Beispiel #1
0
// decompose current F to get rotation
// apply initial rotation to account for aniostropy
Matrix3 MPMBase::GetRtot(void)
{
    // get deformation gradient
    Matrix3 pF = GetDeformationGradientMatrix();

    // Decompose for R
    Matrix3 R;
    Matrix3 U = pF.RightDecompose(&R,NULL);

    // apply initial rotation total rotation from initial material axes
    Matrix3 R0 = GetInitialRotation();
    Matrix3 Rtot = R*R0;

    // return it
    return Rtot;
}
Beispiel #2
0
// Apply Constitutive law, check np to know what type
void TaitLiquid::MPMConstitutiveLaw(MPMBase *mptr,Matrix3 du,double delTime,int np,void *properties,ResidualStrains *res) const
{
#ifdef NO_SHEAR_MODEL
    // get incremental deformation gradient
	const Matrix3 dF = du.Exponential(incrementalDefGradTerms);
    
    // decompose dF into dR and dU
    Matrix3 dR;
    Matrix3 dU = dF.RightDecompose(&dR,NULL);
	
	// current deformation gradient
    double detdF = dF.determinant();
	Matrix3 pF = mptr->GetDeformationGradientMatrix();
    Matrix3 F = dR*pF;
    if(np==THREED_MPM)
        F.Scale(pow(detdF,1./3.));
    else
        F.Scale2D(sqrt(detdF));
	
	// new deformation matrix with volume change onle
    mptr->SetDeformationGradientMatrix(F);
#else

	// Update total deformation gradient, and calculate trial B
	double detdF = IncrementDeformation(mptr,du,NULL,np);
#endif
    
    // Get new J and save result on the particle
	double J = detdF * mptr->GetHistoryDble(J_history);
    mptr->SetHistoryDble(J_history,J);
    
    // account for residual stresses
	double dresStretch,resStretch = GetResidualStretch(mptr,dresStretch,res);
	double Jres = resStretch*resStretch*resStretch;
    double Jeff = J/Jres;

    // new Kirchhoff pressure (over rho0) from Tait equation
	double p0=mptr->GetPressure();
    double pressure = J*TAIT_C*Ksp*(exp((1.-Jeff)/TAIT_C)-1.);
    mptr->SetPressure(pressure);
    
	// incremental energy per unit mass - dilational part
    double avgP = 0.5*(p0+pressure);
    double delV = 1. - 1./detdF;
    double workEnergy = -avgP*delV;
    
	// incremental residual energy per unit mass
	double delVres = 1. - 1./(dresStretch*dresStretch*dresStretch);
	double resEnergy = -avgP*delVres;
	
    // viscosity term = 2 eta (0.5(grad v) + 0.5*(grad V)^T - (1/3) tr(grad v) I)
    // (i.e., divatoric part of the symmetric strain tensor, 2 is for conversion to engineering shear strain)
    Matrix3 shear;
    double c[3][3];
    c[0][0] = (2.*du(0,0)-du(1,1)-du(2,2))/3.;
    c[1][1] = (2.*du(1,1)-du(0,0)-du(2,2))/3.;
    c[2][2] = (2.*du(2,2)-du(0,0)-du(1,1))/3.;
    c[0][1] = 0.5*(du(0,1)+du(1,0));
    c[1][0] = c[0][1];
    if(np==THREED_MPM)
    {   c[0][2] = 0.5*(du(0,2)+du(2,0));
        c[2][0] = c[0][2];
        c[1][2] = 0.5*(du(1,2)+du(2,1));
        c[2][1] = c[1][2];
        shear.set(c);
    }
    else
        shear.set(c[0][0],c[0][1],c[1][0],c[1][1],c[2][2]);
    
    // Get Kirchoff shear stress (over rho0)
    shear.Scale(J*TwoEtasp/delTime);
    
    // update deviatoric stress
	Tensor *sp=mptr->GetStressTensor();
    sp->xx = shear(0,0);
    sp->yy = shear(1,1);
    sp->zz = shear(2,2);
    sp->xy = shear(0,1);
    if(np==THREED_MPM)
    {   sp->xz = shear(0,2);
        sp->yz = shear(1,2);
    }
    
    // shear work per unit mass = tau.du = tau.tau*delTime/TwoEtasp
    double shearWork = sp->xx*sp->xx + sp->yy*sp->yy + sp->zz*sp->zz + 2.*sp->xy*sp->xy;
    if(np==THREED_MPM) shearWork += 2.*(sp->xz*sp->xz + sp->yz*sp->yz);
    shearWork *= delTime/TwoEtasp;
    mptr->AddWorkEnergyAndResidualEnergy(workEnergy+shearWork,resEnergy);
    
    // particle isentropic temperature increment dT/T = - J (K/K0) gamma0 Delta(V)/V
    // Delta(V)/V = 1. - 1/detdF (total volume)
	double Kratio = Jeff*(1.+pressure/(TAIT_C*Ksp));
	double dTq0 = -J*Kratio*gamma0*mptr->pPreviousTemperature*delV;
    
    // heat energy is Cv (dT - dTq0) -dPhi
	// Here do Cv (dT - dTq0)
    // dPhi = shearWork is lost due to shear term
    IncrementHeatEnergy(mptr,res->dT,dTq0,shearWork);
}
Beispiel #3
0
// Apply Constitutive law, check np to know what type
void TaitLiquid::MPMConstitutiveLaw(MPMBase *mptr,Matrix3 du,double delTime,int np,void *properties,
									ResidualStrains *res,int historyOffset) const
{
#ifdef NO_SHEAR_MODEL
    // get incremental deformation gradient
	const Matrix3 dF = du.Exponential(incrementalDefGradTerms);
    
    // decompose dF into dR and dU
    Matrix3 dR;
    Matrix3 dU = dF.RightDecompose(&dR,NULL);
	
	// current deformation gradient
    double detdF = dF.determinant();
	Matrix3 pF = mptr->GetDeformationGradientMatrix();
    Matrix3 F = dR*pF;
    if(np==THREED_MPM)
        F.Scale(pow(detdF,1./3.));
    else
        F.Scale2D(sqrt(detdF));
	
	// new deformation matrix with volume change onle
    mptr->SetDeformationGradientMatrix(F);

#else
#ifdef ELASTIC_B_MODEL
    // get incremental deformation gradient
	const Matrix3 dF = du.Exponential(incrementalDefGradTerms);
	double detdF = dF.determinant();
	
	// current deformation gradient
	Matrix3 pF = mptr->GetDeformationGradientMatrix();
	
	// new deformation matrix
	const Matrix3 F = dF*pF;
    mptr->SetDeformationGradientMatrix(F);
#else

	// Update total deformation gradient, and calculate trial B
	double detdF = IncrementDeformation(mptr,du,NULL,np);
#endif
#endif
    
    // Get new J and save result on the particle
	double J = detdF * mptr->GetHistoryDble(J_History,historyOffset);
    mptr->SetHistoryDble(J_History,J,historyOffset);

#ifdef ELASTIC_B_MODEL
	// store pressure strain as elastic B
    Tensor *pB = mptr->GetAltStrainTensor() ;
    if(np==THREED_MPM || np==AXISYMMETRIC_MPM)
	{	double J23 = pow(J,2./3.);
		pB->xx = J23;
		pB->yy = J23;
		pB->zz = J23;
	}
	else
	{	pB->xx = J;
		pB->yy = J;
	}
#endif
    
    // account for residual stresses
	double dJres = GetIncrementalResJ(mptr,res);
	double Jres = dJres * mptr->GetHistoryDble(J_History+1,historyOffset);
	mptr->SetHistoryDble(J_History+1,Jres,historyOffset);
    double Jeff = J/Jres;

    // new Kirchhoff pressure (over rho0) from Tait equation
	double p0=mptr->GetPressure();
    double pressure = J*TAIT_C*Ksp*(exp((1.-Jeff)/TAIT_C)-1.);
    mptr->SetPressure(pressure);
    
	// incremental energy per unit mass - dilational part
    double avgP = 0.5*(p0+pressure);
    double delV = 1. - 1./detdF;
    double workEnergy = -avgP*delV;
    
	// incremental residual energy per unit mass
	double delVres = 1. - 1./dJres;
	double resEnergy = -avgP*delVres;
	
    // viscosity term = 2 eta (0.5(grad v) + 0.5*(grad V)^T - (1/3) tr(grad v) I) = 2 eta dev(grad v)
    // (i.e., deviatoric part of the symmetric strain tensor, 2 is for conversion to engineering shear strain)
	// simple shear rate = |2 dev(grad v)|
    Matrix3 shear;
    double c[3][3];
	double shearRate;
    c[0][0] = (2.*du(0,0)-du(1,1)-du(2,2))/3.;
    c[1][1] = (2.*du(1,1)-du(0,0)-du(2,2))/3.;
    c[2][2] = (2.*du(2,2)-du(0,0)-du(1,1))/3.;
    c[0][1] = 0.5*(du(0,1)+du(1,0));
    c[1][0] = c[0][1];
	shearRate = c[0][0]*c[0][0] + c[1][1]*c[1][1] + c[2][2]*c[2][2]
	+ 2.*c[0][1]*c[0][1];
    if(np==THREED_MPM)
    {   c[0][2] = 0.5*(du(0,2)+du(2,0));
        c[2][0] = c[0][2];
        c[1][2] = 0.5*(du(1,2)+du(2,1));
        c[2][1] = c[1][2];
		shearRate += 2.*(c[0][2]*c[0][2] + c[1][2]*c[1][2]);
        shear.set(c);
    }
    else
        shear.set(c[0][0],c[0][1],c[1][0],c[1][1],c[2][2]);
	shearRate = 2.*sqrt(shearRate)/delTime;
	
	// Store shear rate
	mptr->SetHistoryDble(J_History+2,shearRate,historyOffset);
	
	// Get effective visocisy
	double twoetaspRate = 0.;
	if(numViscosity==1)
	{	twoetaspRate = TwoEtasp[0];
	}
	else
	{	shearRate = log10(shearRate);
		if(shearRate < logShearRate[0])
			twoetaspRate = TwoEtasp[0];
		else if(shearRate > logShearRate[numViscosity-1])
			twoetaspRate = TwoEtasp[numViscosity-1];
		else
		{	// interpolate
			for(int i=1;i<numViscosity;i++)
			{	if(shearRate <= logShearRate[i])
				{	// between i-1 and i
					double fract = (logShearRate[i]-shearRate)/(logShearRate[i]-logShearRate[i-1]);
					twoetaspRate = fract*TwoEtasp[i-1] + (1.-fract)*TwoEtasp[i];
					break;
				}
			}
		}
	}
    
    // Get Kirchoff shear stress (over rho0)
    shear.Scale(J*twoetaspRate/delTime);
    
    // update deviatoric stress
	Tensor *sp=mptr->GetStressTensor();
    sp->xx = shear(0,0);
    sp->yy = shear(1,1);
    sp->zz = shear(2,2);
    sp->xy = shear(0,1);
    if(np==THREED_MPM)
    {   sp->xz = shear(0,2);
        sp->yz = shear(1,2);
    }
    
    // shear work per unit mass = tau.du = tau.tau*delTime/twoetaspRate
    double shearWork = sp->xx*sp->xx + sp->yy*sp->yy + sp->zz*sp->zz + 2.*sp->xy*sp->xy;
    if(np==THREED_MPM) shearWork += 2.*(sp->xz*sp->xz + sp->yz*sp->yz);
    shearWork *= delTime/twoetaspRate;
    mptr->AddWorkEnergyAndResidualEnergy(workEnergy+shearWork,resEnergy);
    
    // particle isentropic temperature increment dT/T = - J (K/K0) gamma0 Delta(V)/V
    // Delta(V)/V = 1. - 1/detdF (total volume)
	double Kratio = Jeff*(1.+pressure/(TAIT_C*Ksp));
	double dTq0 = -J*Kratio*gamma0*mptr->pPreviousTemperature*delV;
    
    // heat energy is Cv (dT - dTq0) -dPhi
	// Here do Cv (dT - dTq0)
    // dPhi = shearWork is lost due to shear term
    IncrementHeatEnergy(mptr,res->dT,dTq0,shearWork);
}
Beispiel #4
0
// Entry point for large rotation
void Elastic::LRConstitutiveLaw(MPMBase *mptr,Matrix3 du,double delTime,int np,void *properties,ResidualStrains *res) const
{
	// get previous deformation gradient
	Matrix3 pFnm1 = mptr->GetDeformationGradientMatrix();
	
    // get incremental deformation gradient and decompose it
	const Matrix3 dF = du.Exponential(incrementalDefGradTerms);
    Matrix3 dR;
    Matrix3 dU = dF.RightDecompose(&dR,NULL);

	// get pinitial rotation R0
	Matrix3 R0 = mptr->GetInitialRotation();
	
	// get previous rotation and stretch
    Matrix3 Rnm1;
	Matrix3 Unm1 = pFnm1.RightDecompose(&Rnm1,NULL);
	
	// get strain increments de = R0T.[(Rnm1T.dU.Rnm1 - I).Unm1].R0
	Matrix3 dUrot = dU.RTMR(Rnm1);
	dUrot(0,0) -= 1.;
	dUrot(1,1) -= 1.;
	dUrot(2,2) -= 1.;
	dUrot *= Unm1;
	
	// apply initial rotation to get strain increment in the material coordinates
	Matrix3 de = dUrot.RTMR(R0);
	Matrix3 Rtotnm1M3 = Rnm1*R0;
	Matrix3 *Rtotnm1 = &Rtotnm1M3;
	
	// get total rotation
	Matrix3 Rtot = dR*Rtotnm1M3;
	if(np==THREED_MPM) mptr->SetRtot(Rtot);
	
	// Update total deformation gradient
	Matrix3 pF = dF*pFnm1;
	mptr->SetDeformationGradientMatrix(pF);
	
	// cast pointer to material-specific data
	ElasticProperties *p = GetElasticPropertiesPointer(properties);

    // residual strains (thermal and moisture) in material axes
	double exxr,eyyr,ezzr;
	if(np==THREED_MPM)
	{	exxr = p->alpha[0]*res->dT;
		eyyr = p->alpha[1]*res->dT;
		ezzr = p->alpha[2]*res->dT;
		if(DiffusionTask::active)
		{	exxr += p->beta[0]*res->dC;
			eyyr += p->beta[1]*res->dC;
			ezzr += p->beta[2]*res->dC;
		}
	}
	else
	{	exxr = p->alpha[1]*res->dT;
		eyyr = p->alpha[2]*res->dT;
		ezzr = p->alpha[4]*res->dT;
		if(DiffusionTask::active)
		{	exxr += p->beta[1]*res->dC;
			eyyr += p->beta[2]*res->dC;
			ezzr += p->beta[4]*res->dC;
		}
	}
	Matrix3 er = Matrix3(exxr,0.,0.,eyyr,ezzr);
	
	// finish up
	LRElasticConstitutiveLaw(mptr,de,er,Rtot,dR,Rtotnm1,np,properties,res);
}