Optimization of Constitutive Parameters for Hyperelastic Models Satisfying the Baker-Ericksen Inequalities

Abstract

Hyperelastic models are used to model the mechanical behavior of rubber-like materials ranging from elastomers, such as natural rubber and silicon, to biologic materials, such as muscles and skin tissue. Once the desired hyperelastic model has its parameters fitted to the available experimental results, these hyperelastic parameters have to fulfill the requirements imposed by the Baker-Ericksen inequalities in order to guarantee a plausible physical behavior to the material. When applied to an incompressible isotropic hyperelastic model, these inequalities state that the first derivative of the strain energy density function with respect to the first strain invariant must be positive and the first derivative of the strain energy density function with respect to the second strain invariant must be non-negative. The aim of this work is to present an algorithm used to fit hyperelastic models to experimental data so that the parameters automatically fulfill the requirements of the Baker-Ericksen inequalities. This is accomplished through a constrained optimization procedure. Results obtained for natural rubber and silicon samples considering classical and newly developed hyperelastic models are shown and discussed.