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tamaas/tests/IsotropicLinearHardeningPlasticity.mfront
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IsotropicLinearHardeningPlasticity.mfront
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@DSL DefaultDSL;
@Behaviour IsotropicLinearHardeningPlasticity;
@Author Thomas Helfer;
@Date 14 / 10 / 2016;
@Description {
An implicit implementation of a simple
isotropic plasticity behaviour with
isotropic linear hardening.
The yield surface is defined by:
"\["
" f(\sigmaeq,p) = \sigmaeq-s_{0}-H\,p"
"\]"
}
@StateVariable StrainStensor eel;
eel.setGlossaryName("ElasticStrain");
@StateVariable strain p;
p.setGlossaryName("EquivalentPlasticStrain");
@Parameter young = 70.e9;
young.setGlossaryName("YoungModulus");
@Parameter nu = 0.34;
nu.setGlossaryName("PoissonRatio");
@Parameter H = 10.e9;
H.setEntryName("HardeningSlope");
@Parameter s0 = 300.e6;
s0.setGlossaryName("YieldStress");
/*!
* computation of the prediction operator: we only provide the elastic
* operator.
*
* We could also provide a tangent operator, but this would mean
* saving an auxiliary state variable stating if a plastic loading
* occured at the previous time step.
*/
@PredictionOperator {
const auto lambda = computeLambda(young, nu);
const auto mu = computeMu(young, nu);
Dt = lambda * Stensor4::IxI() + 2 * mu * Stensor4::Id();
}
/*!
* behaviour integration using a fully implicit Euler-backwark scheme.
*/
@ProvidesSymmetricTangentOperator;
@Integrator {
const auto lambda = computeLambda(young, nu);
const auto mu = computeMu(young, nu);
// elastic loading
eel += deto;
if(computeTangentOperator_){
Dt = lambda * Stensor4::IxI() + 2 * mu * Stensor4::Id();
}
// trial equivalent stress
const auto se = 2 * mu * deviator(eel);
const auto seq_e = sigmaeq(se);
const auto plastic_loading = seq_e - s0 - H * p > stress{0};
// plastic loading
if (plastic_loading) {
const auto iseq_e = 1 / seq_e;
const auto n = eval(3 * se / (2 * seq_e));
const auto cste = 1 / (H + 3 * mu);
dp = (seq_e - s0 - H * p) * cste;
eel -= dp * n;
if ((computeTangentOperator_) && (smt == CONSISTENTTANGENTOPERATOR)) {
Dt -= 4 * mu * mu *
(dp * iseq_e * (Stensor4::M() - (n ^ n)) + cste * (n ^ n));
}
}
// stress update
sig = lambda * trace(eel) * Stensor::Id() + 2 * mu * eel;
}
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