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Three-Field Mixed Finite Element Methods in Elasticity

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Advanced Finite Element Technologies

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 566))

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Abstract

This chapter comprises a unified account of three-field mixed formulations for problems in elasticity. Various well-known formulations such as mixed enhanced strains and enhanced assumed strains are shown to be special cases of the general formulation. Conditions for locking-free convergence of finite element approximations are established for the linear problem. The linearized incremental problem arising from an application of Newton’s method is analyzed along similar lines, and conditions for locking-free behaviour and uniform convergence established. Numerical examples illustrate the performance of the mixed formulations.

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Acknowledgments

The support of the South African Department of Science and Technology and National Research Foundation through the South African Research Chair in Computational Mechanics is gratefully acknowledged.

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Authors and Affiliations

  1. Centre for Research in Computational and Applied Mechanics, University of Cape Town, Rondebosch, South Africa

    Batmanathan Dayanand Reddy

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  1. Batmanathan Dayanand Reddy
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Correspondence to Batmanathan Dayanand Reddy .

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Editors and Affiliations

  1. Institute of Mechanics, University of Duisburg-Essen, Essen, Germany

    Jörg Schröder

  2. University of Hannover, Hannover, Germany

    Peter Wriggers

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Reddy, B.D. (2016). Three-Field Mixed Finite Element Methods in Elasticity. In: Schröder, J., Wriggers, P. (eds) Advanced Finite Element Technologies. CISM International Centre for Mechanical Sciences, vol 566. Springer, Cham. https://doi.org/10.1007/978-3-319-31925-4_3

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  • DOI: https://doi.org/10.1007/978-3-319-31925-4_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-31923-0

  • Online ISBN: 978-3-319-31925-4

  • eBook Packages: EngineeringEngineering (R0)

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