J2 Plasticity Material - OpenSeesWiki

J2 Plasticity Material

From OpenSeesWiki

Jump to: navigation, search




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

σ = K * tracee) + (2 * G) * deve)

Yield Function

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

Saturation Isotropic Hardening with linear term

 q(xi) = \sigma_0 + (\sigma_\inf - \sigma_0)*exp(-delta*\xi) + H*\xi

Flow Rules

 \dot {\epsilon_p} =  \gamma * \frac{\partial \phi}{\partial \sigma}

 \dot \xi  = -\gamma * \frac{\partial \phi}{\partial q}

Linear Viscosity

\gamma = \frac{\phi}{\eta} ( if φ > 0 )

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

set η = 0 for rate independent case



Code Developed by: Ed Love

Personal tools