J2 Plasticity Material: Difference between revisions

Latest revision as of 19:57, 16 March 2016

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 [[1]]

J2 isotropic hardening material class

Elastic Model

<math> \sigma = K*trace(\epsilon_e) + (2*G)*dev(\epsilon_e)</math>

Yield Function

<math> \phi(\sigma,q) = || dev(\sigma) || - \sqrt(\tfrac{2}{3}*q(xi)</math>

Saturation Isotropic Hardening with linear term

<math> q(xi) = \sigma_0 + (\sigma_\inf - \sigma_0)*exp(-delta*\xi) + H*\xi </math>

Flow Rules

<math> \dot {\epsilon_p} = \gamma * \frac{\partial \phi}{\partial \sigma} </math>

<math> \dot \xi = -\gamma * \frac{\partial \phi}{\partial q} </math>

Linear Viscosity

<math>\gamma = \frac{\phi}{\eta} </math> ( if <math> \phi > 0</math> )

Backward Euler Integration Routine Yield condition enforced at time n+1

set <math> \eta = 0 </math> for rate independent case

Code Developed by: Ed Love

@@ Line 1: / Line 1: @@
+{{CommandManualMenu}}
 This command is used to construct an multi dimensional material object that has a von Mises (J2) yield criterium and isotropic hardening.
 {|
-| style="background:yellow; color:black; width:800px" | '''nDmaterial J2Plasticity $matTag $K $G $sig0 $sigInf $delta $H'''
+| style="background:yellow; color:black; width:800px" | '''nDMaterial J2Plasticity $matTag $K $G $sig0 $sigInf $delta $H'''
 |}
 ----
@@ Line 10: / Line 13: @@
 |  style="width:150px" | '''$matTag ''' || integer tag identifying material
 |-
-|  '''$E ''' || elastic Modulus
+|  '''$K ''' || bulk modulus
 |-
-|  '''$G ''' || shear Modulus
+|  '''$G ''' || shear modulus
 |-
 |  '''$sig0''' || initial yield stress