COMPACT BASIS FREE RELATIONS FOR STRESS TENSORS CONJUGATE TO HILL'S STRAIN MEASURES

摘要

If the double contraction of a stress tensor such as T and rate of a Lagrangean strain tensor such as E, i.e. T: E, 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 dimensional Euclidean inner product space and the case of distinct eigenvalues of the right stretch tensor U.