WYPIWYG hyperelasticity for isotropic, compressible materials

Nowadays the most common approach to model elastic behavior at large strains is through hyperelasticity. Hyperelastic models usually specify the shape of the stored energy function. This shape is modulated by some material parameters that are computed so the predicted stresses best fit the experimental data. Many stored energy functions have been proposed in the literature for isotropic and anisotropic materials, either compressible or incompressible. What-You-Prescribe-Is-What-You-Get (WYPIWYG) formulations present a different approach which may be considered an extension of the infinitesimal framework. The shape of the stored energy is not given beforehand but computed numerically from experimental data solving the equilibrium equations. The models exactly fit the experimental data without any material parameter. WYPIWYG procedures have comparable efficiency in finite element procedures as classical hyperelasticity. In this work we present a WYPIWYG numerical procedure for compressible isotropic materials and we motivate the formulation through an equivalent infinitesimal model.

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