## Mathematical Elasticity: Three-dimensional elasticity, Volume 1This 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. |

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### 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

A(tr applied body force applied forces applied surface force arbitrary assume assumption Ball boundary condition boundary value problem Cauchy stress tensor Cauchy stress vector Ciarlet condition of place constitutive equation continuous converges convex function defined definition deformed configuration denote density differentiable displacement-traction problem domain elastic material equivalent Exercise existence results F G M3 given Green's formula Hence hyperelastic material implicit function theorem implies inequality injective isotropic lower semi-continuous Lp(fl M3 x M3 mapping matrix minimizer nonlinear normed vector space notation open set open subset orthogonal matrix p(dfl p(fl partial derivatives Piola-Kirchhoff stress tensor polyconvex proof of Theorem pure displacement problem pure traction problem reference configuration relation Remark response function satisfies Sect sequence set fl Show smooth Sobolev space solution St Venant-Kirchhoff material stored energy function strain tensor symmetric tensor field topology vector field Vi/r

### 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 |