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Use and Abuse of the Method of Virtual Power in Generalized Continuum Mechanics and Thermodynamics

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Generalized Models and Non-classical Approaches in Complex Materials 1

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 89))

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Abstract

The method of virtual power, put forward by Paul Germain and celebrated by Gérard A. Maugin, is used (and abused) in the present work in combination with continuum thermodynamics concepts in order to develop generalized continuum, phase field, higher order temperature and diffusion theories. The systematic and effective character of the method is illustrated in the case of gradient and micromorphic plasticity models. It is then tentatively applied to the introduction of temperature and concentration gradient effects in diffusion theories leading to generalized heat and mass diffusion equations.

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Authors and Affiliations

  1. Centre des Matériaux, CNRS, UMR 7633, Mines ParisTech, Paris, France

    Samuel Forest

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  1. Samuel Forest
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Correspondence to Samuel Forest .

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Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität, Magdeburg, Germany

    Holm Altenbach

  2. Université Pierre et Marie Curie, Institut Jean Le Rond d’Alembert, Paris, France

    Joël Pouget

  3. Université Pierre et Marie Curie, Institut Jean Le Rond d’Alembert, Paris, France

    Martine Rousseau

  4. Université Pierre et Marie Curie, Institut Jean Le Rond d'Alembert, Paris Cedex 05, France

    Bernard Collet

  5. Institut Jean le Rond d'Alembert, Université Pierre et Marie Curie, Paris, France

    Thomas Michelitsch

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Forest, S. (2018). Use and Abuse of the Method of Virtual Power in Generalized Continuum Mechanics and Thermodynamics. In: Altenbach, H., Pouget, J., Rousseau, M., Collet, B., Michelitsch, T. (eds) Generalized Models and Non-classical Approaches in Complex Materials 1. Advanced Structured Materials, vol 89. Springer, Cham. https://doi.org/10.1007/978-3-319-72440-9_16

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  • DOI: https://doi.org/10.1007/978-3-319-72440-9_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72439-3

  • Online ISBN: 978-3-319-72440-9

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