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Variational Methods in Continuum Damage and Fracture Mechanics

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Encyclopedia of Continuum Mechanics

Synonyms

Variational approach to damage and fracture mechanics; Variational formulation of damage and fracture mechanics

Definitions

Damage is defined as the loss of material stiffness under loading conditions. This process is intrinsically irreversible and, therefore, dissipative. When the stiffness vanishes, fracture is achieved. In order to derive governing equations, variational methods have been employed. Standard variational methods for non-dissipative systems are here formulated in order to contemplate dissipative systems as the ones considered in continuum damage mechanics.

Principle of Least Action for Dissipative Systems

Variational principles and calculus of variations have always been important tools for formulating mathematical models of physical phenomena (dell’Isola and Placidi, 2011). Indeed, they are the main tool for the axiomatization of physical theories because they provide an efficient and elegant way to formulate and solve mathematical problems which are of...

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Author information

Authors and Affiliations

  1. International Telematic University Uninettuno, Rome, Italy

    Luca Placidi

  2. Dipartimento di Ingegneria Strutturale e Geotecnica, Università degli Studi di Roma “La Sapienza”, Rome, Italy

    Emilio Barchiesi & Ugo Andreaus

  3. International Research Center for the Mathematics and Mechanics of Complex Systems, Università degli Studi dell’Aquila, L’Aquila, Italy

    Luca Placidi, Emilio Barchiesi & Anil Misra

  4. Civil, Environmental and Architectural Engineering Department, The University of Kansas, Lawrence, KS, USA

    Anil Misra

Authors
  1. Luca Placidi
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  2. Emilio Barchiesi
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  3. Anil Misra
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  4. Ugo Andreaus
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Corresponding author

Correspondence to Luca Placidi .

Editor information

Editors and Affiliations

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

    Holm Altenbach

  2. Griffith University (Gold Coast Campus), Griffith School of Engineering Griffith University (Gold Coast Campus), Southport, Queensland, Australia

    Andreas Öchsner

Section Editor information

  1. Dipartimento di Ingegneria, Strutturale e Geotecnica, Università di Roma "La Sapienza", Via Eudossiana, 18, 00184, Roma, Italia

    Francesco dell'Isola

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Placidi, L., Barchiesi, E., Misra, A., Andreaus, U. (2018). Variational Methods in Continuum Damage and Fracture Mechanics. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_199-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_199-1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

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