Inverse analysis method to find local constitutive relations

Abstract

This paper presents an analysis method to find local elastic moduli from the displacement for a heterogeneous elastic body in a state of plane stress or strain. Instead of considering the whole body, this method chooses a small block in which displacement is measured on the boundary and at some inner points. Since the deformation of this block is determined by the boundary displacement, the elastic moduli can be identified by considering the equilibrium of the block at the inner points. The procedures of finding the elastic moduli from the displacement data are developed, which include a method of excluding measurement errors to a certain extent. In numerical simulation, it is shown that the proposed method can determine local elastic moduli when displacement data of sufficient quantity and quality are available.