Waves generated by an incident shock in a peculiar hyperelastic material

A finite transverse shock wave propagates through an unbounded medium and is reflected at a plane boundary or reflected-refracted at a plane interface between two joined elastic half-spaces. The problem is not solvable in general, and we look for some kind of degeneracy in it, which make the solution possible. Two cases: clamped boundary and frictionless-rigid boundary are considered particular numerically for different assumptions. Both reflection patterns assumed here: either shock or simple wave, give the unique result in its range of admittace. There are two different critical angles: for shock as well as for simple wave, but in contrast with the second one, the first one has the pure geometrical meaning only.