Finite Volume Analysis of Nonlinear Thermo-mechanical Dynamics of Shape Memory Alloys

TL;DR

This paper develops a finite volume method to analyze nonlinear thermo-mechanical dynamics of shape memory alloys, capturing phase transformations, hysteresis, and wave interactions in 1D and 2D structures.

Contribution

It introduces a novel finite volume approach for coupled thermo-mechanical analysis of shape memory alloys, including phase transformations and hysteresis effects.

Findings

Successful simulation of phase transformations and hysteresis in 1D structures.

Analysis of thermo-mechanical wave interactions in shape memory alloy rods and patches.

Demonstration of square-to-rectangular martensitic transformations under mechanical loads.

Abstract

In this paper, the finite volume method is developed to analyze coupled dynamic problems of nonlinear thermoelasticity. The major focus is given to the description of martensitic phase transformations essential in the modelling of shape memory alloys. Computational experiments are carried out to study the thermo-mechanical wave interactions in a shape memory alloy rod, and a patch. Both mechanically and thermally induced phase transformations, as well as hysteresis effects, in a one-dimensional structure are successfully simulated with the developed methodology. In the two-dimensional case, the main focus is given to square-to-rectangular transformations and examples of martensitic combinations under different mechanical loadings are provided.