## 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

Generalization | 14 |

Principal axes of a symmetric tensor of the second order | 21 |

Integral theorems | 28 |

Curvilinear coordinates | 34 |

State of Stress | 43 |

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

Hydrostatics | 56 |

Instantaneous Motion | 62 |

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 |

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### Common terms and phrases

According angle basic invariants boundary conditions boundary layer Chapter coefficients considered constant constitutive equation continuum coordinate system corresponding cross section cylinder defined denoted density derivative differential equation dimensionless discussion elastic equation of motion equilibrium exterior normal Figure filament follows furnishes grad gradient hypoelastic material incompressible fluid infinitesimal initial instantaneous linear material line elements material rate Newtonian fluid normal obtained perfect fluid positive pressure principal axes principal direction principal values rate of change rate of deformation relation represents respect rotation satisfy scalar shear line shearing stress shows simple shear specific body force strain tensor stream function stream lines stress components stress field stress rate stress tensor surface element surface traction symmetric tensor theorem tion Unabridged republication unit vector vanishes variables vector gradient velocity components velocity field velocity potential visco-plastic material vortex lines vorticity written zero