Projection scheme for a perfect plasticity model with a time-dependent constraint set

TL;DR

This paper presents a new numerical scheme for a perfect plasticity model with a time-dependent yield surface, proving its stability, convergence, and the existence of an exact solution.

Contribution

The paper introduces a novel projection-based numerical scheme specifically designed for perfect plasticity models with evolving constraints, ensuring stability and convergence.

Findings

The scheme is proven to be stable under appropriate norms.

Strong convergence of the scheme to the exact solution is established.

Existence of an exact solution is demonstrated through the scheme's stability.

Abstract

This paper introduces a new numerical scheme for a system that includes evolution equations describing a perfect plasticity model with a time-dependent yield surface. We demonstrate that the solution to the proposed scheme is stable under suitable norms. Moreover, the stability leads to the existence of an exact solution, and we also prove that the solution to the proposed scheme converges strongly to the exact solution under suitable norms.