motion or equilibrium requires that the nondimensionalized second gradient of the displacement also be small. We show by example that the resulting limitation on the domain of validity of the linearized theory can be severe.

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.