Title | Some remarks on the theory of elasticity for compressible Neohookean materials. |

Publication Type | Journal Article |

Year of Publication | 2003 |

Authors | Conti S., De Lellis C. |

Journal | Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V |

Volume | 2 |

Pagination | 521–549 |

Publisher | Scuola Normale Superiore di Pisa |

Type of Article | calculus of variations |

ISSN | 0391-173X |

Abstract | 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. |

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

URL | http://www.numdam.org/item/ASNSP_2003_5_2_3_521_0/ |

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