Archive for Rational Mechanics and Analysis

, Volume 197, Issue 2, pp 619–655 | Cite as

Invertibility and Weak Continuity of the Determinant for the Modelling of Cavitation and Fracture in Nonlinear Elasticity

  • Duvan HenaoEmail author
  • Carlos Mora-Corral


In this paper, we present and analyze a variational model in nonlinear elasticity that allows for cavitation and fracture. The main idea in unifying the theories of cavitation and fracture is to regard both cavities and cracks as phenomena of the creation of a new surface. Accordingly, we define a functional that measures the area of the created surface. This functional has relationships with the theory of Cartesian currents. We show that the boundedness of that functional implies sequential weak continuity of the determinant of the deformation gradient, and that the weak limit of one-to-one almost everywhere deformations is also one-to-one almost everywhere. We then use these results to obtain the existence of minimizers of variational models that incorporate elastic energy and this created surface energy, taking into account orientation-preserving and non-interpenetration conditions.


Cavitation Elastic Energy Nonlinear Elasticity Lipschitz Boundary Existence Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Laboratoire Jacques-Louis LionsUniversité Pierre et Marie CurieParis Cedex 05France
  2. 2.Basque Center for Applied Mathematics (BCAM)Parque Tecnológico de BizkaiaDerio (Vizcaya)Spain

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