void AbaqusUserMaterial :: giveFirstPKStressVector_3d(FloatArray &answer, GaussPoint *gp,
const FloatArray &vF, TimeStep *tStep)
{
AbaqusUserMaterialStatus *ms = static_cast< AbaqusUserMaterialStatus * >( this->giveStatus(gp) );
/* User-defined material name, left justified. Some internal material models are given names starting with
* the “ABQ_” character string. To avoid conflict, you should not use “ABQ_” as the leading string for
* CMNAME. */
//char cmname[80];
// Sizes of the tensors.
int ndi = 3;
int nshr = 3;
int ntens = ndi + nshr;
FloatArray stress(9); // PK1
FloatArray strainIncrement;
// compute Green-Lagrange strain
FloatArray strain;
FloatArray vS;
FloatMatrix F, E;
F.beMatrixForm(vF);
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);
strain.beSymVectorFormOfStrain(E);
strainIncrement.beDifferenceOf(strain, ms->giveStrainVector());
FloatArray state = ms->giveStateVector();
FloatMatrix jacobian(9, 9); // dPdF
int numProperties = this->properties.giveSize();
// Temperature and increment
double temp = 0.0, dtemp = 0.0;
// Times and increment
double dtime = tStep->giveTimeIncrement();
///@todo Check this. I'm just guessing. Maybe intrinsic time instead?
double time [ 2 ] = {
tStep->giveTargetTime() - dtime, tStep->giveTargetTime()
};
double pnewdt = 1.0; ///@todo Right default value? umat routines may change this (although we ignore it)
/* Specific elastic strain energy, plastic dissipation, and “creep” dissipation, respectively. These are passed
* in as the values at the start of the increment and should be updated to the corresponding specific energy
* values at the end of the increment. They have no effect on the solution, except that they are used for
* energy output. */
double sse, spd, scd;
// Outputs only in a fully coupled thermal-stress analysis:
double rpl = 0.0; // Volumetric heat generation per unit time at the end of the increment caused by mechanical working of the material.
FloatArray ddsddt(ntens); // Variation of the stress increments with respect to the temperature.
FloatArray drplde(ntens); // Variation of RPL with respect to the strain increments.
double drpldt = 0.0; // Variation of RPL with respect to the temperature.
/* An array containing the coordinates of this point. These are the current coordinates if geometric
* nonlinearity is accounted for during the step (see “Procedures: overview,” Section 6.1.1); otherwise,
* the array contains the original coordinates of the point */
FloatArray coords;
gp->giveElement()->computeGlobalCoordinates( coords, gp->giveNaturalCoordinates() ); ///@todo Large deformations?
/* Rotation increment matrix. This matrix represents the increment of rigid body rotation of the basis
* system in which the components of stress (STRESS) and strain (STRAN) are stored. It is provided so
* that vector- or tensor-valued state variables can be rotated appropriately in this subroutine: stress and
* strain components are already rotated by this amount before UMAT is called. This matrix is passed in
* as a unit matrix for small-displacement analysis and for large-displacement analysis if the basis system
* for the material point rotates with the material (as in a shell element or when a local orientation is used).*/
FloatMatrix drot(3, 3);
drot.beUnitMatrix();
/* Characteristic element length, which is a typical length of a line across an element for a first-order
* element; it is half of the same typical length for a second-order element. For beams and trusses it is a
* characteristic length along the element axis. For membranes and shells it is a characteristic length in
* the reference surface. For axisymmetric elements it is a characteristic length in the
* plane only.
* For cohesive elements it is equal to the constitutive thickness.*/
double celent = 0.0; /// @todo Include the characteristic element length
/* Array containing the deformation gradient at the beginning of the increment. See the discussion
* regarding the availability of the deformation gradient for various element types. */
FloatMatrix dfgrd0(3, 3);
/* Array containing the deformation gradient at the end of the increment. The components of this array
* are set to zero if nonlinear geometric effects are not included in the step definition associated with
* this increment. See the discussion regarding the availability of the deformation gradient for various
* element types. */
FloatMatrix dfgrd1(3, 3);
dfgrd0.beMatrixForm( ms->giveFVector() );
dfgrd1.beMatrixForm(vF);
int noel = gp->giveElement()->giveNumber(); // Element number.
int npt = 0; // Integration point number.
// We intentionally ignore the layer number since that is handled by the layered cross-section in OOFEM.
int layer = 0; // Layer number (for composite shells and layered solids)..
int kspt = 0; // Section point number within the current layer.
int kstep = tStep->giveMetaStepNumber(); // Step number.
int kinc = 0; // Increment number.
///@todo No idea about these parameters
double predef;
double dpred;
// Change to Abaqus's component order
stress.changeComponentOrder();
strain.changeComponentOrder();
strainIncrement.changeComponentOrder();
OOFEM_LOG_DEBUG("AbaqusUserMaterial :: giveRealStressVector - Calling subroutine");
this->umat(stress.givePointer(), // STRESS
state.givePointer(), // STATEV
jacobian.givePointer(), // DDSDDE
& sse, // SSE
& spd, // SPD
& scd, // SCD
& rpl, // RPL
ddsddt.givePointer(), // DDSDDT
drplde.givePointer(), // DRPLDE
& drpldt, // DRPLDT
strain.givePointer(), // STRAN
strainIncrement.givePointer(), // DSTRAN
time, // TIME
& dtime, // DTIME
& temp, // TEMP
& dtemp, // DTEMP
& predef, // PREDEF
& dpred, // DPRED
this->cmname, // CMNAME
& ndi, // NDI
& nshr, // NSHR
& ntens, // NTENS
& numState, // NSTATV
properties.givePointer(), // PROPS
& numProperties, // NPROPS
coords.givePointer(), // COORDS
drot.givePointer(), // DROT
& pnewdt, // PNEWDT
& celent, // CELENT
dfgrd0.givePointer(), // DFGRD0
dfgrd1.givePointer(), // DFGRD1
& noel, // NOEL
& npt, // NPT
& layer, // LAYER
& kspt, // KSPT
& kstep, // KSTEP
& kinc); // KINC
// Change to OOFEM's component order
stress.changeComponentOrder();
strain.changeComponentOrder();
strainIncrement.changeComponentOrder();
jacobian.changeComponentOrder();
if ( mStressInterpretation == 0 ) {
FloatMatrix P, cauchyStress;
P.beMatrixForm(stress);
FloatArray vP;
vP.beVectorForm(P);
cauchyStress.beProductTOf(P, F);
cauchyStress.times( 1.0 / F.giveDeterminant() );
FloatArray vCauchyStress;
vCauchyStress.beSymVectorForm(cauchyStress);
ms->letTempStrainVectorBe(strain);
ms->letTempStressVectorBe(vCauchyStress);
ms->letTempStateVectorBe(state);
ms->letTempTangentBe(jacobian);
ms->letTempPVectorBe(vP);
ms->letTempFVectorBe(vF);
answer = vP;
} else {
FloatArray vP;
FloatMatrix P, sigma, F_inv;
F_inv.beInverseOf(F);
sigma.beMatrixForm(stress);
P.beProductOf(F, sigma);
vP.beVectorForm(P);
answer = vP;
// Convert from sigma to S
FloatMatrix S;
S.beProductOf(F_inv, P);
vS.beSymVectorForm(S);
// @todo Should convert from dsigmadE to dSdE here
// L2=detF*matmul( matmul ( inv(op_a_V9(F,F), cm-op_a_V9(ident,Tau)-op_b_V9(Tau,ident) ), inv(op_a_V9(Ft,Ft)))
ms->letTempStrainVectorBe(strain);
ms->letTempStressVectorBe(vS);
ms->letTempStateVectorBe(state);
ms->letTempTangentBe(jacobian);
ms->letTempPVectorBe(vP);
ms->letTempFVectorBe(vF);
}
OOFEM_LOG_DEBUG("AbaqusUserMaterial :: giveRealStressVector_3d - Calling subroutine was successful");
}
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);
}
