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Advancements in the Computational Calculus of Variations

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IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials

Part of the book series: IUTAM Bookseries ((IUTAMBOOK,volume 21))

Abstract

The aim of this paper is a survey on some state-of-the-art techniques in the numerical analysis of minimisation problems in nonlinear elasticity and on the concepts of quasi and polyconvexity in the calculus of variations. The issue of the approximation of singular minimisers is addressed via a penalty finite element method (PFEM) and macroscopic deformations are computed via the relaxation finite element method (RFEM). New numerical results are presented for the scalar doublewell problem as a benchmark in computational microstructures with adaptive meshrefining, in order to recover optimal convergence in the presence of singularities at interfaces.

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Author information

Authors and Affiliations

  1. Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Carsten Carstensen & Cataldo Manigrasso

  2. Department of Computational Science and Engineering, Yonsei University, 120-749, Seoul, Korea

    Carsten Carstensen

Authors
  1. Carsten Carstensen
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  2. Cataldo Manigrasso
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Corresponding author

Correspondence to Cataldo Manigrasso .

Editor information

Editors and Affiliations

  1. LS Allgemeine Mechanik, Universität Bochum, Bochum, Germany

    Klaus Hackl

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Carstensen, C., Manigrasso, C. (2010). Advancements in the Computational Calculus of Variations. In: Hackl, K. (eds) IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials. IUTAM Bookseries, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9195-6_3

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  • DOI: https://doi.org/10.1007/978-90-481-9195-6_3

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-9194-9

  • Online ISBN: 978-90-481-9195-6

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