Parameter identification for finite deformation elasto-plasticity in principal directions

This work is concerned with identification of material parameters based on experimental data, which represent nonuniform distributions of stresses and deformations within the volume of the specimen. Both elastic and inelastic material non-linearities in the frame of a finite deformation theory are taken into account. Gradient-based descent methods (e.g. Gauss-Newton method, Quasi-Newton method) are used for minimization of a least-squares function. To this end a sensitivity analysis is performed, and the resulting expressions are presented in a spatial and a material setting. In particular, the cases of an isotropic hyperelastic model and a multiplicative plasticity model with an exponential type integration scheme, both formulated in principal directions, are considered. Two numerical examples, based on simulated data and experimental data obtained by a grating method, demonstrate the versatility of our approach.