## Three-Dimensional ElasticityThis volume is a thorough introduction to contemporary research in elasticity, and may be used as a working textbook at the graduate level for courses in pure or applied mathematics or in continuum mechanics. It provides a thorough description (with emphasis on the nonlinear aspects) of the two competing mathematical models of three-dimensional elasticity, together with a mathematical analysis of these models. The book is as self-contained as possible. |

### Contents

Geometrical and other preliminaries | 3 |

The equations of equilibrium and the principle | 57 |

Exercises | 85 |

Hyperelasticity | 137 |

The boundary value problems of threedimensional | 199 |

Existence theory based on the implicit function | 269 |

Existence theory based on the minimization of | 345 |

409 | |

435 | |

### Common terms and phrases

analysis applied arbitrary associated assume assumption Ball Banach space body boundary condition boundary value problem bounded called Cauchy stress Chapter closed compute consequence consider constants contains continuous converges convex corresponding defined definition deformation deformed configuration denote derivative differentiable displacement domain elasticity element equations equivalent established example Exercise exists expression extended field forces formula given Hence holds hyperelastic implies inequality injective isotropic linear Lipschitz-continuous mapping material mathematical matrix mean value theorem method minimizers models natural nonlinear norm observation obtain open subset orthogonal matrix particular problem proof prove pure reference configuration relation Remark respect response function result satisfies Sect sequence Show smooth solution stored energy function strain stress tensor surface symmetric Theorem theory variations vector vector space weak

### References to this book

The Mathematical Theory of Finite Element Methods Susanne Brenner,L. Ridgway Scott Limited preview - 2002 |

Nonlinear Functional Analysis and Its Applications: Part 2 B: Nonlinear ... E. Zeidler No preview available - 1989 |