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Title: A variational treatment of material configurations with application to interface motion and microstructural evolution

We present a unified variational treatment of evolving configurations in crystalline solids with microstructure. The crux of our treatment lies in the introduction of a vector configurational field. This field lies in the material, or configurational, manifold, in contrast with the traditional displacement field, which we regard as lying in the spatial manifold. We identify two distinct cases which describe (a) problems in which the configurational field's evolution is localized to a mathematically sharp interface, and (b) those in which the configurational field's evolution can extend throughout the volume. The first case is suitable for describing incoherent phase interfaces in polycrystalline solids, and the latter is useful for describing smooth changes in crystal structure and naturally incorporates coherent (diffuse) phase interfaces. These descriptions also lead to parameterizations of the free energies for the two cases, from which variational treatments can be developed and equilibrium conditions obtained. For sharp interfaces that are out-of-equilibrium, the second law of thermodynamics furnishes restrictions on the kinetic law for the interface velocity. The class of problems in which the material undergoes configurational changes between distinct, stable crystal structures are characterized by free energy density functions that are non-convex with respect to configurational strain. For physicallymore » meaningful solutions and mathematical well-posedness, it becomes necessary to incorporate interfacial energy. This we have done by introducing a configurational strain gradient dependence in the free energy density function following ideas laid out by Toupin (Arch. Rat. Mech. Anal., 11, 1962, 385-414). The variational treatment leads to a system of partial differential equations governing the configuration that is coupled with the traditional equations of nonlinear elasticity. The coupled system of equations governs the configurational change in crystal structure, and elastic deformation driven by elastic, Eshelbian, and configurational stresses. As a result, numerical examples are presented to demonstrate interface motion as well as evolving microstructures of crystal structures.« less
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  1. Univ. of Michigan, Ann Arbor, MI (United States)
Publication Date:
OSTI Identifier:
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Journal of the Mechanics and Physics of Solids
Additional Journal Information:
Journal Name: Journal of the Mechanics and Physics of Solids; Journal ID: ISSN 0022-5096
Research Org:
Univ. of Michigan, Ann Arbor, MI (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING; free energy; thermodynamic driving force; gradient regularization; configurational stress; spline basis functions