A simple orthotropic, transversely isotropic hyperelastic constitutive equation for large strain computations

This paper presents a simple transversely isotropic hyperelastic constitutive equation that can be used to model fiber oriented elastic materials in the fully nonlinear range. The hyperelastic strain energy function that defines this material is given in terms of three new material parameters and equations relating these material parameters to the Poisson ratio and the Young modules of the material along the fiber direction and on the orthogonal plane are derived. Expressions for the second Piola-Kirchhoff tensor, the Cauchy stress tensor and the Lagrangian and Eulerian elasticity tensors are also obtained. Static and dynamic applications of this material are used to illustrate its performance. (C) 1998 Elsevier Science S.A. All rights reserved.