On the robustness of an inverse optimization approach based on the Levenberg-Marquardt method for the mechanical behavior of polycrystals

The robustness of an inverse optimization approach based on the Levenberg-Marquardt method to obtain the critical resolved shear stresses for the different slip and twinning systems of a polycrystalline Mg alloy is analyzed. In particular, the influence of the input information (in terms of the number of stress-strain curves) and of the initial properties of the single crystals on the optimization results was ascertained. It was found that the optimization method was very robust and the results were independent of the initial conditions in the optimization process. It was also found that a minimum of two stress-strain curves (one in which deformation along the c axis is controlled by twinning and another in which is controlled by prismatic and pyramidal 〈c + a〉 slip) are necessary to obtain accurate results. Possible avenues to improve the accuracy of this optimization strategy in polycrystals are indicated.