Inverse determination of elastic constants of a hyper-elastic member with inclusions using simple displacement/length measurements

There are many engineering parts and natural soft members, which consist of several phases with different mechanical properties. Identification of material parameters of multi-material members is an important issue that has attracted considerable attention. In this article, a finite-element-based inverse method for identification of material parameters of a body made of several hyper-elastic materials is presented. In the presented inverse method, the unknowns are computed using a few simple displacement/length measurements in a few elasto-static experiments. The inverse analysis can be carried out without any full-field measurements. Both plane strain and plane stress conditions are considered. In the plane strain case, displacements of several sampling points on the boundary of the problem domain are used as measured data. In the plane stress case, some characteristic lengths of the member in the deformed configuration are used as measured data. A cost function in terms of the differences between calculated and measured values is defined and the Gauss–Newton method is used to minimize it. The multi-material sensitivity analysis in the optimization process is made by analytical differentiation of the weak form of the problem. Both numerical and experimental studies are made to demonstrate the effectiveness and accuracy of the proposed methods.