Thermodynamics of non-simple elastic materials

Elastic materials whose local state depends upon the first and second order gradients of the deformation, the temperature, its gradient and the time rate of change of the temperature are studied according to an inequality proposed by Green and Laws. It is shown that in such materials either thermal disturbances can propagate with finite speed in the linear theory, and the constitutive quantities do not depend upon the second order gradients of the deformation or the constitutive quantities may depend upon the second order gradients of the deformation and in the linear theory thermal disturbances do not propagate with finite speed. In the latter case the entropy inequality reduces to the Clausius-Duhem inequality.