A two-speed model for finite-strain elasto-plasticity

TL;DR

This paper introduces a novel two-speed modeling framework for finite-strain elasto-plasticity that captures both slow and fast dynamics, providing a rigorous description of energetics during jump transients and bridging rate-dependent and rate-independent behaviors.

Contribution

It develops the concept of two-speed solutions, integrating slow and fast time scales, to accurately model elasto-plasticity with detailed energetic analysis of jump transients.

Findings

The two-speed model captures rate-dependent and rate-independent behaviors.

A new solution concept for elasto-plasticity with jump transients is proposed.

Energetics during jump transients are rigorously characterized.

Abstract

This work presents a new modeling approach to macroscopic, polycrystalline elasto-plasticity starting from first principles and a few well-defined structural assumptions, incorporating the mildly rate-dependent (viscous) nature of plastic flow and the microscopic origins of plastic deformations. For the global dynamics, we start from a two-stage time-stepping scheme, expressing the fact that in most real materials plastic flow is much slower than elastic deformations, and then perform a detailed analysis of the slow-loading limit passage. In this limit, a rate-independent evolution can be expected, but this brings with it the possibility of jumps (relative to the "slow" time). Traditionally, the dynamics on the jump transients often remain unspecified, which leads to ambiguity and deficiencies in the energy balance. In order to remedy this, the present approach precisely describes the energetics on the jump transients as the limit of the rate-dependent evolutions at "singular points". It turns out that rate-dependent behavior may (but does not have to) prevail on the jump transients. Based on this, we introduce the new solution concept of "two-speed solutions" to the elasto-plastic evolutionary system, which incorporates a "slow" and a "fast" time scale, the latter of which parametrizes the jump transients.