# Collisions in shape memory alloys

## TL;DR

This paper develops a predictive model for instantaneous collisions in shape memory alloys, incorporating macroscopic and microscopic velocities, phase changes, and thermodynamics, with proven existence and uniqueness of solutions and numerical simulations.

## Contribution

It introduces a novel model for SMA collisions that accounts for microscopic phase change velocities and provides mathematical proofs of solution existence and uniqueness.

## Key findings

- Proven existence and uniqueness of solutions in 2D and 3D.
- Numerical simulations demonstrating collision effects in 2D SMA.
- Model captures phase change dynamics during collisions.

## Abstract

We present here a model for instantaneous collisions in a solid made of shape memory alloys (SMA) by means of a predictive theory which is based on the introduction not only of macroscopic velocities and temperature, but also of microscopic velocities responsible of the austenite-martensites phase changes. Assuming time discontinuities for velocities, volume fractions and temperature, and applying the principles of thermodynamics for non-smooth evolutions together with constitutive laws typical of SMA, we end up with a system of nonlinearly coupled elliptic equations for which we prove an existence and uniqueness result in the 2 and 3 D cases. Finally, we also present numerical results for a SMA 2D solid subject to an external percussion by an hammer stroke.