Nonlinear Hardening 1

In this nonlinear hardening law, the yield stress is given by

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

where [math]\displaystyle{ \sigma_{Y0} }[/math] is initial yield stress, α is cumulative equivalent plastic strain, and K and n are dimensionless hardening law coefficients. If K < 0, the law is softening instead of hardening. The amount of softening can be limited by the yieldMin property.

An alternate nonlinear hardening law is also available.

Hardening Law Properties

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

Property	Description	Units	Default
yield	The initial yield stress. This stress corresponds to the axial stress at yield during uniaxial, 3D loading.	pressure units	Large
Khard	The hardening parameter K for nonlinear hardening.	dimensionless	0
nhard	The hardening exponent parameter (n) in the nonlinear hardening law. If n=1, it is more efficient to use linear hardening instead.	dimensionless	1
yieldMin	The minimum yield stress. This minimum only matters when using negative Khard or when modeling softening plasticity	pressure units	0

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 dε_p is the incremental plastic strain tensor in one time step.