Dynamic Plasticity

1st Edition, Volume 4 - January 1, 1967
Author: N. Cristescu
Language: English
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 1 6 3 2 9 - 3

Dynamic Plasticity discusses the problems encountered in the theory of dynamic deformation of plastic bodies. The book describes one-dimensional problems involving a single… Read more

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Dynamic Plasticity discusses the problems encountered in the theory of dynamic deformation of plastic bodies. The book describes one-dimensional problems involving a single component of stress, particle velocity, and single spatial coordinate. The propagation of longitudinal elastic-plastic waves in thin rods or wires is a simple example of this problem of dynamic plasticity. Another one-dimensional problem, which has various possible transverse motions, is the dynamics of extensible strings. This problem is associated in calculations dealing with cables of suspension bridges, of elevator cables, of electric cables. The analogy with the mechanics of extensible strings can be extended to circular and rectangular membranes such as explained by Karunes and Onat. Karunes and Onat analyzed the propagation of transverse and longitudinal shock waves in such membranes using the Rakhmatulin theory for strings. The text also discusses axi-symmetrical problems and the problems of soil mechanics when applied to soft soils. The book can prove valuable to civil engineers, structural engineers, physicist, and students of mechanical engineering or industrial design.

Ch. I. IntroductionCh. II. The Propagation of Longitudinal Stress Waves in Thin Rods § 1. The Equation of Motion § 2. The Finite Constitutive Equation § 3. Integration Methods § 4. The Unloading Problem § 5. Determination of the Loading/Unloading Boundary § 6. Equations of Motion in Eulerian Coordinates § 7. The Plastic/Rigid Solution § 8. Shock Waves § 9. The Finite Bar § 10. Non-Homogeneous Rods § 11. Bars with Variable Cross SectionCh. III. The Rate Influence on the Propagation of Longitudinal Elastic/Viscoplastic Waves; One-Dimensional Problems § 1. Introduction § 2. Differential Constitutive Equations § 3. Instantaneous Plastic Response § 4. Non-Instantaneous Plastic Response § 5. Plastic/Rigid Material § 6. Observations and Comments § 7. Loading/Unloading Criteria § 8. Examples § 9. Experimental Verifications § 10. ConclusionsCh. IV. Mechanics of Extensible Strings § 1. Introduction § 2. Equations of Motion § 3. The Finite Constitutive Equation: Basic Formulae § 4. The Order of Propagation of Waves § 5. Boundary and Initial Conditions § 6. Special Case § 7. The Integration Scheme § 8. Examples § 9. Extensible Cables Used to Brake High Speed Moving Bodies § 10. The Motion of Two Bodies Connected by an Extensible Cable § 11. Observations and Comments § 12. Rate Influence § 13. Shock Waves § 14. Transverse Impact of BeamsCh. V. Mechanics of Circular Membranes § 1. Introduction § 2. High-Rate Forming of Circular Blanks § 3. The Simplified Scheme § 4. Equations of Motion § 5. The Finite Constitutive Equation § 6. Differential Constitutive Equations § 7. Initial and Boundary Conditions § 8. Loading/Unloading Criteria § 9. Integration SchemeCh. VI. Axi-Symmetrical Problems § 1. Introduction § 2. Impact of Plates by a Rigid Circular Cylinder § 3. Enlargement of Holes. Plate Perforation § 4. Plastic/Rigid Thin Plates § 5. Cylindrical Elastic-Plastic Waves § 6. Coupling of Elastic/Viscoplastic Waves § 7. MiscellaneousCh. VII. Thick Rods. Plane Waves § 1. Introduction § 2. Plane Waves § 3. Axi-Symmetrical Thick Rods. Differential Constitutive Equation § 4. Experimental StudiesCh. VIII. Shock Waves in Solids § 1. Introduction § 2. Conservative Laws § 3. Jump Conditions § 4. The Case of the Solid Body with Small Strains § 5. Constitutive Equations § 6. Example for a Certain Constitutive Equation § 7. The Constitutive Equation for the Case σij = σδij § 8. The One-Dimensional Strain Case § 9. Shock Waves in Bodies Comprising Phase Transitions § 10. Elastic and Plastic Shock Waves § 11. An Example of Moderate Unloading § 12. CrateringCh. IX. Plastic Waves in Soils § 1. Introduction § 2. Soil Compaction § 3. Yield Condition § 4. Loading and Unloading Concepts § 5. Stress-Strain Relations § 6. The "Plastic Gas" Model § 7. The Plastic Locking Medium § 8. Other Models which Consider the Unloading Process § 9. Multi-Phase Media § 10. The Method of CharacteristicsCh. X. Appendix. Differential Constitutive Equations Used in Dynamic Plasticity § 1. Semi-Linear Constitutive Equations § 2. Quasi-Linear Constitutive EquationsReferencesSubject Index