Identification of material parameters is a key step in understanding the mechanical response of structures, particularly when only displacement data and geometry are available. The aim of this research was to develop and compare different optimization approaches for determining the elastic modulus and Poisson’s ratio of linear-elastic materials based on data from numerical simulations in Abaqus. Since the reference values of the parameters were known in advance, it was possible to evaluate the convergence rate, precision, and robustness of each method without the influence of measurement noise or other uncertainties. The procedure is based on reconstructing the stress field from displacements, formulating an objective function derived from mechanical equilibrium conditions, and performing optimization using the Gauss–Newton, bisection, and progressive methods. The comparative analysis revealed differences in the speed and stability of the methods and confirmed that the choice of an appropriate approach significantly affects the success of the identification process. The results provide a basis for improving existing algorithms and developing new procedures capable of operating effectively under conditions of greater complexity and incomplete input data.
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