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Finite element modelling of non-linear deformation of rate-dependent materials using a R-minimum strategy

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Abstract

A R-minimum strategy, which was proposed and successfully applied to analyse the non-linear rate-independent finite deformation (including the thermal–mechanical coupling and frictional contact) of elasto-plastic materials, is extended and applied here to simulate the deformation of rate-dependent materials. It involves no iterations, thus belongs to the static-explicit algorithm and avoids the convergence problem resulting from nonlinearities. The R-minimum strategy-based adaptive control scheme of the time step size is proposed and applied to the related analysis of the rate-dependent materials with both the time-dependent and the time-independent viscosity. Both the simple benchmark test and the practical application in evaluation of the effect of the Earth materials on its response to the centrifugal force are carried out to demonstrate the stability, efficiency and usefulness of this algorithm.

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Acknowledgments

Support is gratefully acknowledged by the relevant national projects of ARC DP066620, LP0560932 and NSFC 40728004. The authors are grateful to the three anonymous reviewers for their advice/comments that allowed this paper to be improved.

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Authors and Affiliations

  1. Earth Systems Science Computational Centre (ESSCC), The University of Queensland, Sir James Foots Building (47A), St. Lucia, Brisbane, QLD 4072, Australia

    H. L. Xing & J. Zhang

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  1. H. L. Xing
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  2. J. Zhang
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Correspondence to H. L. Xing.

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Xing, H.L., Zhang, J. Finite element modelling of non-linear deformation of rate-dependent materials using a R-minimum strategy. Acta Geotech. 4, 139–148 (2009). https://doi.org/10.1007/s11440-009-0090-7

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  • DOI: https://doi.org/10.1007/s11440-009-0090-7

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