Mechanically induced phase combination in shape memory alloys by Chebyshev collocation methods

A mathematical model is constructed to simulate the martensitic phase combinations in shape memory alloy samples. Governing equations are obtained on the basis of the momentum balance law and a modified Landau–Ginzburg free energy functional. The Chebyshev collocation method is applied for the numerically analysis of the constructed model. Computational experiments with given mechanical loadings and boundary conditions demonstrate that the phase combinations between martensite variants in the 2D shape memory alloy samples can be successfully simulated with the developed methodology.