Generalized conjugate stress and strain tensors

We present a methodology for the systematic derivation of objective left and right strain tensors. We use a unified method for determining pairs of conjugate stress and strain tensors, which generalizes the known methods. We obtain new pairs of conjugate tensors that may be useful in the formulation of constitutive relations in nonlinear continuum mechanics. Since it is not desirable to use certain known pairs of conjugate stress and strain tensors in the equations of continuum mechanics, we select pairs of conjugate stress and strain tensors useful in applications. We emphasize the utility of right and left tensors of logarithmic strains in equations of the deformation of inelastic media. We give conjugate pairs of stress and logarithmic strain tensors. These pairs differ from the standard ones often used in investigations in nonlinear continuum mechanics. We note the advantage of the pairs we introduce over standard pairs.