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

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Abstract

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.

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Authors and Affiliations

  1. School of Civil Engineering and Geosciences, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK

    R. A. Hiley & M. Rouainia

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  1. R. A. Hiley
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  2. M. Rouainia
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Correspondence to M. Rouainia.

Additional information

This work was undertaken with the financial support of the UK Engineering and Physical Sciences Research Council: Grant no. GR/S84897/01.

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Hiley, R.A., Rouainia, M. Explicit Runge–Kutta methods for the integration of rate-type constitutive equations. Comput Mech 42, 53–66 (2008). https://doi.org/10.1007/s00466-007-0234-2

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  • DOI: https://doi.org/10.1007/s00466-007-0234-2

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