2nd Ed. — North-Holland Publishing Company, 1971. — 495 p. — (North-Holland series in applied mathematics and mechanics, Vol. 12).The second edition has been substantially revised, reflecting important developments in the progress of the theory during recent years. Thus, more attention has been given to yield surfaces and to the associated yield law, and the chapters devoted to plane stress and the axisymmetric problem have been extended. The section on extremum principles and energetic methods of solution has been essentially rewritten. A new chapter has been included on the theory of shakedown, which is of great significance in connection with the role of varying loads in the origin of rupture. In the last ten years marked progress has been made with the model of a rigid-plastic body in dynamic problems; and so some additions have been introduced in Chapter XI.Preface to the Second Edition Basic Notation Introduction Basic Concepts in the Mechanics of Continuous Media Stress Strain Rate of Strain Differential Equations of Motion. Boundary and Initial Conditions The Mechanical Constitutive Equations of a Body Problems Equations of the Plastic State The Mechanical Properties of Solids Experimental Studies of Plastic Deformations in Complex Stress States. Simple and Complex Loading Yield Criteria. Yield Surface and Yield Curve Condition of Constant Maximum Tangential Stress (Tresca- Saint Venant Criterion) Condition of Constant Intensity of Tangential Stresses (von Mises Criterion) Conditions of Hardening. Loading Surface Conditions of Isotropic Hardening The Theory of Plastic Flow Deformation Theory of Plasticity Connection between Flow Theory and Deformation Theory Generalizations in the Case of Perfect Plasticity. Associated Flow Law Generalizations. Case of a Hardenmg Medium Drucker's Postulate. Convexity of the Loading Surface. Justification of the Associated Flow Law The Equations of Thermoplasticity Problems Equations of Elastic-Plastic Equilibrium. The Simplest Problems System of Equations for Plastic Equilibrium Continuity Conditions at the Boundary of Elastic and Plastic Regions Residual Stresses and Strains Plastic-Rigid Body Elastic-Plastic Bending of a Beam Hollow Sphere under Pressure Cylindrical Tube under Pressure Problems Torsion Torsion of Prismatic Rods. Basic Equations Plastic Torsion Elastic-Plastic Torsion Torsion of Hardening Rods Problems Plane Strain Basic Equations Slip Lines and their Properties Linearization. Simple Stress States Axisymmetric Field Boundary Conditions for Stresses Fundamental Boundary Value Problems Numerical Methods of Solution Determination of the Velocity Field Lines of Discontinuity in Stress and Velocity Non-Uniqueness of the Velocity Field. Criterion for Selection. Complete Solution Extension of a Strip Weakened by Notches Bending of a Strip Weakened by Notches Bending of a Short Cantilever Rectangular Neck Indentation by a Flat Die Wedge under the Action of a One-Sided Pressure Compression of a Layer between Rigid Plates Elastic-Plastic Extension of a Plane with a Circular Hole Steady Plastic Flow. Drawing of a Strip Non-Steady Plastic Flow with Geometric Similarity. Indentation by a Wedge Construction of Compatible Stress and Velocity Fields Problems Plane Stress Equations of Plane Stress Solutions with von Mises Yield Criterion. Discontinuous Solutions Solutions with Tresca-Saint Venant Yield Critenon. Discontinuous Solutions Elastic-Plastic Equilibrium of a Lamina with a Circular Hole under Uniform Pressure Extension of a Strip Weakened by Notches Bending of a Strip with a One-Sided Notch Problems Axisymmetric Strain Equations of Axisymmetric Strain with von Mises Yield Criterion Equations of Axisymmetric Strain with Tresca-Saint Venant Yield Criterion Stress in a Thin Plastic Layer with Tension (Compression) Stress Distribution in the Neck of a Tension Specimen Plastic Bending of Circular Plates Problems Extremum Principles and Energy Methods Extremum Principles Extremum Principles for a Plastic-Rigid Body Theorems on the Limit Load Coefficient Determination of the Limit Load by Energy Methods Minimum Principles in Deformation Theory Ritz's Method. Example: Elastic-Plastic Torsion Extremum Principles in Plastic Flow Theory Problems Theory of Shakedown Behaviour of Elastic-Plastic Bodies under Variable Loads Shakedown Theorems for Elastic-Plastic Bodies Approximate Method of Solution. Example Problems StabUity of Elastic-Plastic Equilibriuin Criteria of Stability Stability of a Compressed Rod. Reduced-Modulus and Tangent-Modulus Loads Stability of a Strip Bent by Couples Stability of Compressed Plates Problems Dynamical Problems Propagation of Elastic-Plastic Waves in a Rod Dynamical Problems for a Plastic-Rigid Body. Some Energy Theorems Longitudinal Impact of a Plastic-Rigid Rod against a Stationary Barrier Bending of a Plastic-Rigid Beam under an Impulsive Load Problems Composite Media. Visco-Plasticity Composite Media Visco-Plastic Medium Creep-Plastic Medium Problems Appendix Bibliography Index
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