C++ Matrix3::LeftDecompose方法代码示例

// Get V-I which is Biot strain rotated into current particle orientation
// It is based on total strain
Matrix3 MPMBase::GetBiotStrain(void) const
{
    Matrix3 F = GetDeformationGradientMatrix();
    Matrix3 V = F.LeftDecompose(NULL,NULL);
    V(0,0) -= 1.;
    V(1,1) -= 1.;
    V(2,2) -= 1.;
    return V;
}

// Entry point for large rotation
void IsoPlasticity::LRConstitutiveLaw(MPMBase *mptr,Matrix3 du,double delTime,int np,void *properties,ResidualStrains *res) const
{
	// current previous deformation gradient and stretch
	Matrix3 pFnm1 = mptr->GetDeformationGradientMatrix();
	
    // get incremental deformation gradient and decompose it
	const Matrix3 dF = du.Exponential(incrementalDefGradTerms);
    Matrix3 dR;
    Matrix3 dV = dF.LeftDecompose(&dR,NULL);
	
	// decompose to get previous stretch
	Matrix3 Vnm1 = pFnm1.LeftDecompose(NULL,NULL);
	
	// get strain increments de = (dV-I) dR Vnm1 dRT
	dV(0,0) -= 1.;
	dV(1,1) -= 1.;
	dV(2,2) -= 1.;
	Matrix3 de = dV*Vnm1.RMRT(dR);
	
	// Update total deformation gradient
	Matrix3 pF = dF*pFnm1;
	mptr->SetDeformationGradientMatrix(pF);
	
    // Effective strain by deducting thermal strain (no shear thermal strain because isotropic)
	//  (note: using unreduced terms in CTE3 and CME3)
	double eres=CTE3*res->dT;
	if(DiffusionTask::active)
		eres+=CME3*res->dC;
	
	// Trial update assuming elastic response
	double delV;
    
    // 3D or 2D
	PlasticProperties *p = (PlasticProperties *)properties;
    if(np==THREED_MPM)
    {   delV = de.trace() - 3.*eres;
        LRPlasticityConstLaw(mptr,de(0,0),de(1,1),de(2,2),2*de(0,1),2.*de(0,2),2.*de(1,2),
                           delTime,np,delV,eres,p,res,&dR);
        return;
    }
	else if(np==PLANE_STRESS_MPM)
		delV = p->psRed*(de(0,0)+de(1,1)-2.*eres);
	else
		delV = de.trace() - 3.*eres;
    LRPlasticityConstLaw(mptr,de(0,0),de(1,1),2.*de(0,1),de(2,2),delTime,np,delV,eres,p,res,&dR);
}

/* Take increments in strain and calculate new Particle: strains, rotation strain,
	stresses, strain energy,
	du are (gradient rates X time increment) to give deformation gradient change
	For Axisymmetry: x->R, y->Z, z->theta, np==AXISYMMETRIC_MPM, otherwise dvzz=0
	This material tracks pressure and stores deviatoric stress only in particle stress tensor
 */
void Viscoelastic::MPMConstitutiveLaw(MPMBase *mptr,Matrix3 du,double delTime,int np,void *properties,ResidualStrains *res,int historyOffset) const
{
	// current previous deformation gradient and stretch
	Matrix3 pFnm1 = mptr->GetDeformationGradientMatrix();
	
    // get incremental deformation gradient and decompose it
	const Matrix3 dF = du.Exponential(incrementalDefGradTerms);
    Matrix3 dR;
    Matrix3 dVstretch = dF.LeftDecompose(&dR,NULL);
	
	// decompose to get previous stretch
	Matrix3 Vnm1 = pFnm1.LeftDecompose(NULL,NULL);
	
	// get strain increments de = (dV-I) dR Vnma dRT
	dVstretch(0,0) -= 1.;
	dVstretch(1,1) -= 1.;
	dVstretch(2,2) -= 1.;
	Matrix3 Vrot = Vnm1.RMRT(dR);
	Matrix3 detot = dVstretch*Vrot;
	
	// Update total deformation gradient
	Matrix3 pF = dF*pFnm1;
	mptr->SetDeformationGradientMatrix(pF);
	
    // Effective strain by deducting thermal strain (no shear thermal strain because isotropic)
	double eres=CTE*res->dT;
	if(DiffusionTask::active)
		eres+=CME*res->dC;
	
	// update pressure
	double dTq0 = 0.,dispEnergy = 0.;
	double traceDe = detot.trace();
	double delV = traceDe - 3.*eres;
#ifdef USE_KIRCHOFF_STRESS
	// tracking J
	double detdF = dF.determinant();
	double **h =(double **)(mptr->GetHistoryPtr(0));
	double J = detdF*h[mptrHistory][MGJ_HISTORY];
	h[mptrHistory][MGJ_HISTORY] = J;
	UpdatePressure(mptr,delV,res,eres,detdF,J,delTime,dTq0,dispEnergy);
#else
	UpdatePressure(mptr,delV,res,eres,&dF,delTime,dTq0,dispEnergy);
#endif
	
	// deviatoric strains increment in de
	// Actually de is finding 2*(dev e) to avoid many multiplies by two
	Tensor de;
	double dV = traceDe/3.;
	de.xx = 2.*(detot(0,0) - dV);
	de.yy = 2.*(detot(1,1) - dV);
	de.zz = 2.*(detot(2,2) - dV);
	de.xy = 2.*detot(0,1);
	if(np==THREED_MPM)
	{	de.xz = 2.*detot(0,2);
		de.yz = 2.*detot(1,2);
	}
	
	// Find initial 2*e(t) (deviatoric strain) in ed
	Tensor ed;
	double thirdV = Vrot.trace()/3.;
	ed.xx = 2.*(Vrot(0,0)-thirdV);
	ed.yy = 2.*(Vrot(1,1)-thirdV);
	ed.zz = 2.*(Vrot(2,2)-thirdV);
	ed.xy = 2.*Vrot(0,1);
	if(np==THREED_MPM)
	{	ed.xz = 2.*Vrot(0,2);
		ed.yz = 2.*Vrot(1,2);
	}
	
	// increment particle deviatoric stresses - elastic part
	double dsig[6];
	dsig[XX] = Gered*de.xx;
	dsig[YY] = Gered*de.yy;
	dsig[ZZ] = Gered*de.zz;
	dsig[XY] = Gered*de.xy;
	if(np==THREED_MPM)
	{	dsig[XZ] = Gered*de.xz;
		dsig[YZ] = Gered*de.yz;
	}
	
	// get internal variable increments, update them, add to incremental stress, and get dissipated energy6
	Tensor dak;
    double **ak =(double **)(mptr->GetHistoryPtr(0));
	int k;
    for(k=0;k<ntaus;k++)
    {   double tmp = exp(-delTime/tauk[k]);
		double tmpm1 = tmp-1.;
		double tmpp1 = tmp+1.;
		double arg = 0.25*delTime/tauk[k];					// 0.25 because e's have factor of 2
		dak.xx = tmpm1*ak[XX_HISTORY][k] + arg*(tmpp1*ed.xx + de.xx);
		dak.yy = tmpm1*ak[YY_HISTORY][k] + arg*(tmpp1*ed.yy + de.yy);
		dak.xy = tmpm1*ak[XY_HISTORY][k] + arg*(tmpp1*ed.xy + de.xy);
		dak.zz = tmpm1*ak[ZZ_HISTORY][k] + arg*(tmpp1*ed.zz + de.zz);
		ak[XX_HISTORY][k] += dak.xx;
//.........这里部分代码省略.........