Time-dependence of the threshold function in the perfect plasticity model

TL;DR

This paper investigates the time-dependent threshold function in the perfect plasticity model, establishing well-posedness and solution existence using abstract evolution theory, thus advancing understanding of plasticity models with dynamic thresholds.

Contribution

It introduces a framework for analyzing the well-posedness of perfect plasticity models with time-dependent thresholds using abstract evolution equations.

Findings

Proves existence of solutions under time-dependent thresholds

Establishes well-posedness with weaker assumptions

Utilizes recent abstract evolution theory

Abstract

This paper discusses the time-dependence of the threshold function in the perfect plasticity model. In physical terms, it is natural that the threshold function depends on some unknown variable. Therefore, it is meaningful to discuss the well-posedness of this function under the weaker assumption of time-dependence. Time-dependence is also interesting from the viewpoint of the abstract evolution equation. To prove the existence of a solution to the perfect plasticity model, the recent abstract theory under the continuous class with respect to time is used.