The formulation of constitutive equations in continuum physics. II

In previous papers by Green & Rivlin[1, 2] and an earlier report [3], constitutive equations have been developed describing the mechanical properties of materials possessing memory. A similar topic has been discussed by Noll [4, 5]. In [1, 2] it is assumed that the stress at a fixed particle of the material is a functional of the displacement gradients at the instant of measurement and at times preceding the instant of measurement. In another paper, by Pipkin & Rivlin [6], constitutive equations have been developed governing certain types of physical properties of materials which may be described by the relation between a tensor of order µ on the one hand and the displacement gradients in the material and ν vectors on the other, all the quantities being measured simultaneously. In the present paper, these two problems are combined.