Continuum Mechanics
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Undergraduate text offers an analysis of deformation and stress, covers laws of conservation of mass, momentum, and energy, and surveys the formulation of mechanical constitutive equations. 1992 edition.
Preface1Introduction11.1Continuum mechanics12Introductory matrix algebra42.1Matrices42.2The summation convention62.3Eigenvalues and eigenvectors82.4The Cayley-Hamilton theorem112.5The polar decomposition theorem123Vectors and cartesian tensors143.1Vectors143.2Coordinate transformations163.3The dyadic product193.4Cartesian tensors203.5Isotropic tensors223.6Multiplication of tensors233.7Tensor and matrix notation253.8Invariants of a second-order tensor273.9Deviatoric tensors313.10Vector and tensor calculus314Particle kinematics334.1Bodies and their configurations334.2Displacement and velocity364.3Time rates of change374.4Acceleration394.5Steady motion. Particle paths and streamlines414.6Problems425Stress445.1Surface traction445.2Components of stress455.3The traction on any surface465.4Transformation of stress components495.5Equations of equilibrium515.6Principal stress components, principal axes of stress and stress invariants525.7The stress deviator tensor565.8Shear stress575.9Some simple states of stress575.10Problems606Motions and deformations636.1Rigid-body motions636.2Extension of a material line element666.3The deformation gradient tensor686.4Finite deformation and strain tensors706.5Some simple finite deformations746.6Infinitesimal strain786.7Infinitesimal rotation826.8The rate-of-deformation tensor836.9The velocity gradient and spin tensors856.10Some simple flows876.11Problems887Conservation laws917.1Conservation laws of physics917.2Conservation of mass917.3The material time derivative of a volume integral967.4Conservation of linear momentum977.5Conservation of angular momentum987.6Conservation of energy1007.7The principle of virtual work1027.8Problems1038Linear constitutive equations1048.1Constitutive equations and ideal materials1048.2Material symmetry1068.3Linear elasticity1108.4Newtonian viscous fluids1168.5Linear viscoelasticity1188.6Problems1209Further analysis of finite deformation1239.1Deformation of a surface element1239.2Decomposition of a deformation1259.3Principal stretches and principal axes of deformation1279.4Strain invariants1309.5Alternative stress measures1329.6Problems13410Non-linear constitutive equations13610.1Non-linear theories13610.2The theory of finite elastic deformations13610.3A non-linear viscous fluid14210.4Non-linear viscoelasticity14410.5Plasticity14510.6Problems14911Cylindrical and spherical polar coordinates15311.1Curvilinear coordinates15311.2Cylindrical polar coordinates15311.3Spherical polar coordinates16111.4Problems167AppendixRepresentation theorem for an isotropic tensor function170Answers173Further reading179Index180
