An Improved Method for Numerical Integration of Constitutive Equations of the Work Hardening-Recovery Type

1977 ◽  
Vol 99 (3) ◽  
pp. 275-277 ◽  
Author(s):  
A. K. Miller ◽  
C. F. Shih
Keyword(s):  
Numerical Integration ◽  
Constitutive Equations ◽  
Work Hardening ◽  
Improved Method ◽  
Integration Of Constitutive Equations

Hypo-elasticity and plasticity

1956 ◽  
Vol 234 (1196) ◽  
pp. 46-59 ◽  
Keyword(s):  
General Theory ◽  
Constitutive Equations ◽  
Work Hardening ◽  
Strain Curve ◽  
Simple Extension ◽  
Logarithmic Strain ◽  
Elasticity Equations ◽  
Plastic Materials ◽  
Special Case

A general theory of work-hardening incompressible plastic materials is developed as a special case of Truesdell’s theory of hypo-elasticity. Equations are given in general coordinates for a single loading followed by one unloading, and attention is directed to materials for which the stress-logarithmic strain curve for unloading in simple extension is linear. Using a particular case of the corresponding constitutive equations for loading, which is a generalization of that suggested by Prager, applications are made to a number of specific problems.

Modelling of Cyclic Plasticity With Unified Constitutive Equations: Improvements in Simulating Normal and Anomalous Bauschinger Effects

1980 ◽  
Vol 102 (2) ◽  
pp. 215-222 ◽  
Author(s):  
A. K. Miller
Keyword(s):  
Constitutive Equations ◽  
Work Hardening ◽  
Hysteresis Loops ◽  
Experimental Tests ◽  
Cyclic Hardening ◽  
Back Stress ◽  
Cyclic Softening ◽  
Cyclic Plasticity ◽  
Dislocation Loops ◽  
Work Hardening Coefficient

In simulating cyclic plasticity with several existing “unified” constitutive equations, the predicted hysteresis loops are “oversquare” with respect to experimentally-observed behavior. To eliminate this shortcoming in the constitutive equations developed by the present author, the work-hardening coefficient in the equation controlling the back stress (R) has been made a function of the back stress itself and the sign of the effective modulus-compensated stress σ/E – R. This improvement results in simulated hysteresis loops whose curvature closely resembles that in experimental tests. The improvement preserves all of the previously demonstrated capabilities such as cyclic hardening, cyclic hardening, cyclic softening, etc. The same equations can also simulate some unusual experimentally-observed Bauschinger effects involving local reversals in curvature. The curvature reversals in the simulations result from strain softening of the isotropic work-hardening variable in the equations. The physical significance of the behavior of the constitutive equations is discussed in terms of annihilation of previously-generated dislocation loops by reversing dislocations and experimentally-observed decreases in dislocation density and dissolution of cell walls upon stress reversal.

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