## Nonlinear Solid Mechanics: Bifurcation Theory and Material InstabilityThis book covers solid mechanics for nonlinear elastic and elastoplastic materials, describing the behavior of ductile material subject to extreme mechanical loading and its eventual failure. The book highlights constitutive features to describe the behavior of frictional materials such as geological media. On the basis of this theory, including large strain and inelastic behaviors, bifurcation and instability are developed with a special focus on the modeling of the emergence of local instabilities such as shear band formation and flutter of a continuum. The former is regarded as a precursor of fracture, while the latter is typical of granular materials. The treatment is complemented with qualitative experiments, illustrations from everyday life, and simple examples taken from structural mechanics. |

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### Indice

Elements of tensor algebra and analysis | 91 |

Solid mechanics at ﬁnite strains | 125 |

Isotropic nonlinear hyperelasticity | 152 |

Solutions of simple problems in ﬁnitely deformed nonlinear | 162 |

Constitutive equations and anisotropic elasticity | 188 |

Elastoplastic constitutive equations | 251 |

decomposition of the deformation gradient | 265 |

Moving discontinuities and boundary value problems | 275 |

Incremental bifurcation of elastic solids | 338 |

Applications of local and global uniqueness and stability criteria | 385 |

Wave propagation stability and bifurcation | 403 |

Postcritical behaviour and multiple shear band formation | 427 |

A perturbative approach to material instability | 444 |

nonsymmetric constitutive equations | 457 |

References | 507 |

527 | |

Global conditions of uniqueness and stability | 293 |

Local conditions for uniqueness and stability | 310 |

### Altre edizioni - Visualizza tutto

Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability Davide Bigoni Anteprima limitata - 2012 |

Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability Davide Bigoni Anteprima non disponibile - 2014 |

### Parole e frasi comuni

acoustic tensor analysis anisotropy assumed behaviour bifurcation bifurcation mode Bigoni boundary conditions Cauchy stress comparison solid components compression consider constitutive equations constitutive operator convexity corresponding crack curve cylinder deﬁned deformation gradient denotes deviatoric eigenvalues eigenvectors elastic material elastic tensor elastica elastoplastic equilibrium ﬁeld ﬁgure ﬁnd ﬁnite ﬁrst Piola-Kirchhoff stress ﬁxed ﬂutter instability Green’s function hardening homogeneous inclined incompressible incompressible elastic incremental displacement inﬁnite isotropic JZ-deformation theory Lagrangean linear loading logarithmic strain loss of ellipticity Mooney-Rivlin nominal stress non-associative non-linear Note null obtained occurs parameter perturbation plane strain positive deﬁniteness pre-stress problem propagation Raniecki reference conﬁguration reference system reported in Fig rigid-body rotation satisﬁed scalar Section shear band shown in Fig simple shear small strain so-called softening solution spatial stability strain energy strain localisation sufﬁcient symmetry tractions transformed uniaxial unit vector unloading values velocity wave whereas yield function yield surface