Plotting the Stress-Strain Relationship

 

The Draw button, as shown in Figure 1, in the plastic material dialog box opens the Plastic Hardening Rule plot dialog box containing a plot of the stress-strain relationship defined by the current plastic material input data, as shown in Figure 2.

 

Figure 1  The Draw button in the Plastic Material dialog box

 

Figure 2  The Plastic Hardening Rule plot dialog box

 

The Plastic Hardening Rule dialog box contains a plot that corresponds to the axial stress versus the total axial strain that would be experienced by a specimen of material subjected to a tension and then a compression load in a uniaxial test. The load magnitude follows a pattern like the one shown in Figure 2.

 

Stress load

Figure 3  Hypothetical axial load applied to a specimen

 

For the bilinear and nonlinear isotropic hardening (with or without the kinematic hardening), the load  is 2x the initial yield stress. In the case of the nonlinear isotropic hardening, though, it is possible that the  is unreachable. This occurs when , , and . Therefore, in the case that  and , the load  that is used is

 

In the case of the multi-linear isotropic hardening, the load  is chosen so that at time , the yield stress is . Note that if the kinematic hardening is used,  because the kinematic hardening introduces a back stress .

 

The slope of the total axial strain to axial stress curve during the plastic flow is expected to be

 

where  is the sum of the isotropic hardening modulus and the kinematic hardening modulus.

 

Figure 4  The slope of the total strain vs. stress

 

References

Simo, J. C., and Hughes, T. J. R., Computational Inelasticity, Springer, 1998