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In the present study, a numerical method based on a metaheuristic parametricalgorithm has been developed to identify the constitutive parameters ofhyperelastic models, by using FE simulations and full kinematic fieldmeasurements. The full kinematic field is measured at the surface of acruciform specimen submitted to equibiaxial tension. The sample isreconstructed by FE to obtain the numerical kinematic field to be compared withthe experimental one. The constitutive parameters used in the numerical modelare then modified through the optimization process, for the numerical kinematicfield to fit with the experimental one. The cost function is then formulated asthe minimization of the difference between these two kinematic fields. Theoptimization algorithm is an adaptation of the Particle Swarm Optimizationalgorithm, based on the PageRank algorithm used by the famous search engineGoogle. INTRODUCTION The constitutive parameters of hyperelastic models aregenerally identified from three homogeneous tests, basically the uniaxialtension, the pure shear and the equibiaxial tension. From about 10 years, analternative methodology has been developed [1, 2, 3, 4], and consists inperforming only one heterogeneous test as long as the field is sufficientlyheterogeneous. This is tipically the case when a multiaxial loading is appliedto a 3 branch or a 4-branch cruciform specimen, which induces a large number ofmechanical states at the specimen surface. The induced heterogeneity isgenerally analysed through the distribution of the biaxiality ratio and themaximal eigen value of the strain. The Digital Image Correlation (DIC)technique is generally used to retrieve the different mechanical statesinduces, and provides the full kinematic field at the specimen surface, i.e. alarge number of experimental data to be analysed to identify the constitutiveparameters of the behaviour model considered.

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