Comprehensive discussion on hyperelastic orthotropic constitutive models for finite strains

Abstract

In the classical literature devoted to the study of orthotropic materials under large strains, a lot of emphasis is given to strain invariants, obscuring the association of finite strain constitutive relations with well-established small strains constitutive relations. In this work, this association is established through the comparison of 8 orthotropic models (3 classical and 5 new) for hyperelastic orthotropic materials using the Flory’s decomposition. This is done transforming the initial formalism of different models into complete quadratic polynomials written in terms of the Right-Cauchy-Green stretch and a volumetric control that guaranties the growth condition. A tailoring fiber-reinforced solid model - in which discrete fibers are immersed into continuous matrix - is also presented and used to establish numerical tests, generating basic elastic constants for comparisons. The 5 proposed models are implemented in an in-house FEM code and comparisons among their mechanical behavior are presented. From these comparisons one of the proposed models is selected to successfully simulate a biological tissue, opening the possibilities for future studies.