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

Back to top