The Computational Modeling of Crystalline Materials Using a Stochastic Variational Principle

  • Dennis Cox
  • Petr Klouček
  • Daniel R. Reynolds
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2330)


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.


Shape Memory Alloy Steep Descent Deformation Gradient Differential Inclusion Helmholtz Free Energy 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Dennis Cox
    • 1
  • Petr Klouček
    • 2
  • Daniel R. Reynolds
    • 2
  1. 1.Department of StatisticsRice UniversityHoustonUSA
  2. 2.Department of Computational and Applied MathematicsRice UniversityHoustonUSA

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