After a brief historical introduction, recent achievements in the theory of plasticity are surveyed with emphasis on applications in mechanical engineering.Kinematic models are presented that indicate the complexities of mechanical behaviour in the plastic range. The fundamental theorems of limit analysis are discussed, and their application to two- and three-dimensional problems is illustrated by examples. Shakedown analysis and limit design are defined. Problems involving large plastic deformations are discussed with special reference to metal forming processes. Applications of the theory of plasticity to impact testing and blast damage are reviewed. Recent changes in the theory of structural stability in the plastic range are mentioned. Throughout the lecture, impending developments of the theory of plasticity are indicated.

The Theory of Plasticity: A Survey of Recent Achievements

In this paper, a summary of work performed in the area of modeling of the dynamic metal cutting process is presented. A general view of evolution of the dynamic cutting process models is depicted. Specifically four modeling approaches including analytical, experimental, mechanistic and numerical methods are critically reviewed. A brief assessment offuture research needs is also given.

Machining Process Modeling: A Review

Preface 1. Stress and strain 2. Elastic and inelastic material behaviour 3. Yield 4. Plastic flow 5. Collapse load theorems 6. Slip line analysis 7. Work hardening behaviour A. Non-Cartesian coordinate systems B. Mohr's circles C. Principles of virtual work D. Extremum principles E. Drucker's stability postulate F. The associated flow rule G. A uniqueness theorem for elastic-plastic deformation H. Theorems of limit analysis I. Limit analysis and limiting equilibrium.

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Plasticity and Geomechanics

The formulation of the equations which govern the deformation and flow of granular materials is an outstanding problem in continuum mechanics. This article concentrates on one model for the mechanical behaviour of granular materials, termed the “double-shearing model”, in which deformation is assumed to occur by simultaneous shearing on the two families of characteristic curves of the stress equations. We review the formulation of the equations of the double-shearing model for plane deformations, and describe the known exact solutions of these equations. Further developments of the plane strain theory are then given in which the velocity equations are expressed in a new form from which some general results are derived. In the last part of the article the theory is extended to include problems in three dimensions. The three-dimensional theory is applied to some special cases of nonplanar deformations, and in particular we formulate a new theory of axially symmetric deformations of granular materials, and apply this theory to the solution of some boundary value problems.

Deformation of Ideal Granular Materials

Incorporation of material behavior in modeling of metal forming and machining processes: A review

A Method of Numerical Analysis of Plastic Flow in Plane Strain and Its Application to the Compression of a Ductile Material Between Rough Plates

Expressions are derived for the roll-force P, and torque G, in strip-rolling under tension, as functions of the pressure distribution on the rolls and of the radius of the deformed arc of contact. ...

Rodney Hill

Papers

A Method of Numerical Analysis of Plastic Flow in Plane Strain and Its Application to the Compression of a Ductile Material Between Rough Plates

Relations between Roll-force, Torque, and the Applied Tensions in Strip-rolling*:

A Comparative Study of Some Variational Principles in the Theory of Plasticity

General Features of Plastic-Elastic Problems as Exemplified by Some Particular Solutions