J2 Plasticity Material

• Command_Manual
  • Tcl Commands
  • Modeling_Commands
    • model
    • uniaxialMaterial
    • ndMaterial
    • frictionModel
    • section
    • geometricTransf
    • element
    • node
    • sp commands
      • fix
      • fixX
      • fixY
      • fixZ
    • mp commands
      • equalDOF
      • rigidDiaphragm
      • rigidLink
    • timeSeries
    • pattern
    • mass
    • block commands
      • block2D
      • block3D
    • region
    • rayleigh
  • Analysis Commands
    • constraints Command
    • numberer Command
    • system Command
    • test Command
    • algorithm Command
    • integrator Command
    • analysis Command
    • eigen Command
    • analyze Command
  • Output Commands
    • recorder
    • record
    • print
    • printA
    • logFile
    • RealTime_Output_Commands
  • Misc Commands
    • eleResponse Command
    • getTime Command
    • getEleTags Command
    • getNodeTags
    • loadConst Command
    • nodeCoord Command
    • nodeDisp Command
    • nodeVel Command
    • nodeAccel Command
    • nodeEigenvector Command
    • nodeBounds
    • print Command
    • remove Command
    • reset Command
    • testIter
    • testNorms
    • wipe Command
    • exit Command
  • DataBase Commands
    • Template:DataBaseCommandsMenu

---

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