Advertisement

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)

Abstract

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.

Keywords

Shape Memory Alloy Steep Descent Deformation Gradient Differential Inclusion Helmholtz Free Energy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    B. Dacorogna and P. Marcellini, Implicit partial differential equations, Birkhäuser, 2000.Google Scholar
  2. 2.
    P. Klouček, The steepest descent minimization of double-well stored energies does not yield vectorial microstructures, Rice University (2001), Technical report 01-04, Department of Computational and Applied Mathematics.Google Scholar
  3. 3.
    Luskin M., On the computation of crystalline microstructure, Acta Numerica (1996), 191–257.Google Scholar
  4. 4.
    P. Pedregal, Variational methods in nonlinear elasticity, SIAM, Philadelphia, 2000.zbMATHGoogle Scholar
  5. 5.
    D. Reynolds, Vibration damping using martensticphase transformation, (2002), Ph.D. Thesis, Rice University.Google Scholar
  6. 6.
    W. P. Ziemer, Weakly differentiable functions, Graduate Texts in Math., Springer-Verlag, New York, 1989.Google Scholar

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

Personalised recommendations