A nonsymmetric compliance matrix approach to nonlinear multimodulus orthotropic materials

Abstract

Multimodulus materials have moduli or stiffnesses under tension loading which are different from those under compression loading. Several approaches to their analysis have been suggested recently. Most of these approaches are based on the hypothesis that the compliance matrix in the strain-stress relations must be symmetric. Jones makes the matrix symmetric by weighting the tension compliances and the compression compliances on the basis of the proportion of tensile and compressive stresses. Isabekyan and Khachatryan determine very severe restrictions under which a multimodulus material has a symmetric compliance matrix in all coordinate systems. However, the Jones weighted compliance matrix approach cannot be derived from basic principles. Moreover, the Isabekyan and Khachatryan restricted compliance matrix approach is not realistic because the properties of known multimodulus materials do not satisfy their restrictions. The purpose of this paper is to relax the previously held requirement of compliance matrix symmetry to see whether suitable agreement can be obtained between predicted and measured strain response of ATJ-S graphite to mixed tension and compression loading under plane stress conditions.