J2 Plasticity Material
This command is used to construct an multi dimensional material object that has a von Mises (J2) yield criterium and isotropic hardening.
nDMaterial J2Plasticity $matTag $K $G $sig0 $sigInf
$delta $H
matTag
|
integer tag identifying material |
K
|
bulk modulus |
G
|
shear modulus |
sig0
|
initial yield stress |
sigInf
|
final saturation yield stress |
delta
|
exponential hardening parameter |
H
|
linear hardening parameter |
The material formulations for the J2 object are “ThreeDimensional,” “PlaneStrain,” “Plane Stress,” “AxiSymmetric,” and “PlateFiber.”
Theory
The theory for the non hardening case can be found http://en.wikipedia.org/wiki/Von_Mises_yield_criterion
J2 isotropic hardening material class
Elastic Model
<math> = K*trace(_e) + (2G)dev(_e)</math>
Yield Function
<math> (,q) = || dev() || - (*q(xi)</math>
Saturation Isotropic Hardening with linear term
<math> q(xi) = 0 + (- _0)exp(-delta) + H*</math>
Flow Rules
<math> = </math>
<math> = - </math>
Linear Viscosity
<math>= </math> ( if <math> > 0</math> )
Backward Euler Integration Routine Yield condition enforced at time n+1
set $= 0 $ for rate independent case
Code Developed by: Ed Love