The Mechanics of Non-Linear Materials with Memory

Abstract

The mechanics of non-linear materials with memory has been discussed in previous papers [1, 2] and an earlier report [3]*. In these papers, it was assumed that, in a fixed coordinate system, the stress at a point of the material at any instant of time is determined by the deformation gradients at that instant and at previous instants. The limitations imposed on the form of the constitutive equation by the consideration that it is unaltered by a simultaneous rotation of the body and reference system are determined. In the present paper, we assume initially a constitutive equation in the form of implicit relations between the stress, its time derivatives and gradients of displacement, velocity, acceleration, etc. at a number of instants of time in some time interval. The limitations on the form of the constitutive equation resulting from the fact that it is unaltered by the imposition on the body of an additional arbitrary angular velocity, acceleration, etc. are discussed.