期刊
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
卷 197, 期 2, 页码 619-655出版社
SPRINGER
DOI: 10.1007/s00205-009-0271-4
关键词
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资金
- Catholic University of Chile
- Chilean Ministry of Planning
- Oxford University Press
- The Queen's College Graduate Scholarship
- Spanish Ministry of Education and Science [CGL2006-00524/BOS]
- EPSRC
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.
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