This book examines in detail the Theory of Elasticity which is a branch of the mechanics of a deformable solid. Special emphasis is placed on the investigation of the process of deformation within the framework of the generally accepted model of a medium which, in this case, is an elastic body. A comprehensive list of Appendices is included providing a wealth of references for more in depth coverage. The work will provide both a stimulus for future research in this field as well as useful reference material for many years to come.

Table of Contents

A selection of contents: 1. Deformation of a Continuous Medium. Material coordinates. Spatial coordinates. Vector bases. Deformation gradients. Cauchy-Green and almansi strain measures. Orthogonal tensors accompanying deformation. Dilatation. The oriented elementary area. Variation of the state of strain. The second derivative of a scalar function of a tensor argument. Kinematic relations. Rigid motions. Frame-indifferent tensors. The objective derivative of a tensor. The Rivlin-Ericksen tensors. Tensors of affine deformation. 2. Stress in A Continuous Medium. Body and surface forces. The Cauchy stress tensor. The equations of motion of a continuous medium. The tensor of stress functions. On polar media. Alternative definitions of the stress tensor. The incremental work. 3. The State Equations. The simple body. The principle of material frame-indifference. Elastic materials. The symmetry group of a material. Orthogonal transformation. Isotropic material. The solid body. An isotropic solid material. An elastic fluid. 4. The Equations of Nonlinear Theory of Elasticity and the Statement of Problems. The specific stored energy of deformation. The state equation of an elastic isotropic material. Variation of the stress state. The equilibrium equations for a varied stress state. The relaxation tensor of an isotropic medium. Equations of motion and equilibrium for an isotropic elastic body. Methods of analysis of equilibrium boundary-value problems for a nonlinearly elastic body. The theorem of Ericksen. The principle of stationary complementary energy. The Hamilton-Ostrogradskii principle. 5. The State Equations for a Nonlinearly Elastic Material. On the choice of a state equation for an isotropic elastic body. Seth's body. Signorini's body. Murnaghan's material. A quasi-linear John material. The energy of dilatation and distortion. Empirical criterion. Convexity of the s


© 1990
North Holland
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