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. |
Contents
VECTOR AND TENSOR THEORY | 9 |
BASIC KINEMATICS | 48 |
BALANCE LAWS FIELD EQUATIONS AND JUMP CONDITIONS | 85 |
CONSTITUTIVE EQUATIONS | 122 |
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Common terms and phrases
3-direction arbitrary tensor arbitrary vector body forces boundary components constitutive equation continuum mechanics current configuration cylinder deduce defined deformation gradient density differentiable e₁ e₂ elastic material Exercise field equations formula function given grad Hence incompressible isochoric jump conditions material body material region material surface motion non-zero observer transformation obtain orthonormal basis particle paths plane polar decomposition principal axes principal stretches Problem proper numbers proper orthogonal tensor proper vectors properties quantum 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 description spherical spin tensor strain tensor stress vector stretching tensor surface segment symmetric tensor tensor field theorem theory tion torque triple product unit normal unit vectors v₁ v₂ vector field velocity viscous fluid vorticity x₁ x₂ zero