The Computational Modeling of Crystalline Materials Using a Stochastic Variational Principle
We introduce a variational principle suitable for the computational modeling of crystalline materials. We consider a class of materials that are described by non-quasiconvex variational integrals. We are further focused on equlibria of such materials that have non-attainment structure, i.e., Dirichlet boundary conditions prohibit these variational integrals from attaining their infima. Consequently, the equilibrium is described by probablity distributions. The new variational principle provides the possibility to use standard optimization tools to achieve stochastic equilibrium states starting from given initial deterministic states.
KeywordsShape Memory Alloy Steep Descent Deformation Gradient Differential Inclusion Helmholtz Free Energy
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