## Continuum Mechanics: Concise Theory and ProblemsThis comprehensive treatment offers 115 solved problems and exercises to promote understanding of vector and tensor theory, basic kinematics, balance laws, field equations, jump conditions, and constitutive equations. Expressed in a common, efficient notation, the clear and formally precise steps for solving each problem foster quick comprehension. |

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problemas resueltos de mecanica del continuo

### Contents

VECTOR AND TENSOR THEORY | 11 |

BASIC KINEMATICS | 50 |

BALANCE LAWS FIELD EQUATIONS AND JUMP CONDITIONS | 87 |

CONSTITUTIVE EQUATIONS | 124 |

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### Common terms and phrases

arbitrary tensor arbitrary vector associated axial vector axis body forces boundary circulation preserving components constitutive equation continuum mechanics current configuration cylinder deduce defined deformation gradient denoted density differentiable direction Exercise field equations follows formula function given grad Hence integral isochoric jump conditions material body material region material surface non-zero normal stress observer transformation obtain orthonormal basis plane polar decomposition positive constant positive definite principal axes principal invariants principal stresses principal stretches principle of objectivity Problem proper orthogonal tensor proper vectors properties rectangular Cartesian system reference configuration referential and current referential and spatial relation relative result rotation scalar field Show simple shear singular surface skew-symmetric skew-symmetric tensor Solution spatial coordinates spatial description spherical spin tensor strain tensor stress tensor stress vector stretching tensor surface segment symmetric tensor tensor field theorem theory tion torque triple product unit normal unit vectors vector field vorticity zero