Continuum mesoscale theory inspired by plasticity

TL;DR

This paper introduces a mesoscale field theory inspired by plasticity, modeling deformation with a scalar field that captures key features like yield stress and work hardening through cusp singularities.

Contribution

It proposes a novel scalar-field-based mesoscale model that reproduces essential plasticity phenomena using a Hamilton-Jacobi evolution equation.

Findings

Reproduces yield stress and work hardening behaviors.

Captures irreversibility and cell boundary formation.

Demonstrates cusp singularities lead to plastic-like irreversibilities.

Abstract

We present a simple mesoscale field theory inspired by rate-independent plasticity that reflects the symmetry of the deformation process. We parameterize the plastic deformation by a scalar field which evolves with loading. The evolution equation for that field has the form of a Hamilton-Jacobi equation which gives rise to cusp-singularity formation. These cusps introduce irreversibilities analogous to those seen in plastic deformation of real materials: we observe a yield stress, work hardening, reversibility under unloading, and cell boundary formation.