Development of an inverse identification method for identifying constitutive parameters by metaheuristic optimization algorithm: Application to hyperelastic materials

Abstract

In the present study, a numerical method based on a metaheuristic parametric algorithm has been developed to identify the constitutive parameters of hyperelastic models, by using FE simulations and full kinematic field measurements. The full kinematic field is measured at the surface of a cruciform specimen submitted to equibiaxial tension. The sample is reconstructed by FE to obtain the numerical kinematic field to be compared with the experimental one. The constitutive parameters used in the numerical model are then modified through the optimization process, for the numerical kinematic field to fit with the experimental one. The cost function is then formulated as the minimization of the difference between these two kinematic fields. The optimization algorithm is an adaptation of the Particle Swarm Optimization algorithm, based on the PageRank algorithm used by the famous search engine Google. INTRODUCTION The constitutive parameters of hyperelastic models are generally identified from three homogeneous tests, basically the uniaxial tension, the pure shear and the equibiaxial tension. From about 10 years, an alternative methodology has been developed [1, 2, 3, 4], and consists in performing only one heterogeneous test as long as the field is sufficiently heterogeneous. This is tipically the case when a multiaxial loading is applied to a 3 branch or a 4-branch cruciform specimen, which induces a large number of mechanical states at the specimen surface. The induced heterogeneity is generally analysed through the distribution of the biaxiality ratio and the maximal eigen value of the strain. The Digital Image Correlation (DIC) technique is generally used to retrieve the different mechanical states induces, and provides the full kinematic field at the specimen surface, i.e. a large number of experimental data to be analysed to identify the constitutive parameters of the behaviour model considered.