Multiple bifurcations and local energy minimizers in thermoelastic martensitic transformations

Thermoelastic martensitic transformations in shape memory alloys can be modeled on the basis of nonlinear elastic theory. Microstructures of fine phase mixtures are local energy minimizers of the total energy. Using a one-dimensional effective model, we have shown that such microstructures are inhomogeneous solutions of the nonlinear Euler–Lagrange equation and can appear upon loading or unloading to certain critical conditions, the bifurcation conditions. A hybrid numerical method is utilized to calculate the inhomogeneous solutions with a large number of interfaces. The characteristics of the solutions are clarified by three parameters: the number of interfaces, the interface thickness, and the oscillating amplitude. Approximated analytical expressions are obtained for the interface and inhomogeneity energies through the numerical solutions.