## Introduction to Mechanics of ContinuaA classic in the field, this book meets the demands of courses that establish groundwork in hydrodynamics, gas dynamics, plasticity and elasticity, and it provides typical continua problems for nonspecialists. The author addresses the major aspects of continuum studies: geometrical foundations, state of stress, instantaneous motion, fundamental laws, perfect fluids, viscous fluids, visco-plastic and perfectly plastic materials, hypoelastic materials, finite strain, and elastic and hyperelastic materials. The text’s broad converge and numerous applications include more than 160 problems and examples, and the only prerequisites are first- and second-year college calculus. 1961 ed. |

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### Contents

Geometrical Foundations | 3 |

Tensor | 11 |

The ttensor | 19 |

Tensor fields | 26 |

Curvilinear coordinates | 34 |

State of Stress | 43 |

Mohrs representation of states of stress Plane state of stress | 50 |

Hydrostatics | 56 |

Viscoplastic and Perfectly Plastic Materials | 136 |

Plane plastic flow | 144 |

Hypoelastic Materials Classical Theory of Elasticity | 154 |

Hypoelastic materials in the neighborhood of stressfree state | 160 |

Torsion of cylindrical bars | 166 |

Extremum principles | 172 |

Elastic waves | 178 |

Finite Strain | 188 |

Instantaneous Motion | 62 |

Conditions of jntegrabjljty | 70 |

Fundamental Laws | 81 |

Simple constitutive equations | 87 |

Viscous Fluids | 114 |

boundary layer equations | 124 |

Other strain tensors | 196 |

Elastic and Hyperelastic Materials | 204 |

Uniqueness and stability | 215 |

Index | 223 |

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### Common terms and phrases

According angle axis basic invariants boundary conditions boundary layer Cartesian coordinate system Chapter coefficients considered constant constitutive equation continuum coordinate system corresponding cross section curl cylinder denoted density derivative differential equation discussion elastic equation of motion exterior normal Figure filament follows furnishes grad gradient infinitesimal instantaneous integral linear material line elements material rate obtained orthogonal perfect fluid positive pressure principal axes principal direction principal stresses principal values problem rate of change rate of deformation rectangular Cartesian coordinate relation represents respect rotation scalar field shear line shear rate shearing stress Show specific body force strain tensor stream function stream lines stress components stress field stress rate stress tensor subscripts surface element surface traction symbolic notation symmetric tensor theorem tion transformation Unabridged republication unit vector vanishes variables vector field vector gradient velocity field velocity potential viscous fluid vortex lines vorticity written zero