## Continuum Mechanics: Elasticity, Plasticity, ViscoelasticityMost books on continuum mechanics focus on elasticity and fluid mechanics. But whether student or practicing professional, modern engineers need a more thorough treatment to understand the behavior of the complex materials and systems in use today. Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity offers a complete tour of the subject that includes not only elasticity and fluid mechanics but also covers plasticity, viscoelasticity, and the continuum model for fatigue and fracture mechanics. In addition to a broader scope, this book also supplies a review of the necessary mathematical tools and results for a self-contained treatment. The author provides finite element formulations of the equations encountered throughout the chapters and uses an approach with just the right amount of mathematical rigor without being too theoretical for practical use. Working systematically from the continuum model for the thermomechanics of materials, coverage moves through linear and nonlinear elasticity using both tensor and matrix notation, plasticity, viscoelasticity, and concludes by introducing the fundamentals of fracture mechanics and fatigue of metals. Requisite mathematical tools appear in the final chapter for easy reference. Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity builds a strong understanding of the principles, equations, and finite element formulations needed to solve real engineering problems. |

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### Contents

Fundamentals of Continuum Mechanics | 11 |

5 | 17 |

Nonlinear Elasticity | 49 |

9 | 74 |

Linear Elasticity | 113 |

Properties of Solutions | 119 |

Plasticity | 159 |

Viscoelasticity | 213 |

Fracture and Fatigue | 239 |

Mathematical Tools for Continuum Mechanics | 253 |

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### Common terms and phrases

alternative applies approximation assumed balance base becomes behavior body boundary conditions calculated called coefficients complete components condition conservation of mass consider constant constitutive relations continuous coordinates crack defined deformation denote depends derivative determined direction displacement dissipation elastic element energy equal equations example exists expressed field FIGURE fixed follows force formula function given gives gradient hardening hold independent indices initial integration invariants isotropic material linear loading matrix measure mechanics method modulus motion nodal normal basis notation Note obtain occurs parameters particle physical plane plastic plastic strain positive potential energy principal problem reference configuration requirement respect result rotation satisfy scalar shear solution space strain stress tensor stretch suppose symmetric temperature tensile test theory unit vector viscoelastic yield surface zero