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Stratified Energies: Ground States with Cracks

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IUTAM Symposium on Progress in the Theory and Numerics of Configurational Mechanics

Part of the book series: IUTAM Bookseries ((IUTAMBOOK,volume 17))

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Abstract

Elastic bodies admitting cracks are analyzed. Separated pairs of displacement fields and cracks are found as minimizers of the energy in large strain setting. The crack patterns are constructed in terms of varifolds. The discontinuity set of the displacement field is contained in the cracks and may or may not coincide with them.

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References

  1. Bourdin, B., Francfort, G.A., Marigo, J.-J., The variational approach to fracture. J. Elasticity 91, 2008, 5–148.

    Article  MATH  MathSciNet  Google Scholar 

  2. Dal Maso, G., Francfort, G.A., Toader, R., Quasi-static growth in finite elasticity. Arch. Rat. Mech. Anal. 176, 2005, 165–225.

    Article  MATH  MathSciNet  Google Scholar 

  3. Francfort, G.A., Marigo, J.-J., Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46(8), 1998, 1319–1342.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  4. Francfort, G.A., Mielke, A., Existence results for a class of rate-independent matrerial models with non convex elastic energies. J. Reine Angew. Math. 595, 2006, 55–91, 2006.

    MATH  MathSciNet  Google Scholar 

  5. Giaquinta, M., Mariano, P.M., Modica, G., Mucci, D., Ground states of simple bodies that may undergo brittle fractures, preprint, 2008.

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  6. Giaquinta, M., Modica, G., Souček, J., Cartesian Currents in the Calculus of Variations, Vols. I and II. Springer-Verlag, Berlin, 1998.

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  7. Hutchinson, J.E., Second fundamental form for varifolds, existence of surfaces minimizing curvature, Indiana Univ. Math. J. 35, 1986, 45–71.

    Article  MATH  MathSciNet  Google Scholar 

  8. Mantegazza, C., Curvature varifolds with boundary. J. Diff. Geom. 43, 1996, 807–843.

    MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Scuola Normale Superiore, piazza dei Cavalieri 7, Pisa, I-56126, Italy

    M. Giaquinta

  2. DICeA, University of Florence, via Santa Marta 3, Firenze, I-50139, Italy

    P. M. Mariano

  3. Dipartimento di Matematica Applicata “G. Sansone”, University of Florence, via Santa Marta 3, Firenze, I-50139, Italy

    G. Modica

  4. Dipartimento di Matematica, University of Parma, v.le G.P. Usberti 53/A, Parma, I-43100, Italy

    D. Mucci

Authors
  1. M. Giaquinta
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  2. P. M. Mariano
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  3. G. Modica
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  4. D. Mucci
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Corresponding author

Correspondence to M. Giaquinta .

Editor information

Editors and Affiliations

  1. Chair of Applied Mechanics, University of Erlangen-Nuremberg, Erlangen, Germany

    P. Steinmann

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© 2009 Springer Science + Business Media B.V.

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Giaquinta, M., Mariano, P.M., Modica, G., Mucci, D. (2009). Stratified Energies: Ground States with Cracks. In: Steinmann, P. (eds) IUTAM Symposium on Progress in the Theory and Numerics of Configurational Mechanics. IUTAM Bookseries, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3447-2_15

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