PARAMETER IDENTIFICATION FOR THE NONLINEAR-ELASTIC MURNAGHAN MODEL BASED ON EVOLUTIONARY ALGORITHMS

The aim of the study is to develop and test a computational scheme for identifying the material parameters of the Murnaghan model, which describes the nonlinear elastic properties of solid bodies based on experimental data obtained through traditional static tests for tension, torsion, and bending of samples. Instead of real experiments, their computational models based on the application of the semi-inverse method of nonlinear elasticity theory are used. The input data for the identification process consists of loading diagrams constructed based on numerical studies of chains of nonlinear boundary value problems or, in the simplest case, uniaxial tension problems, through analytical investigation of nonlinear algebraic equations. Three types of diagrams are considered: the dependence of the rod elongation on the tensile force, the dependence of the angle of the section of a twisted shaft on the torque, and the dependence of the change in the plate thickness on the bending moment. All diagrams are constructed under the assumption of finite deformations; the last of the three diagrams is associated with the manifestation of extremely nonlinear material properties. To verify the stability of the developed scheme, artificially noisy versions of loading diagrams are also used for identification. The computational scheme for material parameters identification is based on the solution of the problem of minimizing the mean square deviation between the loading diagram constructed for these parameters and the “experimental” diagram. The relief of the minimized function is quite complex for gradient methods; therefore, a differential evolution algorithm was chosen to find the minimum. Its application allows one to achieve satisfactory retrieving of the nonlinear elastic model, including cases of noisy input data. At the same time, it was found that the sensitivity of the considered deformation models to material parameters can vary significantly, up to the impossibility of identifying one of the parameters based on the chosen mechanical experiment.