Mechanics Today

Contributors

Preface

Summary

I. Dynamic Effects in Brittle Fracture


1. Introduction


2. The Balance of Rates of Energies


3. Analysis of the Elasto-dynamic Field around a Propagating Crack


3.1 Anti-Plane Motions


3.2 Motions in Plane Strain


4. Quasi-Static Loading and Quasi-Static Fracture


4.1 Anti-Plane Strain


4.2 Plane Strain


4.3 Conclusions


5. Quasi-Static Loading and Dynamic Fracture


5.1 Anti-Plane Motions


5.2 In-Plane Motions


5.3 Conclusions


6. Dynamic Loading and Dynamic Fracture


6.1 Anti-Plane Motions


6.2 In-Plane Motions


6.3 Conclusions


7. Dynamic Loading and Quasi-Static Fracture


7.1 Anti-Plane Motions


7.2 In-Plane Motions


7.3 Conclusions


8. Summary and Discussion


9. References

Appendix — Some Results of Dynamic Elasticity

II Qualitative Theory of the Ordinary Differential Equations of Nonlinear Elasticity


1. Introduction


2. Formulation of the Boundary-Value Problems


3. Integrals of the Governing Equations


4. Flexure, Extension, and Shear under Terminal Loads


5. Flexure and Extension under Hydrostatic Pressure


6. Flexure, Extension, and Shear under Hydrostatic Pressure


7. Necking


8. Conclusion


9. References

III Plastic Waves: Theory and Experiment


1. Introduction


2. Plastic Wave Theory


2.1 Governing Equations


2.2 Characteristics


2.3 Transport Equation


2.4 Simple Waves


3. Waves of One-Dimensional Stress


3.1 Acceleration Waves


3.2 Simple Waves


4. Waves of One-Dimensional Strain


4.1 Analysis of Deformation


4.2 Constitutive Equations


4.3 Continuous Waves


4.4 Waves of Strong Discontinuity


4.5 Plate-Impact Experiments


4.6 Steady Waves


5. Waves of Combined Stresses


5.1 Rate Independent Plasticity


5.2 Rate Dependent Plasticity


6. References

IV. Modern Continuum Thermodynamics


1. Introduction


2. Bodies, Sub-bodies, Velocity Fields


3. Energy, Heat, and Power; the First Law


4. Entropy; the Second Law


5. Local Form of the Balance Laws for Forces and Moments


6. Local Form of the First Two Laws


7. The Reduced Dissipation Inequality; Motion-Temperature Pairs; Processes


8. Elastic Materials


9. Elastic Stability


10. Thermodynamics with Internal State Variables


11. References

V. General Variational Principles in Nonlinear and Linear Elasticity with Applications


1. Introduction


1.1 Example


2. Preliminaries


3. Nonlinear Problems with Three Independent Continuous Fields


4. Nonlinear Problems with One and Two Independent Continuous Fields


4.1 Independent Displacement and Stress


4.2 Independent Displacement and Strain


4.3 One Independent Field


5. Nonlinear Problems with Discontinuous Fields


6. Incremental Formulation


7. Linearized Formulation


7.1 Independent Displacement, Strain, and Stress


7.2 Independent Displacement and Stress


7.3 Independent Displacement


8. Application to Eigenvalue Problems


8.1 Harmonic Waves in Elastic Composites


8.2 Heat Conduction in Composites


8.3 Application to Schrödinger's Wave Equation


9. Application to Finite-Element Methods


9.1 Finite Elements with Piecewise Constant Fields


9.2 Finite Elements with Piecewise Linear Fields


9.3 Higher-Order Finite Elements


9.4 Discussion


10. References

VI. A Survey of Theory and Experiment in Viscometric Flows of Viscoelastic Liquids


1. Introduction


2. Kinematically Admissible Viscometric Flows


2.1 Steady Parallel Flows


2.2 Skew Rectilinear Flows


2.3 Steady Circular Flows


2.4 Helical Flows


2.5 Helicoidal Flows


2.6 General Kinematics of Viscometric Flows


3. Stress Response


3.1 Qualitative Behavior of the Viscometric Functions


3.2 Stress Fields


4. Controllable Viscometric Flows


5. Torsional Flow


6. Partially Controllable Flows


7. Skew Rectilinear Motions


8. Poiseuille Flows


9. Couette Flow and Helical Flows


10. Cone and Plate Flow


11. Kinematics of More General Motions


12. Stress in Smooth Motions


13. Consistency among Constitutive Equations


14. Approximate Solution of Flow Problems


15. Pressure-Hole Errors


16. Tube and Channel Flows


17. General Torsional Flows


18. Other Methods and Results


19. Summary of Data


20. List of Symbols


21. References

VII. Concepts in Elastic Structural Stability


1. Introduction


2. Potential Energy


3. Equilibrium and Stability


4. Symmetric Post-Buckling Behavior


5. Bounds on Deflection


6. Implications for Researchers and Designers


6.1 The Southwell Method in Experimental Work


6.2 Random Imperfections


7. Imperfection Sensitivity with Dynamic Loading


8. Multiple Loading on Structures


9. Interaction Between Buckling Modes


10. Concluding Remarks


11. References

Author Index

Subject Index