Numerical Model For Vibration Damping Resulting From the First Order Phase Transformations

TL;DR

This paper presents a numerical model based on Landau-Ginzburg theory to simulate damping effects caused by first order martensite phase transformations in shape memory alloys, highlighting their significance in vibration control.

Contribution

It introduces a coupled nonlinear mechanical-thermal model using spectral methods to analyze phase transformation-induced damping in shape memory alloys.

Findings

Damping effects are significant during phase transformations.

The model accurately captures energy absorption during phase change.

Spectral methods effectively solve the coupled nonlinear equations.

Abstract

A numerical model is constructed for modelling macroscale damping effects induced by the first order martensite phase transformations in a shape memory alloy rod. The model is constructed on the basis of the modified Landau-Ginzburg theory that couples nonlinear mechanical and thermal fields. The free energy function for the model is constructed as a double well function at low temperature, such that the external energy can be absorbed during the phase transformation and converted into thermal form. The Chebyshev spectral methods are employed together with backward differentiation for the numerical analysis of the problem. Computational experiments performed for different vibration energies demonstrate the importance of taking into account damping effects induced by phase transformations.