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.

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
yield	The initial yield stress (enter in pressure units). This stress corresponds to the axial stress at yield during uniaxial, 3D loading.
Khard	The dimensionless parameter K for nonlinear hardening.
nhard	The dimensionless exponent parameter (n) in the nonlinear hardening law. If n=1, it is more efficient to use linear hardening instead.
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.