Inversion of stress from strain without full knowledge of constitutive relations

Abstract

A new inversion method of predicting a stress distribution is proposed. While the method is applicable only to a body in a state of two-dimensional plane stress or strain, it can estimate stress from displacement on the surface and traction along the boundary for a body whose constitutive relations are not fully known; for instance, information that the body is isotropic, not necessarily homogeneous nor linear, is sufficient for the inversion. The present method is a modification of Hori and Kameda's inversion method, which solves boundary value problems of eigenstress that is equivalent with heterogeneity or non-linearity of the material. The present method seeks to identify Airy's stress function and derive a simpler linear boundary value problem from which stress is inverted. Examples such as general linear elastic materials, elasto-plastic materials, or linear or non-linear isotropic materials are considered. The results of stress inversion for model experiments are presented.