Intrinsic Expressions for Arbitrary Stress Tensors Conjugate to General Strain Tensors

In this paper, a unified explicit tensorial relation is sought between two stress tensors conjugate to arbitrary and general Hill strains. The approach used for deriving the tensorial relation is based on the eigenprojection method. The result is, indeed, a generalization of the relations that were derived by Farahani and Naghadabadi [1] in 2003 from a component to intrinsic form. The result is unified in the sense that it is valid for all cases of distinct and coalescent principal stretches. Also, in the case of three dimensional Euclidean inner product space, using the derived unified relation, some expressions for the conjugate stress tensors are presented.