A general polyconvex strain‐energy function for fiber‐reinforced materials

Abstract

The continuum mechanical modeling and numerical simulation of fiber‐reinforced materials, such as carbon‐fiber‐reinforced plastics or collagenous biological tissues, are of great interest in the field of material science. In this regard, various strainenergy functions have been proposed to capture the inherent anisotropy of these types of materials ranging from simple exponential functions applied in biomechanics [5] to more sophisticated formulations based on the theory of invariants [8]. The goal of this contribution is to present an alternative ansatz, which basically adopts the general idea of the wellestablished isotropic hyperelasticity law of Ogden [7]. In particular, a polynomial strain‐energy function formulated in the fiber stretch is proposed, which allows the description of the general nonlinear elastic response of various kinds of fiber materials, such as collagen, nylon or sisal, in a very concise form. Moreover, the formulation still meets the requirements of a stress‐free reference state and material stability, whereas the number of material parameters is kept to a minimum. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)