Phase field modeling of nonlinear material behavior

TL;DR

This paper introduces a systematic phase-field modeling approach to separate elastic and transformational effects in nonlinear materials, simplifying complex energy functions into more manageable linearized problems.

Contribution

It proposes a novel method to split non-convex energy into harmonic and nonharmonic parts, enabling linearization of nonlinear material behavior in phase-field models.

Findings

Method successfully separates elastic and transformational effects.

Application demonstrated on Peierls-Nabarro dislocation model.

Facilitates easier analysis of nonlinear material behavior.

Abstract

Materials that undergo internal transformations are usually described in solid mechanics by multi-well energy functions that account for both elastic and transformational behavior. In order to separate the two effects, physicists use instead phase-field-type theories where conventional linear elastic strain is quadratically coupled to an additional field that describes the evolution of the reference state and solely accounts for nonlinearity. In this paper we propose a systematic method allowing one to split the non-convex energy into harmonic and nonharmonic parts and to convert a nonconvex mechanical problem into a partially linearized phase-field problem. The main ideas are illustrated using the simplest framework of the Peierls-Nabarro dislocation model.