Microcontinuum Field Theories

1 Kinematics.- 1.0 Scope.- 1.1 Physical Picture.- 1.2 Motions and Deformations.- 1.3 Rotation.- 1.4 Microstretch and Micropolar Continua.- 1.5 Strain Measures.- 1.6 Relative Motion, Relative Strain Measures.- 1.7 Compatibility Conditions.- 1.8 Material Time-Rate of Tensors.- 1.9 Objective Tensors.- 1.10 Mass, Inertia, Momenta, Kinetic Energy.- 1 Problems.- 2 Stress.- 2.0 Scope.- 2.1 Balance of Energy.- 2.2 Balance Laws.- 2.3 Second Law of Thermodynamics.- 2.4 Dissipation Potential.- 2 Problems.- 3 Constitutive Equations.- 3.0 Scope.- 3.1 Constitutive Equations of Elastic Solids.- 3.2 Constitutive Equations of Fluids.- 3.3 Thermodynamic Restrictions on Solids.- 3.4 Thermodynamic Restrictions on Fluids.- 3.5 Thermodynamic Restrictions on.- Memory-Dependent Solids.- 3.6 Thermodynamic Restrictions on.- Memory-Dependent Fluids.- 3 Problems.- 4 Electromagnetic Interactions.- 4.0 Scope.- 4.1 Balance Laws.- 4.2 Constitutive Equations of E-M Solids.- 4.3 Constitutive Equations of E-M Fluids.- 4.4 Memory-Dependent E-M Solids.- 4.5 Memory-Dependent E-M Fluids.- 4 Problems.- 5 Theory of Micropolar Elasticity.- 5.0 Scope.- 5.1 Linear Constitutive Equations.- 5.2 Material Symmetry and Stability.- 5.3 Isotropic Solids.- 5.4 Formulation of Problems in Micropolar Elasticity.- 5.5 Mixed Boundary-Initial Value Problems in Linear Theory.- 5.6 Curvilinear Coordinates.- 5.7 Uniqueness Theorem.- 5.8 Reciprocal Theorem.- 5.9 Variational Principles.- 5.10 Conservation Laws.- 5.11 Plane Harmonic Waves.- 5.12 Material Moduli.- 5.13 Experimental Attempts.- 5.14 Displacement Potentials.- 5.15 Micropolar Waves in Half-Space.- 5.16 Micropolar Surface Waves.- 5.17 Micropolar Waves in Plates.- 5.18 Fundamental Solutions.- 5.19 Problems of Sphere and Spherical Cavity.- 5.20 Axisymmetric Problems.- 5.21 Penny-Shaped Crack.- 5.22 Stress Distribution Around an Elliptic Hole.- 5.23 Stress Concentration Around a Circular Hole.- 5.24 Nonlinear Waves.- 5.25 Fundamental Solutions in Micropolar

Microcontinuum field theories constitute an extension of classical field theories to microscopic spaces and short time scales. The ideas developed here are important, for example, in considering the fluid or elastic properties of blood, porous media, polymers, liquid crystals, slurries, and composite materials.