void MisesMat :: giveFirstPKStressVector_3d(FloatArray &answer, GaussPoint *gp, const FloatArray &totalDefGradOOFEM, TimeStep *tStep) { MisesMatStatus *status = static_cast< MisesMatStatus * >( this->giveStatus(gp) ); double kappa, dKappa, yieldValue, mi; FloatMatrix F, oldF, invOldF; FloatArray s; F.beMatrixForm(totalDefGradOOFEM); //(method assumes full 3D) kappa = status->giveCumulativePlasticStrain(); oldF.beMatrixForm( status->giveFVector() ); invOldF.beInverseOf(oldF); //relative deformation radient FloatMatrix f; f.beProductOf(F, invOldF); //compute elastic predictor FloatMatrix trialLeftCauchyGreen, help; f.times( 1./cbrt(f.giveDeterminant()) ); help.beProductOf(f, status->giveTempLeftCauchyGreen()); trialLeftCauchyGreen.beProductTOf(help, f); FloatMatrix E; E.beTProductOf(F, F); E.at(1, 1) -= 1.0; E.at(2, 2) -= 1.0; E.at(3, 3) -= 1.0; E.times(0.5); FloatArray e; e.beSymVectorFormOfStrain(E); FloatArray leftCauchyGreen; FloatArray leftCauchyGreenDev; double leftCauchyGreenVol; leftCauchyGreen.beSymVectorFormOfStrain(trialLeftCauchyGreen); leftCauchyGreenVol = computeDeviatoricVolumetricSplit(leftCauchyGreenDev, leftCauchyGreen); FloatArray trialStressDev; applyDeviatoricElasticStiffness(trialStressDev, leftCauchyGreenDev, G / 2.); s = trialStressDev; //check for plastic loading double trialS = computeStressNorm(trialStressDev); double sigmaY = sig0 + H * kappa; //yieldValue = sqrt(3./2.)*trialS-sigmaY; yieldValue = trialS - sqrt(2. / 3.) * sigmaY; //store deviatoric trial stress(reused by algorithmic stiffness) status->letTrialStressDevBe(trialStressDev); //the return-mapping algorithm double J = F.giveDeterminant(); mi = leftCauchyGreenVol * G; if ( yieldValue > 0 ) { //dKappa =sqrt(3./2.)* yieldValue/(H + 3.*mi); //kappa = kappa + dKappa; //trialStressDev.times(1-sqrt(6.)*mi*dKappa/trialS); dKappa = ( yieldValue / ( 2 * mi ) ) / ( 1 + H / ( 3 * mi ) ); FloatArray n = trialStressDev; n.times(2 * mi * dKappa / trialS); ////return map s.beDifferenceOf(trialStressDev, n); kappa += sqrt(2. / 3.) * dKappa; //update of intermediate configuration trialLeftCauchyGreen.beMatrixForm(s); trialLeftCauchyGreen.times(1.0 / G); trialLeftCauchyGreen.at(1, 1) += leftCauchyGreenVol; trialLeftCauchyGreen.at(2, 2) += leftCauchyGreenVol; trialLeftCauchyGreen.at(2, 2) += leftCauchyGreenVol; trialLeftCauchyGreen.times(J * J); } //addition of the elastic mean stress FloatMatrix kirchhoffStress; kirchhoffStress.beMatrixForm(s); kirchhoffStress.at(1, 1) += 1. / 2. * K * ( J * J - 1 ); kirchhoffStress.at(2, 2) += 1. / 2. * K * ( J * J - 1 ); kirchhoffStress.at(3, 3) += 1. / 2. * K * ( J * J - 1 ); FloatMatrix iF, Ep(3, 3), S; FloatArray vF, vS, ep; //transform Kirchhoff stress into Second Piola - Kirchhoff stress iF.beInverseOf(F); help.beProductOf(iF, kirchhoffStress); S.beProductTOf(help, iF); this->computeGLPlasticStrain(F, Ep, trialLeftCauchyGreen, J); ep.beSymVectorFormOfStrain(Ep); vS.beSymVectorForm(S); vF.beVectorForm(F); answer.beVectorForm(kirchhoffStress); status->setTrialStressVol(mi); status->letTempLeftCauchyGreenBe(trialLeftCauchyGreen); status->setTempCumulativePlasticStrain(kappa); status->letTempStressVectorBe(answer); status->letTempStrainVectorBe(e); status->letTempPlasticStrainBe(ep); status->letTempPVectorBe(answer); status->letTempFVectorBe(vF); }