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

The paper discusses algorithms for the computation of stresses and elastici ty moduli for stored energy functions which are given in terms of a Seth-Hi ll-type generalized strain measure. The key contribution is distinct comput ational representations of a chain rule representation for the stresses and moduli which may serve as a basic tool for an effective numerical implemen tation of complex elasticity models. The representations are formulated in the Lagrangian geometric setting based on a spectral decomposition of the r ight Cauchy-Green tensor and contain particular representations for the cas e of equal eigenvalues. Two algorithmic boxes are pointed out for three- an d two-dimensional problems, respectively. Furthermore, a distinct algorithm ic 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 th e stress response in connection with generalized Hookean laws is considered as a simple application. Copyright (C) 2001 John Wiley & Sons, Ltd.