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SUMMARYThe 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 e ective 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.

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