Governing Equations 2.1 Mathematical Description of Shape Changes in Solids 2.1.1 The displacement and velocity fields 2.1.2 The displacement gradient and deformation gradient tensors 2.1.3 Deformation gradient resulting from two successive deformations 2.1.4 The Jacobian of the deformation gradient 2.1.5 The Lagrange strain tensor 2.1.6 The Eulerian strain tensor 2.1.7 The infinitesimal strain tensor 2.1.8 Engineering shear strains 2.1.9 Decomposition of infinitesimal strain into volumetric and deviatoric parts 2.1.10 The infinitesimal rotation tensor 2.1.11 Principal values and directions of the infinitesimal strain tensor 2.1.12 Cauchy-Green deformation tensors 2.1.13 Rotation tensor, Left and Right stretch tensors 2.1.14 Principal stretches 2.1.15 Generalized strain measures 2.1.16 The velocity gradient 2.1.17 Stretch rate and spin tensors 2.1.18 Infinitesimal strain rate and rotation rate 2.1.19 Other deformation rate measures 2.1.20 Strain equations of compatibility for infinitesimal strains 2.2 Mathematical Description of Internal Forces in Solids 2.2.1 Surface traction and body force 2.2.2 Traction acting on planes within a solid 2.2.3 The Cauchy (true) stress tensor 2.2.4 Other stress measures - Kirchhoff, Nominal and Material stress 2.2.5 Stress measures for infinitesimal deformations 2.2.6 Principal stresses and directionsĢ.2.7 Hydrostatic stress, Deviatoric stress, and Von Mises effective stress 2.2.8 Stresses near an external surface or edge – boundary conditions 2.3 Equations of motion and equilibrium for deformable solids 2.3.1 Linear momentum balance in terms of Cauchy stress 2.3.2 Angular momentum balance in terms of Cauchy stress 2.3.3 Equations of motion in terms of other stress measures 2.4 Work done by stresses Principle of Virtual Work 2.4.1 Work done by Cauchy stresses 2.4.2 Rate of mechanical work in terms of other stress measures 2.4.3 Rate of mechanical work for infinitesimal deformations 2.4.4 The principle of Virtual Work 2.4.5 The Virtual Work equation in terms of other stress measures 2.4.6 The Virtual Work equation for infinitesimal deformations 3. Objectives and Applications of Solid Mechanics 1.1 Defining a Problem in Solid Mechanics 1.1.1 Deciding what to calculate 1.1.2 Defining the geometry of the solid 1.1.3 Defining loading 1.1.4 Deciding what physics to include in the model 1.1.5 Defining material behavior 1.1.6 A representative initial value problem in solid mechanics 1.1.7 Choosing a method of analysis 2.
5.6 Solutions to Dynamic Problems/span>ġ.10.5 Simplified Shells: Membranes and Plates.10.3 Simplified Rods - Strings and Beams.9.2 Stress/Strain Based Failure Criteria.5.5 Plane Problems for Anisotropic Solids.5.3 Plane Problems: Complex Variable Solutions.
5.2 Plane Problems: Airy Function Solutions.4.3 Axially/Spherically Symmetric Hyperelasticity.4.2 Axially/Spherically Symmetric plasticity.
4.1 Axially/Spherically Symmetric elasticity.
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