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Hill R. The Mathematical Theory of Plasticity

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Hill R. The Mathematical Theory of Plasticity
Oxford University Press, 1998. — IX, 355 p. — ISBN: 0198503679.
Written by one of the leaders in the field and first published in 1950, this book remains a classic treatment of the mathematical theory of plastic materials.
Contents.
Introductio.
Definition of the subject.
Historica loutline.
Physical background.
The stress-strain curve.
Foundations of the Theory.
The ideal plastic body.
The criterion of yielding.
Strain-hardening.
The complete stress-strain relations.
The Levy-Mise s and Reuse equations.
The Henck y stress-strain equations.
Other theories.
General Theorems.
The plastic potential.
Uniqueness of a stress distribution under given boundary conditions.
Extremum and variational principles.
The Solution of Plastic-Elastic Problems.
Introduction.
Theory of Hohenemser's experiment.
Combined torsion an d tension of a thin-walled tube.
Combined torsion and tension of a cylindrica l bar.
Compression under conditions of plane strain.
Bending under conditions of plane strain.
Bending of a prismatic beam.
Torsion of a prismatic bar.
Torsion of a bar of non-uniform section.
The Solution of Plastic-Elastic Problems.
The expansion of a spherical shell.
The expansion of a cylindrica l tube.
Theory of the autofrettage process.
Expansion of a cylindrica l cavity in an infinite medium.
Plane Plastic Strain and the Theory of the Slip Line Field.
Assumption of a plastic-rigid material.
The plane strain equations referred to Cartesian coordinates.
The plane strain, equations referred to the slip-lines.
Geometry of the slip-line field.
The numerical calculation of slip-line fields.
The numerical calculation of the velocity distribution.
Analyti c integration of the plane strain equations.
Discontinuities in the stress.
Two-DimensionaL Problems of Steady Motion.
Formulation of the problem.
Sheet-drawing.
Ironing of a thin-walled cup.
Sheet-extrusion.
Piercing.
Strip-rolling.
Machining.
Flow through a converging channel.
Non-Steady Motion Problems in Two Dimensions.
Geometric similarity and the unit diagram.
Wedge-indentation.
Compression of a wedge by a flat die Expansion of a semi-cylindrical cavity i n a surface.
Compression of a block between rough plates.
Non-Steady Motion Problems in Two Dimensions.
Introduction.
Formulation of the problem.
Yielding of notched bars under tension.
Plastic yielding round a cavit y indentation and the theory of hardness tests.
Axial Symmetry.
Fundamental equations.
Extrusion from a contracting cylindrical container.
Compression of a cylinder under certain distributed loads.
Cylindrical tube under axial tension and internal pressure.
Tube-sinking.
Stress distribution i n the neck of a tension specimen.
Compression of a cylinder between rough plates.
Relations along slip-lines and flow-lines.
Miscellaneous Topics.
Deep-drawing.
General theory of sheet-bending.
Plane strain of a general plastic material.
The theory of plane plastic stress, with applications.
Completely plastic states of stress in a prismatic bar.
Plastic Anisotropy.
The yield criterion.
Relations between stress and strain-increment.
Plastic anisotropy of rolled sheet.
Length changes in a twisted tube.
The earing of deep-drawn cups.
Variation of the anisotropic parameters during cold-work.
Theory of plane strain for anisotropic metals.
Appendixes.
Author Index.
Subject Index.
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