Numerical Modeling of Transversely Isotropic Elastic Material at Small and Finite Strains

Abstract

This paper describes three‐dimensional constitutive equations for transversely isotropic elastic material at small and finite strains. A significant contribution of this work is the linearization of the finite strain model in order to relate the finite strain model to the small strain model where the constitutive equation is developed in terms of the structure tensor. Stress‐update procedures for transversely isotropic constitutive model in finite strain has been developed and implemented in a finite element framework including the calculation of the exact material elasticity (tangent) tensor. Numerical example is presented to illustrate the comparison between small strain, finite strain and the linearized models.