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IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials pp 221–232Cite as

Polyconvex Energies for Trigonal, Tetragonal and Cubic Symmetry Groups

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

Abstract

In large strain elasticity the existence of minimizers is guaranteed if the variational functional to be minimized is sequentially weakly lower semicontinuous (s.w.l.s.) and coercive. Therefore, for the description of hyperelastic materials polyconvex functions which are always s.w.l.s. should be preferably used. A variety of isotropic and anisotropic polyconvex energies, in particular for the triclinic, monoclinic, rhombic and transversely isotropic symmetry groups, already exist. In this contribution we propose a new approach for the description of trigonal, tetragonal and cubic hyperelastic materials in the framework of polyconvexity. The anisotropy of the material is described by invariants in terms of the right Cauchy’Green tensor and a specific fourth-order structural tensor. In order to show the adaptability of the introduced polyconvex energies for the approximation of real anisotropic material behavior we focus on the fitting of a trigonal fourth-order tangent moduli near the reference state to experimental data.

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Authors and Affiliations

  1. Institut für Mechanik, Abteilung Bauwissenschaften, Fakultät für Ingenieurwissenschaften, Universität Duisburg-Essen, Universitätsstraße 15, 45117, Essen, Germany

    Jörg Schröder & Vera Ebbing

  2. Lehrstuhl für Nichtlineare Analysis und Modellierung, Fakultät für Mathematik, Universität Duisburg-Essen, Universitätsstraße 2, 45117, Essen, Germany

    Patrizio Neff

Authors
  1. Jörg Schröder
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  2. Patrizio Neff
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  3. Vera Ebbing
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Corresponding author

Correspondence to Jörg Schröder .

Editor information

Editors and Affiliations

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

    Klaus Hackl

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Schröder, J., Neff, P., Ebbing, V. (2010). Polyconvex Energies for Trigonal, Tetragonal and Cubic Symmetry Groups. 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_17

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  • DOI: https://doi.org/10.1007/978-90-481-9195-6_17

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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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