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Explicit Runge-Kutta methods for the integration of rate-type constitutive equations

Lookup NU author(s): Robert Hiley, Dr Mohamed Rouainia


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Modern constitutive models have the potential to improve the quality of engineering calculations involving non-linear anisotropic materials. The adoption of complex models in practice, however, depends on the availability of reliable and accurate solution methods for the stress point integration problem. This paper presents a modular implementation of explicit Runge-Kutta methods with error control, that is suitable for use, without change, with any rate-type constitutive model. The paper also shows how the complications caused by the algebraic constraint of conventional plasticity are resolved through a simple subloading modification. With this modification any rate-independent model can be implemented without difficulty, using the integration module as an accurate and robust standard procedure. The effectiveness and efficiency of the method are demonstrated through a comparative evaluation of second and fifth-order formulas, applied to a complex constitutive model for natural clay, full details of which are given. © 2007 Springer-Verlag.

Publication metadata

Author(s): Hiley RA, Rouainia M

Publication type: Article

Publication status: Published

Journal: Computational Mechanics

Year: 2008

Volume: 42

Issue: 1

Pages: 53-66

ISSN (print): 0178-7675

ISSN (electronic): 1432-0924

Publisher: Springer Berlin


DOI: 10.1007/s00466-007-0234-2


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