On stresses conjugate to Eulerian strains

Summary. A stress is considered conjugate to a strain if the product of the stress and an objective rate of the strain has a trace which is equal to the rate of work per unit volume. Using Kronecker product relations, apparently new expressions for stresses conjugate to the Finger strain B, the Euler strain , the Eulerian (right) stretch tensor V, and log(V) are determined. In addition, a nonclassical strain p is introduced which permits a constitutive equation expressing its Truesdell rate in terms of B and the Truesdell rate of the Cauchy stress. We regard a tensor as a strain if (a) it is not affected by rigid body motion and (b) its current value, given suitable compatibility conditions, determines the current displacement field to within a rigid body translation and rotation. By these criteria e is not strictly a strain and instead we later refer to it as a pseudostrain.