Nonlinear Effects in Fluids and Solids

1. On Structural Changes in Two-Phase Materials.- 1. Introduction.- 2. Stochastic State-Space and Operators in Z.- 3. Evolution of States during the Transient Period.- 4. Structural Changes of the Aluminum - Resin Composite.- References.- 2. Introduction to Nonlinear Elasticity.- 1. Introduction.- 2. Kinematics of Finite Deformation.- 3. Cauchy Stress Principle and Equations of Motion.- 4. Mechanical Energy Principle and Hyperelasticity.- 5. Change of Frame and Material Frame Indifference.- 6. Material Symmetry Transformations.- 7. Isotropic Hyperelastic Materials.- 8. Blatz - Ko Constitutive Equation.- 9. Incompressible Materials.- 10. Rivlin - Saunders Strain Energy Function.- 11. Inflation Response of a Balloon.- 12. Remarks on Other Kinds of Internal Constraints.- 13. Boundary-Value Problems and Nonuniqueness in Elastostatics.- 14. Universal Inverse Solutions.- 15. Nonuniversal Inverse Solutions: Example.- 16. Class of Universal Relations.- 17. Truesdell’s Problem: Restrictions on Constitutive Equations.- 18. Elastic Stability and Nonuniqueness.- 19. Concluding Remarks.- References.- 3. Propagating and Static Exponential Solutions in a Deformed Mooney - Rivlin Material.- 1. Introduction.- 2. Mooney - Rivlin Materials.- 3. Small Deformations Superimposed on Large.- 4. Propagating and Static Exponential Solutions.- 5. Propagation Condition - Secular Equation.- 6. Homogeneous Waves.- 7. Propagating Evanescent Solutions.- 8. Static Exponential Solutions.- References.- 4. Circularly Polarized Waves of Finite Amplitude in Elastic Dielectrics.- 1. Introduction.- 2. Basic Equations.- 3. Simple Shearing and Polarization.- 4. Circularly Polarized Progressive Waves.- 5. Circularly Polarized Standing Waves.- 6. Approximations.- References.- 5. Static Theory of Point Defectsin Nematic Liquid Crystals.- 1. Introduction.- 2. Basic Theory.- 3. Dirichlet Problems.- 4. Stable Point Defects.- Acknowledgments.- References.- 6. Function Spaces and Fading Memory.- 1. Introduction.- 2. Stability of the Solution of a Volterra Integral Equation.- 3. Cauchy Problem for the Laplace Equation.- 4. Concept of Fading Memory for an Elastic Solid.- References.- 7. On Thermomechanical Formulation of Theories of Continuous Media.- 1. Introduction.- 2. General Thermomechanical Theory.- 3. Thermomechanical Theory of Shells and Plates.- 4. Thermomechanical Theory of Rods.- Acknowledgment.- References.- Supplementary Reference.- 8. Steady Flow of Slightly Viscoelastic Fluids.- 1. Introduction.- 2. Theorem Concerning the Flow of Slightly Viscoelastic Fluids.- 3. Some General Remarks on Flows with Axial Symmetry.- 4. Convergent Flow in a Right-Circular Cone.- References.- Supplementary References.- 9. Some Anomalies in the Structure of Elastic-Plastic Theory at Finite Strain.- 1. Introduction.- 2. Elastic - Plastic Coupling.- 3. Objectivity.- 4. Elastic - Plastic Constitutive Relations.- Acknowledgment.- References.- Supplementary Reference.- 10. Nonlinear Thermoelastic Constitutive Equations for Transversely Isotropic and Orthotropic Materials.- 1. Introduction.- 2. Notation and General Theory.- 3. Constitutive Equations for Transversely Isotropic Materials.- 4. Transverse Isotropy — Simple Shearing Deformations.- 5. Constitutive Equations for Orthotropic Materials.- 6. Orthotropy — Simple Shearing Deformations.- Acknowledgment.- References.- 11. Energy Minimization for Membranes.- 1. Introduction.- 2. Inextensible Networks.- 3. Networks with Shearing Stiffness.- 4. Rubber Membranes.- 5. Stress.- Acknowledgment.- References.- 12. On Boundary Layer-LikeStructures in Finite Thermoelasticity.- 1. Introduction.- 2. Governing Equations.- References.- 13. On the Thickness Limitation for Euler Buckling.- 1. Introduction.- 2. Potential Energy.- 3. Neutral Equilibrium of Critical States.- 4. Further Developments for the General Material.- 5. Asymptotic Analysis for a Thin Plate.- 6. Results for a Neo-Hookean Plate.- 7. Bifurcation Conditions for a Thick Plate.- References.- 14. Irreducible Constitutive Expressions.- 1. Introduction.- 2. Decomposition Procedure.- 3. Generating Functions.- 4. Procedure for Generating Irreducible Expressions.- References.- 15. Determination of the Strain Energy Density Function for Compressible Isotropic Nonlinear Elastic Solids by Torsion-Normal Force Experiments.- 1. Introduction.- 2. Governing Equations.- 3. Change of Variables.- 4. Axial Force, Twisting Moment.- 5. Material Identification by Torsion Experiments.- 6. Summary.- References.