ON EXTRAORDINARY SEMISIMPLE MATRIX N(V) FOR ANISOTROPIC ELASTIC-MATERIALS

The 6 x 6 real matrix N(v) for anisotropic elastic materials under a t wo-dimensional steady-state motion with speed v is extraordinary semis imple when N(v) has three identical complex eigenvalues p and three in dependent associated eigenvectors. We show that such an N(v) exists wh en v not equal 0. The eigenvalues are purely imaginary. The material c an sustain a steady-state motion such as a moving line dislocation. Ex plicit expressions of the Barnett-Lothe tensors for v not equal 0 are presented. However, N(v) cannot be extraordinary semisimple for surfac e waves. When v = 0, N(0) can be extraordinary semisimple if the strai n energy of the material is allowed to be positive semidefinite. Expli cit expressions of the Barnett-Lothe tensors and Green's functions for the infinite space and half-space are presented. An unusual phenomeno n for the material with positive semidefinite strain energy considered here is that it can support an edge dislocation with zero stresses ev erywhere. In the special case when p = i is a triple eigenvalue, this material is an un-pressurable material in the sense that it can change its (two-dimensional) volume with zero pressure. ft is a counterpart of an incompressible material (whose strain energy is also positive se midefinite) that can support pressure with zero volume change.