Linear Hardening

In the linear hardening law, the yield stress is given by

[math]\displaystyle{ \sigma_y = \sigma_{Y0} + E_p\alpha = \sigma_{Y0}(1+K\alpha) }[/math]

where [math]\displaystyle{ \sigma_{Y0} }[/math] is initial yield stress, E_p is the plastic modulus, α is cumulative equivalent plastic strain, and K is a hardening coefficient.

Hardening Law Properties

The material parameters in this hardening law are defined with the following properties:

Property	Description
yield	The initial yield stress (enter in units of MPa). This stress corresponds to the axial stress at yield during uniaxial, 3D loading.
Ep	The plastic modulus (enter in units of MPa). This modulus is the slope of total stress as a function of plastic strain during uniaxial, 3D loading. The default is 0.0 which results in an elastic-perfectly plastic material or a material with no work hardening.
Khard	Alternatively, you can enter this dimensionless parameter for hardening. It is only used if Ep is not entered and when entered, it is convert to Ep using Ep = [math]\displaystyle{ \sigma_{Y0}K }[/math].

History Data

This hardening law defines one history variable, which is stored as history variable #1. It stores the the cumulative equivalent plastic strain (absolute) defined as

[math]\displaystyle{ \alpha = \sum \sqrt{2\over3}\ ||d\varepsilon_p|| }[/math]

where ε_p is the incremental plastic strain tensor in one time step.