Computation of the sensitivity matrix used for Elasto-plastic material parameter identification by inverse methods

Inverse methods offer a powerful tool for the determination of the elasto-plastic material properties. Contrary to standard tests, these methods can deal with heterogeneous stress and strain-fields which have a larger information contents and hence allow the simultaneous identification of several material parameters. Moreover, it is expected that the obtained material parameters are more accurate, since these heterogeneous deformation fields are much closer to those occurring in real (metal) forming operations. The principle of the inverse method for the identification of material parameters presented in this paper is to compare an experimentally measured strain field to that computed by a Finite Element (FE) model. The material parameters in the FE model are iteratively tuned in such a way that both strain fields match each other as closely as possible. One of the building blocks in this identification procedure is the updating algorithm for the material parameters in the FE model. The key problem of this updating algorithm is the determination of the sensitivity matrix, which expresses the sensitivities of the strains with respect to the material parameters. This paper presents an analytical method for the calculation of this sensitivity matrix in case of simple tensile tests.