Elements of plasticity theory

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Plane Strain ◽  
Classical Theory ◽  
Slip Line ◽  
Plasticity Theory ◽  
Eshelby Tensor ◽  
Modern Theory ◽  
Material Symmetry ◽  
Plastic Deformations ◽  
Line Theory

Chapter 13 develops the modern theory for finite elastic-plastic deformations. It covers dissipation and highlights the role of the Eshelby tensor, and recovers the classical theory for isotropic materials using material symmetry arguments. Also developed are the equations of classical slip-line theory for plane-strain deformations.

Prediction of the Geometry Changes of the Free Boundary During Upsetting by the Slip-Line Theory

1971 ◽  
Vol 93 (2) ◽  
pp. 586-592 ◽  
Author(s):  
A. H. Shabaik
Keyword(s):  
Shear Stress ◽  
Free Boundary ◽  
Plane Strain ◽  
Slip Line ◽  
Normal Pressure ◽  
Friction Condition ◽  
Grid Pattern ◽  
Distorted Grid ◽  
Line Theory ◽  
Good Agreement

Local values of shear stress at the tool-workpiece interface in plane-strain upsetting were determined from experimental observation of the distorted grid pattern. The friction condition at the interface was formulated and used to develop the slip-line net. This slip-line net was used to predict the geometry changes of the free boundary. Results of this method showed good agreement when compared with those obtained experimentally. Using Hencky’s equations, the normal pressure was determined at the interface. From the normal pressure values, the load was calculated and compared to that measured during experiment.

Slip Line Field Analysis of a Simple Plane Strain Closed-Die Forging

1989 ◽  
Vol 203 (2) ◽  
pp. 91-99
Author(s):  
M V Srinivas ◽  
P Alva ◽  
S K Biswas
Keyword(s):  
Velocity Field ◽  
Plane Strain ◽  
Slip Line ◽  
Field Analysis ◽  
Line Field ◽  
Slip Line Field ◽  
Die Forging ◽  
Closed Die Forging ◽  
Cavity Filling ◽  
Single Cavity

A slip line field is proposed for symmetrical single-cavity closed-die forging by rough dies. A compatible velocity field is shown to exist. Experiments were conducted using lead workpiece and rough dies. Experimentally observed flow and load were used to validate the proposed slip line field. The slip line field was used to simulate the process in the computer with the objective of studying the influence of flash geometry on cavity filling.

scholarly journals Plane-Strain Slip-Line Fields for Metal-Deformation Processes

1983 ◽  
Vol 50 (3) ◽  
pp. 702-702 ◽  
Author(s):  
W. Johnson ◽  
R. Sowerby ◽  
R. D. Venter ◽  
S. Kobayashi
Keyword(s):  
Plane Strain ◽  
Slip Line ◽  
Metal Deformation ◽  
Deformation Processes

Non-equilibrium dynamics and stochastic processes

2020 ◽  
pp. 40-52
Author(s):  
Karen C. Abbott
Keyword(s):  
Stochastic Processes ◽  
Density Dependence ◽  
Classical Theory ◽  
Ecological Theory ◽  
Ecological Processes ◽  
Transient Phenomena ◽  
Equilibrium Dynamics ◽  
Theoretical Approaches ◽  
Ecological Understanding

Most standard theoretical approaches emphasize the role of deterministic density dependence in creating and maintaining equilibrium dynamics. At the same time, it is widely recognized that ecological processes are inherently stochastic, and that disturbances and variation in the environment and in the fates of individuals prevent many ecological systems from resting at their theoretical equilibrium. A developing body of stochastic ecological theory aims to bridge the gap between the deterministic tools of classical theory and the stochastic, non-equilibrial questions that real systems present to us. This chapter provides an overview of this developing theory, with an emphasis on approaches that confront the complex interplay between deterministic density dependence, and perturbations. Although intuition may suggest that stochasticity and transient phenomena should obscure ecological understanding, they can actually strengthen it when viewed through the appropriate lens, as illustrated in this chapter.

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