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Defect and Material Mechanics pp 163–172Cite as

Conservation laws, duality and symmetry loss in solid mechanics

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Abstract

The paper deals with conservation laws which are not of the pure divergence type and thus do not provide a path-independent integral for use in Fracture Mechanics. It is shown that Duality is the right tool to re-establish the symmetry between equations and to provide conservation laws of the pure divergence type. The loss of symmetry of some energetic expressions is exploited to derive a new method for solving some inverse problems. In particular, the earthquake inverse problem is solved analytically.

Keywords

  • Conservation laws
  • Duality
  • Symmetry
  • Symmetry loss
  • Inverse problem

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Author information

Authors and Affiliations

  1. Department of Mechanics, Laboratory of Solid Mechanics, Ecole Polytechnique, Palaiseau, France

    Huy Duong Bui

  2. Lamsid/CNRS Electricite de France, Clamart, France

    Huy Duong Bui

Authors
  1. Huy Duong Bui
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Corresponding author

Correspondence to Huy Duong Bui .

Editor information

Editors and Affiliations

  1. University J. Fourier, Grenoble, France

    Cristian Dascalu

  2. University Pierre et Marie Curie, Paris, France

    Gérard A. Maugin

  3. Ecole Polytechnique, Palaiseau, France

    Claude Stolz

Additional information

Dedicated to George Herrmann.

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© 2007 Springer Science+Business Media B.V.

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Bui, H.D. (2007). Conservation laws, duality and symmetry loss in solid mechanics. In: Dascalu, C., Maugin, G.A., Stolz, C. (eds) Defect and Material Mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6929-1_15

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  • DOI: https://doi.org/10.1007/978-1-4020-6929-1_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-6928-4

  • Online ISBN: 978-1-4020-6929-1

  • eBook Packages: EngineeringEngineering (R0)

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