Preprint 19/2007

Existence of minimizers for a polyconvex energy in a crystal with dislocations

Stefan Müller and Mariapia Palombaro

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Submission date: 21. Feb. 2007
Pages: 12
published in: Calculus of variations and partial differential equations, 31 (2008) 4, p. 473-482 
DOI number (of the published article): 10.1007/s00526-007-0120-y
MSC-Numbers: 74N05, 58A25, 74B20, 49J45, 46E40
Keywords and phrases: Crystals, dislocations, currents, nonlinear elasticity
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We provide existence theorems in nonlinear elasticity for minimum problems modeling the deformations of a crystal with a given dislocation. A key technical difficulty is that due to the presence of a the dislocation the elastic deformation gradient cannot be in formula3. Thus one needs to consider elastic energies with slow growth, to which the original results of Ball cannot be applied directly.

18.10.2019, 02:13