Isogeometric Analysis of a Dynamic Thermo-Mechanical Phase-Field Model Applied to Shape Memory Alloys

This paper focuses on the numerical simulation of martensitic transformations in shape memory alloys (SMAs) using a phase-field model. We developed a dynamic thermo-mechanical model for SMAs, using strain based order parameter, having bi-directional coupling between structural and thermal physics via strain, strain rate and temperature. The model involves fourth order spatial derivatives representing a domain wall. We propose an isogeometric analysis (IGA) numerical formulation for straightforward solution to the fourth order differential equations. We present microstructure evolution under different loading conditions and dynamic loading simulations of the evolved microstuctures of SMAs of different geometries to illustrate the flexibility, accuracy and stability of our numerical method. The simulation results are in agreement with the numerical and experimental results from the literature.