TitleSome remarks on the theory of elasticity for compressible Neohookean materials.
Publication TypeJournal Article
Year of Publication2003
AuthorsConti S., De Lellis C.
JournalAnnali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
PublisherScuola Normale Superiore di Pisa
Type of Articlecalculus of variations

In Neohookean elasticity one minimizes functionals which depend on the L2 norm of the deformation gradient, plus a nonlinear function of the determinant, with some notion of invertibility to represent non-interpenetrability of matter. An existence theory which includes a precise notion of invertibility and allows for cavitation was formulated by Müller and Spector, however only for the case where some Lp-norm of the gradient with p \ensuremath> 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, which has interesting consequences even in other frameworks.


Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 2 (2003), no. 3, 521–549.