Anisotropic Hyperelastic Material Characterization: Stability Criterion and Inverse Calibration with Evolutionary Strategies

Abstract

In this work, we propose a reliable and stable procedure to characterize anisotropic hyperelastic materials. For this purpose, a metaheuristic optimization method known as evolutionary strategies is used. The advantage of this technique with respect to traditional methods used for non-linear optimization, such as the Levenberg–Marquardt Method, is that this metaheuristic algorithm is oriented to the global optimization of a problem, is independent of gradients and allows to solve problems with constraints. These features are essential when characterizing hyperelastic materials that have non-linearities and are conditioned to regions of stability. To characterize the mechanical behavior of the arteries analyzed in this work, the anisotropic hyperelastic models of Holzapfel–Gasser–Ogden and Gasser–Holzapfel–Ogden are used. An important point of the analysis is that these models may present a non-physical behavior: this drawback is overcome by defining a new criterion of stabilization in conjunction with the evolutionary strategies. Finally, the finite element simulations are used in conjunction with the evolutionary strategies to characterize experimental data of the artery pressurization test, ensuring that the parameters obtained are stable and representative of the material response.