Algorithms for computation of stresses and elasticity moduli in terms of Seth–Hill's family of generalized strain tensors

Abstract

AbstractThe paper discusses algorithms for the computation of stresses and elasticity moduli for stored energy functions which are given in terms of a Seth–Hill‐type generalized strain measure. The key contribution is distinct computational representations of a chain rule representation for the stresses and moduli which may serve as a basic tool for an effective numerical implementation of complex elasticity models. The representations are formulated in the Lagrangian geometric setting based on a spectral decomposition of the right Cauchy–Green tensor and contain particular representations for the case of equal eigenvalues. Two algorithmic boxes are pointed out for three‐ and two‐dimensional problems, respectively. Furthermore, a distinct algorithmic setting is developed for applications of the Seth–Hill‐type measures to the isochoric part of the deformation based on a spectral decomposition of the unimodular part of the right Cauchy–Green tensor. The computation of the stress response in connection with generalized Hookean laws is considered as a simple application. Copyright © 2001 John Wiley & Sons, Ltd.