## A First Course in Continuum MechanicsA concise account of various classic theories of fluids and solids, this book is for courses in continuum mechanics for graduate students and advanced undergraduates. Thoroughly class-tested in courses at Stanford University and the University of Warwick, it is suitable for both applied mathematicians and engineers. The only prerequisites are an introductory undergraduate knowledge of basic linear algebra and differential equations. Unlike most existing works at this level, this book covers both isothermal and thermal theories. The theories are derived in a unified manner from the fundamental balance laws of continuum mechanics. Intended both for classroom use and for self-study, each chapter contains a wealth of exercises, with fully worked solutions to odd-numbered questions. A complete solutions manual is available to instructors upon request. Short bibliographies appear at the end of each chapter, pointing to material which underpins or expands upon the material discussed. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

9 | |

2 | 44 |

representations in particular we write | 45 |

χx | 50 |

v v vijj ei vijj ei | 54 |

Fig 21 Graphical illustration of a regular region consisting of | 55 |

242 TensorValued Functions | 63 |

Bibliographic Notes | 65 |

TO 0 | 155 |

417 a For the given deformation we find | 160 |

5 | 167 |

which is the desired result | 182 |

pmXtdetFXt p0X VXeB t 0 | 191 |

3 From the definitions of jf2fa if2t Tf2fz and rQt | 214 |

6 | 221 |

E D | 227 |

3 | 75 |

+ | 79 |

34 Equilibrium | 85 |

4 | 112 |

B | 113 |

Fig 42 A small region Ω in B is mapped | 115 |

3 Many texts employ the notation v xw in | 134 |

Fig 48 Two conﬁgurations Bt and Bt in the motion | 135 |

2 The ﬁeld deﬁned by JXt detFXt is typically | 139 |

Sa 2µL 2µQLQT QSaQT | 250 |

together with the boundary condition | 257 |

FVdetCn FhdetCp0C1 | 266 |

7 | 271 |

8 | 324 |

813 FrameIndiﬀerence Considerations | 330 |

4 A process in a material body is called reversible | 334 |

9 | 355 |

914 FrameIndifference Considerations | 364 |

### Other editions - View all

### Common terms and phrases

angular momentum arbitrary open subset assume axiom of material balance laws balance of linear body force boundary condition Cauchy stress ﬁeld chain rule Clausius-Duhem inequality components consider constant constitutive equations continuum body coordinate frame deduce deﬁned deﬁnition deformation gradient denote derivative diﬀerent Divergence Theorem eigenvalues elastic body elastic ﬂuid elastic solid elasticity tensor entropy Exercise ﬁeld per unit ﬁnd ﬁrst ﬁxed fluid fourth-order tensor given hyperelastic ideal ﬂuid implies inﬁnitesimal initial-boundary value problem internal energy irrotational isothermal isotropic linear elastic linear momentum linear momentum equation mass density material frame-indiﬀerence Newtonian ﬂuid obtain open subset particular perfect gas Proof properties reference conﬁguration relation satisﬁes satisfy scalar second-order tensor solution spatial velocity field strain tensor stress response function stress tensor symmetric temperature tensor field thermal unit mass unit normal vector field zero

### Popular passages

Page 4 - Truesdell, C. and Toupin, RA, The Classical Field Theories, in Handbuch der Physik, Vol.