Location of Repository

Numerical analysis of a relaxed variational model of hysteresis in two-phase solids

By Carsten Carstensen and Petr Plechac

Abstract

This paper presents the numerical analysis for a variational formulation of rate-independent phase transformations in elastic solids due to Mielke et al. The new model itself suggests an implicit time-discretization which is combined with the finite element method in space. A priori error estimates are established for the quasioptimal spatial approximation of the stress field within one time-step. A posteriori error estimates motivate an adaptive mesh-refining algorithm for efficient discretization. The proposed scheme enables numerical simulations which show that the model allows for hysteresis

Topics: QA, QC
Publisher: EDP Sciences
Year: 2001
OAI identifier: oai:wrap.warwick.ac.uk:3826

Suggested articles

Preview

Citations

  1. (1999). A mathematical model for rate-independent phase transformations with hysteresis,
  2. (1996). A review of a posteriori error estimation and adaptive mesh-re techniques,
  3. A variational formulation of rate-independent phase transformations using an extremum principle. Submitted to Arch. Rational Mech. doi
  4. (1999). A-quasiconvexity, lower semicontinuity and Young measures. doi
  5. (2000). and Petr Plech a c, Numerical analysis of compatible phase transitions in elastic solids. doi
  6. (2000). Constants in Cl ement-interpolation error and residual based a posteriori estimates in nite element methods.
  7. (1987). Fine phase mixtures as minimisers of energy.
  8. (2000). Fully reliable localised error control in the FEM. doi
  9. (1995). Introduction to adaptive methods for dierential equations, doi
  10. (2001). Local regularity of solutions of variational problems for the equilibrium con of an incompressible, multiphase elastic body. doi
  11. Local stress regularity in scalar non-convex variational problems. In preparation. doi
  12. (1978). Martensitic transformation as a typical phase transformation in solids, doi
  13. (1999). Modelling of hysteresis in two-phase systems.
  14. (1986). Numerical study of a relaxed variational problem from optimal design. doi
  15. (1996). On the computation of crystalline microstructure, in Acta Numerica,A .I s e r l e s ,E d . ,C a m b r i d g eU n i v e r s i t y Press, doi
  16. (1997). Plech a c, Numerical solution of the scalar double-well problem allowing microstructure. doi
  17. (1992). Proposed experimental tests of the theory of microstructure and the two{well problem. doi
  18. (1978). The Finite Element Method for Elliptic Problems. doi
  19. (1994). The mathematical theory of element methods, doi
  20. (1996). The regularity properties of solutions of variational problems in the theory of phase transitions in an elastic body.
  21. (1991). The relaxation of a double-well energy. doi
  22. (1983). Theory of Structural Transformations in Solids.
  23. (1999). Variational convergence for nonlinear shell models with directors and related semicontinuity and relaxation results. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.