Twin branching in shape memory alloys: a 1D continuum model with energy dissipation effects

We develop a 1D continuum model of twin branching in shape memory alloys. The free energy of the branched microstructure comprises the interfacial and elastic strain energy contributions, both expressed in terms of the average twin spacing treated as a continuous function of the position. The total free energy is then minimized, and the corresponding Euler-Lagrange equation is solved numerically using the finite element method. The model can be considered as a continuum counterpart of the recent discrete model of Seiner et al. (2020), and our results show a very good agreement with that model in the entire range of physically relevant parameters. Furthermore, our continuum setting facilitates incorporation of energy dissipation into the model. The effect of rate-independent dissipation on the evolution of the branched microstructure is thus studied. The results show that significant effects on the microstructure and energy of the system are expected only for relatively small domain sizes.