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In this paper, conjugate stresses of the Seth-Hill strain measures are treated by means of the definition of energy conjugacy and Hill's principal axis method. This approach results in relations between components of two different conjugate stress tensors. The results are valid for distinct as well as coalescent principal stretches. Illustrative examples are solved to demonstrate the simplicity and usefulness of the derived relations between conjugate stress tensors. © 2000 Elsevier Science Ltd  

In the present paper, some new and compact basis-free expressions are derived for representing stresses conjugate to the Lagrangean Hill's strain measures. Solving a tensor equation in the form of AX + XA = C, a rather simple general expression is obtained for the conjugate stresses in the case of distinct principal stretches. The result decomposes the conjugate stresses additively into two parts, such that one part is coaxial with the right stretch tensor while another part is orthogonal to it. An expression for the case of double-coalescent principal stretches is also obtained. As an example of the general results, simple expressions are obtained for the stress conjugate to the logarithmic... 

The concept of energy conjugacy for stress and strain measures states that a stress tensor T is conjugate to a strain measure E if T: Ė provides the rate of change of the internal energy per unit reference volume of the body in an adiabatic process. The applications of the conjugate stress and strain measures are in the development of the basic relations in nonlinear analysis of solids. In this paper using eigenprojection method, unified explicit basis-free relation between two arbitrary stress tensors T(f) and T (g), respectively conjugate to two measures of Hill's strains is determined. The result is valid for arbitrary dimension of the Euclidean inner product space and for all cases of... 

If the double contraction of a stress tensor such as T and rate of a Lagrangean strain tensor such as E, i.e. T : Ė produces the stress power then these stress and strain tensors are called a conjugate pair. The applications of the conjugate stress and strain measures are in the development of the basic relations in nonlinear continuum mechanics analysis such as modeling of constitutive equations of elastic-plastic materials. In this paper relations for stress tensors conjugate to an arbitrary Lagrangean strain measure of Hill's class are obtained. The results of this paper are more compact and simpler in compare with those available in the literature. The results are valid for the three...