A SIMPLE ORTHOTROPIC, TRANSVERSELY ISOTROPIC HYPERELASTIC CONSTITUTIVE EQUATION FOR LARGE-STRAIN COMPUTATIONS

This paper presents a simple transversely isotropic hyperelastic const itutive equation that can be used to model fiber oriented elastic mate rials in the fully nonlinear range. The hyperelastic strain energy fun ction that defines this material is given in terms of three new materi al parameters and equations relating these material parameters to the Poisson ratio and the Young modules of the material along the fiber di rection and on the orthogonal plane are derived. Expressions for the s econd Piola-Kirchhoff tensor, the Cauchy stress tensor and the Lagrang ian and Eulerian elasticity tensors are also obtained. Static and dyna mic applications of this material are used to illustrate its performan ce. (C) 1998 Elsevier Science S.A. All rights reserved.