scholarly journals Discussion: “Stress-Strain Laws of the Mathematical Theory of Plasticity—A Survey of Recent Progress” (Prager, W., 1948, ASME J. Appl. Mech., 15, pp. 226–233)

1949 ◽  
Vol 16 (2) ◽  
pp. 215-216
Author(s):  
R. Hill
Keyword(s):  
Mathematical Theory ◽  
Recent Progress ◽  
Stress Strain ◽  
Theory Of Plasticity

The Stress-Strain Laws of the Mathematical Theory of Plasticity—a Survey of Recent Progress

1948 ◽  
Vol 15 (3) ◽  
pp. 226-233
Author(s):  
William Prager
Keyword(s):  
Test Data ◽  
Mathematical Theory ◽  
Recent Progress ◽  
Variational Principles ◽  
Stress Strain ◽  
Theory Of Plasticity

Abstract Typical stress-strain laws of flow and deformation types are discussed with particular reference to the conditions of continuity and uniqueness which these laws must fulfill if they are to make sense physically. Alternative forms of some of these laws are presented, and conditions are discussed under which different laws yield identical results. It is shown how these laws may be generalized so as to fit test data more readily. Methods of integration are indicated and the use of variational principles is stressed.

Plasticity and Viscoplasticity

1989 ◽  
Author(s):  
Shiro Kobayashi ◽  
Soo-Ik Oh ◽  
Taylan Altan
Keyword(s):  
Uniaxial Tension ◽  
Metal Forming ◽  
Experimental Studies ◽  
Plasticity Theory ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Stress Strain ◽  
Cross Sectional ◽  
Theory Of Plasticity ◽  
Classical Plasticity

The theory of plasticity describes the mechanics of deformation in plastically deforming solids, and, as applied to metals and alloys, it is based on experimental studies of the relations between stresses and strains under simple loading conditions. The theory described here assumes the ideal plastic body for which the Bauschinger effect and size effects are neglected. The theory also is valid only at temperatures for which recovery, creep, and thermal phenomena can be neglected. The basic theory of classical plasticity is described by Hill, and also in References, in addition to the books listed in Chap. 1. A concise description of the general plasticity theory necessary for metal forming is given in the book by Johnson et al.. In this chapter, certain important aspects of the theory are presented in order to elucidate the developments of the finite-element solutions of metal-forming problems discussed in this book. First, various measures of stress and strain are introduced. Then, the governing equations for plastic deformation and principles that are the foundations for the analysis are described. The extension of the theory of plasticity to time-dependent theory of viscoplasticity is outlined in Section 4.8. Particular references are made, in Sections 4.3 through 4.7, to the books by Hill and by Johnson and Mellor, and to the section on general plasticity theory in the book by Johnson et al.. The basic quantities that may be used to describe the mechanics of deformation when a body deforms from one configuration to another under an external load are the stress, strain, and strain-rate. Various measures of these quantities are defined, depending upon how closely formulations represent actual situations. Although it is not possible to provide the complete mathematical formulations in one-dimensional deformation, these measures are introduced for the case of simple uniaxial tension. Consider the uniaxial tension test of a round specimen whose initial length is l0 and cross-sectional area is A0. The specimen is stretched in the axial direction by the force P to the length l and the cross-sectional area A at time t, as shown in Fig. 4.1. The response of the material is recorded as the load-displacement curve, and converted to the stress-strain curve as shown in the figure. The deformation is assumed to be homogeneous until necking begins.

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