Numerical Method for an Elastoplastic Model with Time-Dependent Thresholds

Kazunori Matsui @ Tokyo University of Marine Science and Technology

Abstract

• This poster proposes a numerical scheme for evolution inclusions involving the perfect plasticity model with a time-dependent threshold function. 

  • • Image of the perfect plasticity model: Please click "完全塑性" at https://sites.google.com/view/akagawa/research
      Direct link: https://yakagawa.github.io/rheological/perfect_plasticity.html 

    • The proposed scheme projects the stress within constraints after solving the linear elliptic PDE at each step, 

    • avoiding the need to solve nonlinear problems. 

• We derive the existence of an exact solution to the original problem using a stability of the scheme.

  • • The major points are that 

      • we weakened the spatial continuity of the threshold function to L2(Ω) and 

      • showed that the threshold function does not need to have a positive lower bound.

Reference

• Y. Akagawa and  K. Matsui.
  Projection scheme for a perfect plasticity model with a time-dependent constraint set.
  Journal of Mathematical Analysis and Applications (2025), 542(2): 128838.
  doi: 10.1016/j.jmaa.2024.128838 arXiv:2406.02218