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Computational Mechanics

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01-01-2015 | Original Paper

Automatic implementation of finite strain anisotropic hyperelastic models using hyper-dual numbers

Authors: Ravi Kiran, Kapil Khandelwal

Published in: Computational Mechanics | Issue 1/2015

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Abstract

The main aim of this paper is to automate the implementation of finite strain anisotropic hyperelastic models into a general finite element framework. The automation presented in this paper enables the end-user to implement a hyperelastic model by programming its Helmholtz free energy function alone. The automation is achieved by employing hyper-dual number system to evaluate analytical quality derivatives. New perturbation techniques are introduced and are employed to extend the hyper-dual numbers system to evaluate tensor derivatives. The capability of the proposed automation scheme is demonstrated by implementing five finite strain anisotropic hyperelastic models. The merits and demerits of the proposed automation scheme are compared to an automation scheme based on the central difference method.

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Title: Automatic implementation of finite strain anisotropic hyperelastic models using hyper-dual numbers
Authors: Ravi Kiran
Kapil Khandelwal
Publication date: 01-01-2015
Publisher: Springer Berlin Heidelberg
Published in: Computational Mechanics / Issue 1/2015
Print ISSN: 0178-7675
Electronic ISSN: 1432-0924
DOI: https://doi.org/10.1007/s00466-014-1094-1

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