## Introduction to Continuum MechanicsContinuum mechanics studies the response of materials to different loading conditions. The concept of tensors is introduced through the idea of linear transformation in a self-contained chapter, and the interrelation of direct notation, indicial notation and matrix operations is clearly presented. A wide range of idealized materials are considered through simple static and dynamic problems, and the book contains an abundance of illustrative examples and problems, many with solutions. Through the addition of more advanced material (solution of classical elasticity problems, constitutive equations for viscoelastic fluids, and finite deformation theory), this popular introduction to modern continuum mechanics has been fully revised to serve a dual purpose: for introductory courses in undergraduate engineering curricula, and for beginning graduate courses. |

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### Contents

1 | |

3 | |

Chpter 3 Kinematics of a Continuum
| 79 |

Chapter 4 Stress
| 173 |

Chapter 5 The Elastic Solid
| 217 |

Chapter 6 Newtonian Viscous Fluid
| 348 |

Chapter 7 Integral Formulation of General Principles
| 427 |

### Other editions - View all

Introduction to Continuum Mechanics W Michael Lai,David H. Rubin,David Rubin,Erhard Krempl Limited preview - 2009 |

### Common terms and phrases

angle antisymmetric axial axis body forces boundary conditions Cauchy stress Cauchy-Green deformation tensor change of frame coefficients Consider constant constitutive equation continuum control volume corresponding cross-section cylindrical coordinates defined deformation gradient denote density derivative detF displacement field eigenvalues eigenvectors elastic solid equations of motion Example Find ﬂow ﬂuid given by Eq indicial notation integral isotropic linear Maxwell mass material coordinates matrix Maxwell ﬂuid modulus Navier-Stokes equations Newtonian ﬂuid nonzero normal stress obtain particle pathline perpendicular Piola-Kirchhoff stress tensor plane strain pressure principal directions Prob problem rate of deformation reﬂection respect right Cauchy-Green rigid body Rivlin-Ericksen tensors satisfied scalar invariants Section shearing stress Show simple shearing Solution spin tensor strain components strain tensor stress components stress field stress function stress vector surface traction theorem transverse unit vector velocity field viscous ﬂuid wave zero