On the thermomechanics of materials that have multiple natural configurations part I: Viscoelasticity and classical plasticity. (English) Zbl 1180.74006

Summary: 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 kinematic 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.


74A15 Thermodynamics in solid mechanics
74N99 Phase transformations in solids
74D05 Linear constitutive equations for materials with memory
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
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