## Mechanics of Solids and MaterialsThis book blends both innovative (large strain, strain rate, temperature, time dependent deformation and localized plastic deformation in crystalline solids, deformation of biological networks) and traditional (elastic theory of torsion, elastic beam and plate theories, contact mechanics) topics in a coherent theoretical framework. Extensive use of transform methods to generate solutions will make this book of interest to structural, mechanical, and aerospace engineers. Plasticity theories, micromechanics, crystal plasticity, and energetics of elastic systems are also covered, as well as an overall review of math and thermodynamics. |

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### Contents

Integrals | 33 |

CONTINUUM MECHANICS | 55 |

Kinetics of Continuum | 92 |

Thermodynamics of Continuum | 113 |

Potentials | 139 |

Nonlinear Elasticity | 148 |

LINEAR ELASTICITY | 161 |

Elastic Beam Problems | 184 |

The Inclusion Problem | 335 |

Forces and Energy in Elastic Systems | 355 |

Micropolar Elasticity | 375 |

THIN FILMS AND INTERFACES | 407 |

Strain Relaxation in Thin Films | 428 |

Stability of Planar Interfaces | 447 |

PLASTICITY AND VISCOPLASTICITY | 461 |

Micromechanics of Crystallographic Slip | 502 |

Solutions in Polar Coordinates | 199 |

Torsion and Bending of Prismatic Rods | 214 |

SemiInfinite Media | 229 |

Isotropic 3D Solutions | 246 |

Anisotropic 3D Solutions | 264 |

Plane Contact Problems | 271 |

Deformation of Plates | 280 |

MICROMECHANICS | 293 |

Dislocations in Anisotropic Media | 299 |

Cracks in Anisotropic Media | 315 |

Crystal Plasticity | 538 |

Localized Plastic | 557 |

Polycrystal Plasticity | 586 |

Laminate Plasticity | 601 |

BIOMECHANICS | 609 |

Constitutive Relations for Membranes | 633 |

SOLVED PROBLEMS | 641 |

833 | |

853 | |

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### Common terms and phrases

anisotropic applied arbitrary array Asaro assumed axis biharmonic equation body forces boundary conditions Burgers vector Cauchy stress configuration Consider constant corresponding couple-stress crack tip crystal defined deformation gradient deformation tensor Derive deviatoric differentiation direction dislocation line displacement field divergence theorem edge dislocation elastic moduli entropy equilibrium equation expression Figure follows Fourier Gibbs energy given gives grain hardening inclusion incompressible increment integral interface isotropic lattice linear loading material matrix Mechanics medium modulus Note obtain orthogonal parameter plane strain plastic deformation potential Problem radius rate of deformation recall relation result rotation scalar shear stress shown in Fig slip plane slip system Solution spherical strain energy strain tensor stress components stress field stress function stress tensor stretch ratio substitution symmetric temperature tensile theory thermodynamic traction transformation uniaxial unit normal unit vector volume yield surface zero