A model for shape memory alloys with the possibility of voids

TL;DR

This paper develops a mathematical model for shape memory alloys that incorporates the formation of voids during phase transitions, providing a comprehensive PDE system to describe their thermomechanical behavior.

Contribution

It introduces a novel PDE model accounting for voids in shape memory alloys during phase changes, and proves the well-posedness of the initial-boundary value problem.

Findings

Model captures void formation during phase change

Proves mathematical well-posedness of the PDE system

Enhances understanding of alloy behavior with voids

Abstract

The paper is devoted to the study of a mathematical model for the thermomechanical evolution of metallic shape memory alloys. The main novelty of our approach consists in the fact that we include the possibility for these materials to exhibit voids during the phase change process. Indeed, in the engineering paper has been recently proved that voids may appear when the mixture is produced by the aggregations of powder. Hence, the composition of the mixture varies (under either thermal or mechanical actions) in this way: the martensites and the austenite transform into one another whereas the voids volume fraction evolves. The first goal of this contribution is hence to state a PDE system capturing all these modelling aspects in order then to establish the well-posedness of the associated initial-boundary value problem.