Constitutive Equations of Elastoplastic Materials With Anisotropic Hardening and Elastic-Plastic Transition

1981 ◽  
Vol 48 (2) ◽  
pp. 297-301 ◽  
Author(s):  
K. Hashiguchi
Keyword(s):  
Yield Surface ◽  
Constitutive Equations ◽  
Kinematic Hardening ◽  
General Rule ◽  
Close Correlation ◽  
Plastic State ◽  
Anisotropic Hardening ◽  
Loading Surface ◽  
Elastic Plastic ◽  
Elastoplastic Materials

Constitutive equations of elastoplastic materials with anisotropic hardening and elastic-plastic transition are presented by introducing three similar surfaces, i.e., a loading surface on which a current stress exists, a subyield surface limiting a size of the loading surface and a distinct-yield surface representing a fully plastic state. The assumption of similarity of these surfaces leads the derived equations to remarkably simple forms. Also a more general rule of the kinematic hardening for the distinct-yield surface is incorporated into the constitutive equations. While they seem to be applicable to various materials, special constitutive equations of metals, for example, are derived from them and are compared with experimental data on a cyclic uniaxial loading of aluminum. A close correlation between theory and experiment is observed in this comparison.

Constitutive Equations of Elastoplastic Materials With Elastic-Plastic Transition

1980 ◽  
Vol 47 (2) ◽  
pp. 266-272 ◽  
Author(s):  
K. Hashiguchi
Keyword(s):  
Yield Surface ◽  
Constitutive Equations ◽  
Granular Media ◽  
Kinematic Hardening ◽  
Careful Consideration ◽  
Elastic Plastic ◽  
Transitional State ◽  
Hardening Behavior ◽  
Softening Behavior ◽  
Elastoplastic Materials

Constitutive equations of elastoplastic materials with an elastic-plastic transition observed in the loading state after a first yield are presented by introducing a new parameter denoting the ratio of the size of a loading surface in the transitional state to that of a yield surface in the classical idealization which ignores the transitional state. These equations involve a reasonably simplified rule for the kinematic hardening. They would describe reasonably not only the hardening behavior but especially the softening behavior which requires our careful consideration about the elastic-plastic transition. From these equations, moreover, we derive plastic constitutive equations specifically of metals and granular media which exhibit very different plastic behaviors. Besides, brief discussions are provided concerning the existing constitutive equations describing the elastic-plastic transition.

A Generalized Anisotropic Hardening Rule Based on the Mroz Multi-Yield-Surface Model

2008 ◽  
Author(s):  
K. S. Choi ◽  
J. Pan
Keyword(s):  
Cyclic Loading ◽  
Yield Surface ◽  
Kinematic Hardening ◽  
Constitutive Relations ◽  
Yield Function ◽  
Surface Model ◽  
Loading Conditions ◽  
Anisotropic Hardening ◽  
Hardening Rule ◽  
Strain Data

In this paper, a generalized anisotropic hardening rule based on the Mroz multi-yield-surface model is derived. The evolution equation for the active yield surface is obtained by considering the continuous expansion of the active yield surface during the unloading/reloading process. The incremental constitutive relation based on the associated flow rule is then derived for a general yield function. As a special case, detailed incremental constitutive relations are derived for the Mises yield function. The closed-form solutions for one-dimensional stress-plastic strain curves are also derived and plotted for the Mises materials under cyclic loading conditions. The stress-plastic strain curves show closed hysteresis loops under uniaxial cyclic loading conditions and the Masing hypothesis is applicable. A user material subroutine based on the Mises yield function, the anisotropic hardening rule and the constitutive relations was then written and implemented into ABAQUS. Computations were conducted for a simple plane strain finite element model under uniaxial monotonic and cyclic loading conditions based on the anisotropic hardening rule and the isotropic and nonlinear kinematic hardening rules of ABAQUS. The results indicate that the plastic response of the material follows the intended input stress-strain data for the anisotropic hardening rule whereas the plastic response depends upon the input strain ranges of the stress-strain data for the nonlinear kinematic hardening rule.

The Elastic-Plastic Analysis of Tubes—I: General Theory

1992 ◽  
Vol 114 (2) ◽  
pp. 213-221 ◽  
Author(s):  
W. Jiang
Keyword(s):  
General Theory ◽  
Constitutive Equations ◽  
Kinematic Hardening ◽  
Elastic Plastic ◽  
Hardening Rule ◽  
Plastic Analysis ◽  
Made In

A study is made in this paper of the elastic-plastic analysis of tubes subjected to various loads and temperatures. The kinematic hardening rule is used in the analysis and constitutive equations are developed for the tube problems. By piecing several elastic and plastic solutions together, various tube problems can be solved in closed forms.

Elasto-plastic state of curve beam system subjected to complex loading

1996 ◽  
Vol 18 (4) ◽  
pp. 14-22
Author(s):  
Vu Khac Bay
Keyword(s):  
Cylindrical Shell ◽  
Solution Method ◽  
Complex Loading ◽  
Numerical Results ◽  
Elastic Solution ◽  
Plastic State ◽  
Curve Beam ◽  
Elastic State ◽  
Elastic Plastic ◽  
Beam System

Investigation of the elastic state of curve beam system had been considered in [3]. In this paper the elastic-plastic state of curve beam system in the form of cylindrical shell is analyzed by the elastic solution method. Numerical results of the problem and conclusion are given.

Study of the elastic-plastic state of cyclically loaded shells of revolution

1976 ◽  
Vol 8 (4) ◽  
pp. 483-486
Author(s):  
I. S. Chernyshenko ◽  
G. K. Sharshukov
Keyword(s):  
Plastic State ◽  
Shells Of Revolution ◽  
Elastic Plastic

scholarly journals Thermo elastic-plastic transition in a thin rotating disc with inclusion

2007 ◽  
Vol 11 (1) ◽  
pp. 103-118 ◽  
Author(s):  
Kumar Gupta ◽  
P Pankaj
Keyword(s):  
Thermal Effect ◽  
Internal Surface ◽  
Angular Speed ◽  
Incompressible Material ◽  
Plastic State ◽  
Percentage Increase ◽  
Compressible Material ◽  
Rotating Disc ◽  
Elastic Plastic ◽  
Different Temperatures

Stresses for the elastic-plastic transition and fully plastic state have been derived for a thin rotating disc with shaft at different temperatures and results have been discussed and depicted graphically. It has been observed that the rotating disc with inclusion and made of compressible material requires lesser angular speed to yield at the internal surface and higher percentage increase in angular speed to become fully plastic as compare to disc made of incompressible material. With the introduction of thermal effect the rotating disc with inclusion required lesser angular speed to yield at the internal surface. Rotating disc made of compressible material with inclusion requires higher percentage increase in angular speed to become fully-plastic as compare to disc made of incompressible material. Thermal effect also increases the values of radial and circumferential stresses at the internal surface for fully-plastic state. .

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