Dynamical stability of planar phase boundaries for hyperelastic materials of Hadamard type

Abstract

The dynamical stability of laminates or planar phase boundaries for hyperelastic materials of Hadamard type in two space dimensions is studied. For that purpose, the stability function, known as the Lopatinskii determinant, is computed for states of deformation at both sides of the planar interface that account for the generalized Legendre-Hadamard conditions derived by Grabovsky and Truskinovsky (J. Elast. 123 (2016), 225--243). The sufficient conditions for the dynamical stability of such configurations are described in terms of the physical parameters of the model, such as the shear modulus, and computed under kinetic conditions across the interface of both Maxwell (conservation of energy) or Abeyaratne and Knowles (dissipation of energy) types.