Multidimensional stability of martensite twins under regular kinetics

This paper considers phase boundaries governed by regular kinetic relations as first proposed by Abeyaratne and Knowles [1990. On the driving traction acting on a surface of strain discontinuity in a continuum. J. Mech. Phys. Solids 38 (3), 345-360; 1991. Kinetic relations and the propagation of phase boundaries in solids. Arch. Ration. Mech. Anal. 114, 119-154]. It shows that static configurations of hyperelastic materials, in which two different martensitic (monoclinic) states meet along a planar interface, are dynamically stable towards fully three-dimensional perturbations. For that purpose, the reduced stability (or reduced Lopatinski) function associated to the static twin [Freistühler and Plaza, 2007. Normal modes and nonlinear stability behavior of dynamic phase boundaries in elastic materials. Arch. Ration. Mech. Anal. 186 (1), 1-24] is computed numerically. The results show that the interface is weakly stable under Maxwellian kinetics expressing conservation of energy across the boundary, whereas it is uniformly stable with respect to linearly dissipative kinetic rules of Abeyaratne and Knowles type.