A variational multi-phase model for elastoplastic materials with microstructure evolution

TL;DR

This paper introduces a variational multi-phase model for elastoplastic materials that captures microstructure evolution during phase transformations using probabilistic and measure-theoretic approaches, verified through FEM simulations.

Contribution

It presents a novel variational framework combining dissipation distance and Young measures to model microstructure evolution in elastoplastic materials with phase transformations.

Findings

Model successfully describes microstructure evolution during phase changes.

Verification through 2D FEM benchmark tests confirms model validity.

Provides a continuous-time description of phase transformation processes.

Abstract

A general model is formulated for elasto-plastic materials undergoing linear kinematic hardening to describe microstructure evolution associated with phase transformations. Using infinitesimal strain theory, the model is based on variational principles for inelastic materials. In our work we combine the so-called dissipation distance, which describes an immediate phase transition in time via an underlying probability matrix. In addition, the volume fractions of the newly emerging phases are represented by Young measures to obtain a time continuous microstructure evolution. The model is verified employing a two-dimensional benchmark test implemented by the Finite Element Method (FEM).