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The quality of Finite Element Analysis (FEM) results relies on the input data, such as the material constitutive models. In order to achieve the best material parameters for the material constitutive models assumed a priori to represent the material, parameter identification inverse problems are considered. These inverse problems attempt to lead to the most accurate results with respect to physical experiments, i.e. minimizing the difference between experimental and numerical results. In this work three constitutive models were considered, namely, a non-linear elastic–plastic hardening model, a hyperelastic model -more specifically the Ogden model- and an elasto-viscoplastic model with isotropic and kinematic work-hardening. For the determination of the best suited material parameter set, two different optimization algorithms were used: (i) the Levenberg–Marquardt algorithm, which is gradient-based and (ii) a real …