On the thermomechanics of materials that have multiple natural configurations Part I: Viscoelasticity and classical plasticity

Abstract.

Many bodies, both solid and fluid, are capable of being stress-free in numerous configurations that are not related to each other through a rigid body motion. Moreover, it is possible that these bodies could have different material symmetries in these different stress-free “natural” configurations. In order to describe the response of such bodies, it is necessary to know the manner in which these “natural” configurations evolve as well as a class of response functions for the stress that are determined by kinematical quantities that are measured from these evolving natural configurations. In this review article, we provide a framework to describe the mechanics of such bodies whose “natural configurations” evolve during a thermodynamic process. The framework is capable of describing a variety of responses and has been used to describe traditional metal plasticity, twinning, traditional viscoelasticity of both solids and fluids, solid-to-solid phase transitions, polymer crystallization, response of multi-network polymers, and anisotropic liquids. The classical theories of elastic solids and viscous fluids are included as special cases of the framework. After a review of the salient features of the framework, we briefly discuss the status of viscoelasicity, traditional plasticity, twinning and solid to solid phase transitions within the context of the framework.