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Kachanov L.M. Foundations of the Theory of Plasticity

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Kachanov L.M. Foundations of the Theory of Plasticity
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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