Parameter identification in anisotropic elastoplasticity by indentation and imprint mapping

Indentation tests are at present frequently employed for the identification of parameters contained in constitutive models of materials at different scales. The indentation curves (namely, the relationship between applied force and penetration depth) provide experimental data for the calibration of mechanical models through traditional semi-empirical formulae or, in recent times, through simulation of the test and inverse analysis. The main material parameters estimated in these ways are Young modulus and yield stress. A recently proposed technique combines the traditional indentation test with the mapping of the residual deformations (imprint), thus providing experimental data apt to identify isotropic material parameters in more accurate fashion and in larger number, including Poisson's ratio, hardening coefficients, friction between the specimen and the indentation tool. In this paper, such new methodology is employed for the calibration of anisotropic material models. Axial-symmetric indenters are referred to. The mapped imprint (which, clearly, does not exhibit axial symmetry because of the specimen anisotropy) provides meaningful experimental data, additional to those deduced from the indentation curves. These curves are almost insensitive to differences of material properties along different directions. On the contrary, residual displacements reflect constitutive anisotropy and turn out to be crucial for the success of the parameter identification procedure. The classical Hill's model for anisotropic perfect elasto-plasticity is adopted herein to describe material behavior. Three-dimensional finite element simulations are performed in finite strain regime by a commercial code. Inverse analysis is carried out by a batch, deterministic approach, using conventional optimization algorithms for the minimization of the discrepancy function. Sensitivity indices are computed in order to assess the identifiability of the parameters and to provide a basis for the design of the experiments. Numerical examples are discussed apt to test the performance of the proposed methodology in terms of result accuracy and computing effort in view of industrial applications.