Remarks on the theory of elasticity
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Sergio Conti [1] ; Camillo de Lellis [1]
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[1] Max Planck Institute for Mathematics in the Sciences
Max Planck Institute for Mathematics in the Sciences
Kreisfreie Stadt Leipzig, Alemania
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- Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 2, Nº 3, 2003, págs. 521-549
- Idioma: inglés
- Enlaces
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Resumen
In compressible Neohookean elasticity one minimizes functionals which are composed by the sum of the L^2 norm of the deformation gradient and a nonlinear function of the determinant of the gradient. Non–interpenetrability of matter is then represented by additional invertibility conditions. An existence theory which includes a precise notion of invertibility and allows for cavitation was formulated by Müller and Spector in 1995. It applies, however, only if some L^p-norm of the gradient with p>2 is controlled (in three dimensions). We first characterize their class of functions in terms of properties of the associated rectifiable current. Then we address the physically relevant p=2 case, and show how their notion of invertibility can be extended to p=2. The class of functions so obtained is, however, not closed. We prove this by giving an explicit construction.
