Dynamic properties of resilient materials: constitutive equations

Abstract

Constitutive equations are formulated for a class of resilient materials for which the stress distribution at any instant is assumed to depend both upon the deformation and upon the time rates of variation of the tensors defining it. Particular attention is given to aeolotropic bodies, the stress deformation relations for orthotropic and transversely isotropic materials being put in forms which exhibit the symmetry properties of the material. In the discussion of symmetry properties, attention is confined to the case where the stress tensor is a polynomial function of two only of the kinematic tensors. Convected co-ordinate systems are employed in the development of the theory, but the method of transformation of the equations to a fixed frame of reference is also given. The modifications which are required for materials exhibiting curvilinear aeolotropy are briefly indicated, and some discussion is included of the manner in which certain types of geometrical constraint can be accounted for in the stress-deformation relations.