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TetrahedralCorotationalFEMForceField.inl
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TetrahedralCorotationalFEMForceField.inl
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/******************************************************************************
* SOFA, Simulation Open-Framework Architecture *
* (c) 2006 INRIA, USTL, UJF, CNRS, MGH *
* *
* This program is free software; you can redistribute it and/or modify it *
* under the terms of the GNU Lesser General Public License as published by *
* the Free Software Foundation; either version 2.1 of the License, or (at *
* your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, but WITHOUT *
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or *
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License *
* for more details. *
* *
* You should have received a copy of the GNU Lesser General Public License *
* along with this program. If not, see <http://www.gnu.org/licenses/>. *
*******************************************************************************
* Authors: The SOFA Team and external contributors (see Authors.txt) *
* *
* Contact information: contact@sofa-framework.org *
******************************************************************************/
#pragma once
#include <sofa/component/solidmechanics/fem/elastic/TetrahedralCorotationalFEMForceField.h>
#include <sofa/core/behavior/ForceField.inl>
#include <sofa/core/visual/VisualParams.h>
#include <sofa/helper/decompose.h>
#include <sofa/core/topology/TopologyData.inl>
namespace sofa::component::solidmechanics::fem::elastic
{
template< class DataTypes>
void TetrahedralCorotationalFEMForceField<DataTypes>::createTetrahedronInformation(Index tetrahedronIndex, TetrahedronInformation& tInfo,
const core::topology::BaseMeshTopology::Tetrahedron& tetra,
const sofa::type::vector<Index>& ancestors,
const sofa::type::vector<SReal>& coefs)
{
SOFA_UNUSED(tInfo);
SOFA_UNUSED(tetra);
SOFA_UNUSED(ancestors);
SOFA_UNUSED(coefs);
const core::topology::BaseMeshTopology::Tetrahedron t=this->m_topology->getTetrahedron(tetrahedronIndex);
Index a = t[0];
Index b = t[1];
Index c = t[2];
Index d = t[3];
switch(method)
{
case SMALL :
computeMaterialStiffness(tetrahedronIndex,a,b,c,d);
initSmall(tetrahedronIndex,a,b,c,d);
break;
case LARGE :
computeMaterialStiffness(tetrahedronIndex,a,b,c,d);
initLarge(tetrahedronIndex,a,b,c,d);
break;
case POLAR :
computeMaterialStiffness(tetrahedronIndex,a,b,c,d);
initPolar(tetrahedronIndex,a,b,c,d);
break;
}
}
template< class DataTypes>
TetrahedralCorotationalFEMForceField<DataTypes>::TetrahedralCorotationalFEMForceField()
: tetrahedronInfo(initData(&tetrahedronInfo, "tetrahedronInfo", "Internal tetrahedron data"))
, f_method(initData(&f_method,std::string("large"),"method","\"small\", \"large\" (by QR) or \"polar\" displacements"))
, _poissonRatio(core::objectmodel::BaseObject::initData(&_poissonRatio,(Real)0.45,"poissonRatio","FEM Poisson Ratio"))
, _youngModulus(core::objectmodel::BaseObject::initData(&_youngModulus,(Real)5000,"youngModulus","FEM Young Modulus"))
, _localStiffnessFactor(core::objectmodel::BaseObject::initData(&_localStiffnessFactor,"localStiffnessFactor","Allow specification of different stiffness per element. If there are N element and M values are specified, the youngModulus factor for element i would be localStiffnessFactor[i*M/N]"))
, _updateStiffnessMatrix(core::objectmodel::BaseObject::initData(&_updateStiffnessMatrix,false,"updateStiffnessMatrix",""))
, _assembling(core::objectmodel::BaseObject::initData(&_assembling,false,"computeGlobalMatrix",""))
, f_drawing(initData(&f_drawing,true,"drawing"," draw the forcefield if true"))
, drawColor1(initData(&drawColor1,sofa::type::RGBAColor(0.0f,0.0f,1.0f,1.0f),"drawColor1"," draw color for faces 1"))
, drawColor2(initData(&drawColor2,sofa::type::RGBAColor(0.0f,0.5f,1.0f,1.0f),"drawColor2"," draw color for faces 2"))
, drawColor3(initData(&drawColor3,sofa::type::RGBAColor(0.0f,1.0f,1.0f,1.0f),"drawColor3"," draw color for faces 3"))
, drawColor4(initData(&drawColor4,sofa::type::RGBAColor(0.5f,1.0f,1.0f,1.0f),"drawColor4"," draw color for faces 4"))
, l_topology(initLink("topology", "link to the topology container"))
{
this->addAlias(&_assembling, "assembling");
_poissonRatio.setWidget("poissonRatio");
_poissonRatio.setRequired(true);
_youngModulus.setRequired(true);
}
template <class DataTypes>
void TetrahedralCorotationalFEMForceField<DataTypes>::init()
{
this->core::behavior::ForceField<DataTypes>::init();
if (l_topology.empty())
{
msg_info() << "link to Topology container should be set to ensure right behavior. First Topology found in current context will be used.";
l_topology.set(this->getContext()->getMeshTopologyLink());
}
m_topology = l_topology.get();
msg_info() << "Topology path used: '" << l_topology.getLinkedPath() << "'";
if (m_topology == nullptr)
{
msg_error() << "No topology component found at path: " << l_topology.getLinkedPath() << ", nor in current context: " << this->getContext()->name << ". This FEM needs to rely on a Tetrahedral Topology.";
this->d_componentState.setValue(sofa::core::objectmodel::ComponentState::Invalid);
return;
}
if (m_topology->getNbTetrahedra() == 0)
{
msg_warning() << "No tetrahedra found in linked Topology.";
}
reinit(); // compute per-element stiffness matrices and other precomputed values
}
template <class DataTypes>
void TetrahedralCorotationalFEMForceField<DataTypes>::reinit()
{
if (f_method.getValue() == "small")
this->setMethod(SMALL);
else if (f_method.getValue() == "polar")
this->setMethod(POLAR);
else this->setMethod(LARGE);
// Need to initialize the _stiffnesses vector before using it
const std::size_t sizeMO=this->mstate->getSize();
if(_assembling.getValue())
{
_stiffnesses.resize( sizeMO * 3 );
}
type::vector<typename TetrahedralCorotationalFEMForceField<DataTypes>::TetrahedronInformation>& tetrahedronInf = *(tetrahedronInfo.beginEdit());
tetrahedronInf.resize(m_topology->getNbTetrahedra());
for (std::size_t i=0; i<m_topology->getNbTetrahedra(); ++i)
{
createTetrahedronInformation(i, tetrahedronInf[i],
m_topology->getTetrahedron(i), (const std::vector< Index > )0,
(const std::vector< SReal >)0);
}
tetrahedronInfo.createTopologyHandler(m_topology);
tetrahedronInfo.setCreationCallback([this](Index tetrahedronIndex, TetrahedronInformation& tInfo,
const core::topology::BaseMeshTopology::Tetrahedron& tetra,
const sofa::type::vector<Index>& ancestors,
const sofa::type::vector<SReal>& coefs)
{
createTetrahedronInformation(tetrahedronIndex, tInfo, tetra, ancestors, coefs);
});
tetrahedronInfo.endEdit();
}
template<class DataTypes>
void TetrahedralCorotationalFEMForceField<DataTypes>::addForce(const core::MechanicalParams* /* mparams */, DataVecDeriv& d_f, const DataVecCoord& d_x, const DataVecDeriv& /* d_v */)
{
VecDeriv& f = *d_f.beginEdit();
const VecCoord& p = d_x.getValue();
switch(method)
{
case SMALL :
{
for(Size i = 0 ; i<m_topology->getNbTetrahedra(); ++i)
{
accumulateForceSmall( f, p, i );
}
break;
}
case LARGE :
{
for(Size i = 0 ; i<m_topology->getNbTetrahedra(); ++i)
{
accumulateForceLarge( f, p, i );
}
break;
}
case POLAR :
{
for(Size i = 0 ; i<m_topology->getNbTetrahedra(); ++i)
{
accumulateForcePolar( f, p, i );
}
break;
}
}
d_f.endEdit();
}
template<class DataTypes>
void TetrahedralCorotationalFEMForceField<DataTypes>::addDForce(const core::MechanicalParams* mparams, DataVecDeriv& d_df, const DataVecDeriv& d_dx)
{
VecDeriv& df = *d_df.beginEdit();
const VecDeriv& dx = d_dx.getValue();
Real kFactor = (Real)sofa::core::mechanicalparams::kFactorIncludingRayleighDamping(mparams, this->rayleighStiffness.getValue());
const auto& tetraArray = m_topology->getTetrahedra();
switch(method)
{
case SMALL :
{
for(Size tetraId = 0; tetraId<tetraArray.size(); ++tetraId)
{
const core::topology::BaseMeshTopology::Tetrahedron& tetra = tetraArray[tetraId];
applyStiffnessSmall( df, dx, tetraId, tetra[0], tetra[1], tetra[2], tetra[3], kFactor );
}
break;
}
case LARGE :
{
for(Size tetraId = 0; tetraId<tetraArray.size(); ++tetraId)
{
const core::topology::BaseMeshTopology::Tetrahedron& tetra = tetraArray[tetraId];
applyStiffnessLarge( df, dx, tetraId, tetra[0], tetra[1], tetra[2], tetra[3], kFactor );
}
break;
}
case POLAR :
{
for(Size tetraId = 0; tetraId<tetraArray.size(); ++tetraId)
{
const core::topology::BaseMeshTopology::Tetrahedron& tetra = tetraArray[tetraId];
applyStiffnessPolar( df, dx, tetraId, tetra[0], tetra[1], tetra[2], tetra[3], kFactor );
}
break;
}
}
d_df.endEdit();
}
template<class DataTypes>
void TetrahedralCorotationalFEMForceField<DataTypes>::computeStrainDisplacement( StrainDisplacementTransposed &J, Coord a, Coord b, Coord c, Coord d )
{
// shape functions matrix
type::Mat<2, 3, Real> M;
M[0][0] = b[1];
M[0][1] = c[1];
M[0][2] = d[1];
M[1][0] = b[2];
M[1][1] = c[2];
M[1][2] = d[2];
J[0][0] = J[1][3] = J[2][5] = - peudo_determinant_for_coef( M );
M[0][0] = b[0];
M[0][1] = c[0];
M[0][2] = d[0];
J[0][3] = J[1][1] = J[2][4] = peudo_determinant_for_coef( M );
M[1][0] = b[1];
M[1][1] = c[1];
M[1][2] = d[1];
J[0][5] = J[1][4] = J[2][2] = - peudo_determinant_for_coef( M );
M[0][0] = c[1];
M[0][1] = d[1];
M[0][2] = a[1];
M[1][0] = c[2];
M[1][1] = d[2];
M[1][2] = a[2];
J[3][0] = J[4][3] = J[5][5] = peudo_determinant_for_coef( M );
M[0][0] = c[0];
M[0][1] = d[0];
M[0][2] = a[0];
J[3][3] = J[4][1] = J[5][4] = - peudo_determinant_for_coef( M );
M[1][0] = c[1];
M[1][1] = d[1];
M[1][2] = a[1];
J[3][5] = J[4][4] = J[5][2] = peudo_determinant_for_coef( M );
M[0][0] = d[1];
M[0][1] = a[1];
M[0][2] = b[1];
M[1][0] = d[2];
M[1][1] = a[2];
M[1][2] = b[2];
J[6][0] = J[7][3] = J[8][5] = - peudo_determinant_for_coef( M );
M[0][0] = d[0];
M[0][1] = a[0];
M[0][2] = b[0];
J[6][3] = J[7][1] = J[8][4] = peudo_determinant_for_coef( M );
M[1][0] = d[1];
M[1][1] = a[1];
M[1][2] = b[1];
J[6][5] = J[7][4] = J[8][2] = - peudo_determinant_for_coef( M );
M[0][0] = a[1];
M[0][1] = b[1];
M[0][2] = c[1];
M[1][0] = a[2];
M[1][1] = b[2];
M[1][2] = c[2];
J[9][0] = J[10][3] = J[11][5] = peudo_determinant_for_coef( M );
M[0][0] = a[0];
M[0][1] = b[0];
M[0][2] = c[0];
J[9][3] = J[10][1] = J[11][4] = - peudo_determinant_for_coef( M );
M[1][0] = a[1];
M[1][1] = b[1];
M[1][2] = c[1];
J[9][5] = J[10][4] = J[11][2] = peudo_determinant_for_coef( M );
// 0
J[0][1] = J[0][2] = J[0][4] = J[1][0] = J[1][2] = J[1][5] = J[2][0] = J[2][1] = J[2][3] = 0;
J[3][1] = J[3][2] = J[3][4] = J[4][0] = J[4][2] = J[4][5] = J[5][0] = J[5][1] = J[5][3] = 0;
J[6][1] = J[6][2] = J[6][4] = J[7][0] = J[7][2] = J[7][5] = J[8][0] = J[8][1] = J[8][3] = 0;
J[9][1] = J[9][2] = J[9][4] = J[10][0] = J[10][2] = J[10][5] = J[11][0] = J[11][1] = J[11][3] = 0;
//m_deq( J, 1.2 ); //hack for stability ??
}
template<class DataTypes>
typename TetrahedralCorotationalFEMForceField<DataTypes>::Real TetrahedralCorotationalFEMForceField<DataTypes>::peudo_determinant_for_coef ( const type::Mat<2, 3, Real>& M )
{
return M[0][1]*M[1][2] - M[1][1]*M[0][2] - M[0][0]*M[1][2] + M[1][0]*M[0][2] + M[0][0]*M[1][1] - M[1][0]*M[0][1];
}
template<class DataTypes>
void TetrahedralCorotationalFEMForceField<DataTypes>::computeStiffnessMatrix( StiffnessMatrix& S,StiffnessMatrix& SR,const MaterialStiffness &K, const StrainDisplacementTransposed &J, const Transformation& Rot )
{
type::MatNoInit<6, 12, Real> Jt;
Jt.transpose(J);
type::MatNoInit<12, 12, Real> JKJt;
JKJt = J * K * Jt;
type::MatNoInit<12, 12, Real> RR, RRt;
RR.clear();
RRt.clear();
for (int i = 0; i < 3; ++i)
{
for (int j = 0; j < 3; ++j)
{
RR[i][j] = RR[i + 3][j + 3] = RR[i + 6][j + 6] = RR[i + 9][j + 9] = Rot[i][j];
RRt[i][j] = RRt[i + 3][j + 3] = RRt[i + 6][j + 6] = RRt[i + 9][j + 9] = Rot[j][i];
}
}
S = RR * JKJt;
SR = S * RRt;
}
template<class DataTypes>
void TetrahedralCorotationalFEMForceField<DataTypes>::computeMaterialStiffness(int i, Index&a, Index&b, Index&c, Index&d)
{
const VecReal& localStiffnessFactor = _localStiffnessFactor.getValue();
type::vector<typename TetrahedralCorotationalFEMForceField<DataTypes>::TetrahedronInformation>& tetrahedronInf = *(tetrahedronInfo.beginEdit());
computeMaterialStiffness(tetrahedronInf[i].materialMatrix, a, b, c, d, (localStiffnessFactor.empty() ? 1.0f : localStiffnessFactor[i*localStiffnessFactor.size()/m_topology->getNbTetrahedra()]));
tetrahedronInfo.endEdit();
}
template<class DataTypes>
void TetrahedralCorotationalFEMForceField<DataTypes>::computeMaterialStiffness(MaterialStiffness& materialMatrix, Index&a, Index&b, Index&c, Index&d, SReal localStiffnessFactor)
{
const Real youngModulus = _youngModulus.getValue()*(Real)localStiffnessFactor;
const Real poissonRatio = _poissonRatio.getValue();
materialMatrix[0][0] = materialMatrix[1][1] = materialMatrix[2][2] = 1;
materialMatrix[0][1] = materialMatrix[0][2] = materialMatrix[1][0] =
materialMatrix[1][2] = materialMatrix[2][0] = materialMatrix[2][1] = poissonRatio/(1-poissonRatio);
materialMatrix[0][3] = materialMatrix[0][4] = materialMatrix[0][5] = 0;
materialMatrix[1][3] = materialMatrix[1][4] = materialMatrix[1][5] = 0;
materialMatrix[2][3] = materialMatrix[2][4] = materialMatrix[2][5] = 0;
materialMatrix[3][0] = materialMatrix[3][1] = materialMatrix[3][2] =
materialMatrix[3][4] = materialMatrix[3][5] = 0;
materialMatrix[4][0] = materialMatrix[4][1] = materialMatrix[4][2] =
materialMatrix[4][3] = materialMatrix[4][5] = 0;
materialMatrix[5][0] = materialMatrix[5][1] = materialMatrix[5][2] =
materialMatrix[5][3] = materialMatrix[5][4] = 0;
materialMatrix[3][3] = materialMatrix[4][4] = materialMatrix[5][5] =
(1-2*poissonRatio)/(2*(1-poissonRatio));
materialMatrix *= (youngModulus*(1-poissonRatio))/((1+poissonRatio)*(1-2*poissonRatio));
// divide by 36 times volumes of the element
const VecCoord X0=this->mstate->read(core::ConstVecCoordId::restPosition())->getValue();
Coord A = (X0)[b] - (X0)[a];
Coord B = (X0)[c] - (X0)[a];
Coord C = (X0)[d] - (X0)[a];
Coord AB = cross(A, B);
Real volumes6 = fabs( dot( AB, C ) );
if (volumes6<0)
{
msg_error() << "Negative volume for tetra " << a << ',' << b << ',' << c << ',' << d << "> = " << volumes6 / 6;
}
// materialMatrix /= (volumes6);//*6 christian
// @TODO: in TetrahedronFEMForceField, the stiffness matrix is divided by 6 compared to the code in TetrahedralCorotationalFEMForceField. Check which is the correct one...
// FF: there is normally a factor 1/6v in the strain-displacement matrix. Times transpose makes 1/36v². Integrating accross the volume multiplies by v, so the factor is 1/36v
materialMatrix /= (volumes6*6);
}
template<class DataTypes>
inline void TetrahedralCorotationalFEMForceField<DataTypes>::computeForce( Displacement &F, const Displacement &Depl, const MaterialStiffness &K, const StrainDisplacementTransposed &J )
{
// Unit of K = unit of youngModulus / unit of volume = Pa / m^3 = kg m^-4 s^-2
// Unit of J = m^2
// Unit of JKJt = kg s^-2
// Unit of displacement = m
// Unit of force = kg m s^-2
/* We have these zeros
K[0][3] K[0][4] K[0][5]
K[1][3] K[1][4] K[1][5]
K[2][3] K[2][4] K[2][5]
K[3][0] K[3][1] K[3][2] K[3][4] K[3][5]
K[4][0] K[4][1] K[4][2] K[4][3] K[4][5]
K[5][0] K[5][1] K[5][2] K[5][3] K[5][4]
J[0][1] J[0][2] J[0][4]
J[1][0] J[1][2] J[1][5]
J[2][0] J[2][1] J[2][3]
J[3][1] J[3][2] J[3][4]
J[4][0] J[4][2] J[4][5]
J[5][0] J[5][1] J[5][3]
J[6][1] J[6][2] J[6][4]
J[7][0] J[7][2] J[7][5]
J[8][0] J[8][1] J[8][3]
J[9][1] J[9][2] J[9][4]
J[10][0] J[10][2] J[10][5]
J[11][0] J[11][1] J[11][3]
*/
type::VecNoInit<6,Real> JtD;
JtD[0] = J[ 0][0]*Depl[ 0]+/*J[ 1][0]*Depl[ 1]+ J[ 2][0]*Depl[ 2]+*/
J[ 3][0]*Depl[ 3]+/*J[ 4][0]*Depl[ 4]+ J[ 5][0]*Depl[ 5]+*/
J[ 6][0]*Depl[ 6]+/*J[ 7][0]*Depl[ 7]+ J[ 8][0]*Depl[ 8]+*/
J[ 9][0]*Depl[ 9] /*J[10][0]*Depl[10]+ J[11][0]*Depl[11]*/;
JtD[1] = /*J[ 0][1]*Depl[ 0]+*/J[ 1][1]*Depl[ 1]+/*J[ 2][1]*Depl[ 2]+*/
/*J[ 3][1]*Depl[ 3]+*/J[ 4][1]*Depl[ 4]+/*J[ 5][1]*Depl[ 5]+*/
/*J[ 6][1]*Depl[ 6]+*/J[ 7][1]*Depl[ 7]+/*J[ 8][1]*Depl[ 8]+*/
/*J[ 9][1]*Depl[ 9]+*/J[10][1]*Depl[10] /*J[11][1]*Depl[11]*/;
JtD[2] = /*J[ 0][2]*Depl[ 0]+ J[ 1][2]*Depl[ 1]+*/J[ 2][2]*Depl[ 2]+
/*J[ 3][2]*Depl[ 3]+ J[ 4][2]*Depl[ 4]+*/J[ 5][2]*Depl[ 5]+
/*J[ 6][2]*Depl[ 6]+ J[ 7][2]*Depl[ 7]+*/J[ 8][2]*Depl[ 8]+
/*J[ 9][2]*Depl[ 9]+ J[10][2]*Depl[10]+*/J[11][2]*Depl[11] ;
JtD[3] = J[ 0][3]*Depl[ 0]+ J[ 1][3]*Depl[ 1]+/*J[ 2][3]*Depl[ 2]+*/
J[ 3][3]*Depl[ 3]+ J[ 4][3]*Depl[ 4]+/*J[ 5][3]*Depl[ 5]+*/
J[ 6][3]*Depl[ 6]+ J[ 7][3]*Depl[ 7]+/*J[ 8][3]*Depl[ 8]+*/
J[ 9][3]*Depl[ 9]+ J[10][3]*Depl[10] /*J[11][3]*Depl[11]*/;
JtD[4] = /*J[ 0][4]*Depl[ 0]+*/J[ 1][4]*Depl[ 1]+ J[ 2][4]*Depl[ 2]+
/*J[ 3][4]*Depl[ 3]+*/J[ 4][4]*Depl[ 4]+ J[ 5][4]*Depl[ 5]+
/*J[ 6][4]*Depl[ 6]+*/J[ 7][4]*Depl[ 7]+ J[ 8][4]*Depl[ 8]+
/*J[ 9][4]*Depl[ 9]+*/J[10][4]*Depl[10]+ J[11][4]*Depl[11] ;
JtD[5] = J[ 0][5]*Depl[ 0]+/*J[ 1][5]*Depl[ 1]*/ J[ 2][5]*Depl[ 2]+
J[ 3][5]*Depl[ 3]+/*J[ 4][5]*Depl[ 4]*/ J[ 5][5]*Depl[ 5]+
J[ 6][5]*Depl[ 6]+/*J[ 7][5]*Depl[ 7]*/ J[ 8][5]*Depl[ 8]+
J[ 9][5]*Depl[ 9]+/*J[10][5]*Depl[10]*/ J[11][5]*Depl[11];
type::VecNoInit<6,Real> KJtD;
KJtD[0] = K[0][0]*JtD[0]+ K[0][1]*JtD[1]+ K[0][2]*JtD[2]
/*K[0][3]*JtD[3]+ K[0][4]*JtD[4]+ K[0][5]*JtD[5]*/;
KJtD[1] = K[1][0]*JtD[0]+ K[1][1]*JtD[1]+ K[1][2]*JtD[2]
/*K[1][3]*JtD[3]+ K[1][4]*JtD[4]+ K[1][5]*JtD[5]*/;
KJtD[2] = K[2][0]*JtD[0]+ K[2][1]*JtD[1]+ K[2][2]*JtD[2]
/*K[2][3]*JtD[3]+ K[2][4]*JtD[4]+ K[2][5]*JtD[5]*/;
KJtD[3] = /*K[3][0]*JtD[0]+ K[3][1]*JtD[1]+ K[3][2]*JtD[2]+*/
K[3][3]*JtD[3] /*K[3][4]*JtD[4]+ K[3][5]*JtD[5]*/;
KJtD[4] = /*K[4][0]*JtD[0]+ K[4][1]*JtD[1]+ K[4][2]*JtD[2]+*/
/*K[4][3]*JtD[3]+*/K[4][4]*JtD[4] /*K[4][5]*JtD[5]*/;
KJtD[5] = /*K[5][0]*JtD[0]+ K[5][1]*JtD[1]+ K[5][2]*JtD[2]+*/
/*K[5][3]*JtD[3]+ K[5][4]*JtD[4]+*/K[5][5]*JtD[5] ;
F[ 0] = J[ 0][0]*KJtD[0]+/*J[ 0][1]*KJtD[1]+ J[ 0][2]*KJtD[2]+*/
J[ 0][3]*KJtD[3]+/*J[ 0][4]*KJtD[4]+*/J[ 0][5]*KJtD[5] ;
F[ 1] = /*J[ 1][0]*KJtD[0]+*/J[ 1][1]*KJtD[1]+/*J[ 1][2]*KJtD[2]+*/
J[ 1][3]*KJtD[3]+ J[ 1][4]*KJtD[4] /*J[ 1][5]*KJtD[5]*/;
F[ 2] = /*J[ 2][0]*KJtD[0]+ J[ 2][1]*KJtD[1]+*/J[ 2][2]*KJtD[2]+
/*J[ 2][3]*KJtD[3]+*/J[ 2][4]*KJtD[4]+ J[ 2][5]*KJtD[5] ;
F[ 3] = J[ 3][0]*KJtD[0]+/*J[ 3][1]*KJtD[1]+ J[ 3][2]*KJtD[2]+*/
J[ 3][3]*KJtD[3]+/*J[ 3][4]*KJtD[4]+*/J[ 3][5]*KJtD[5] ;
F[ 4] = /*J[ 4][0]*KJtD[0]+*/J[ 4][1]*KJtD[1]+/*J[ 4][2]*KJtD[2]+*/
J[ 4][3]*KJtD[3]+ J[ 4][4]*KJtD[4] /*J[ 4][5]*KJtD[5]*/;
F[ 5] = /*J[ 5][0]*KJtD[0]+ J[ 5][1]*KJtD[1]+*/J[ 5][2]*KJtD[2]+
/*J[ 5][3]*KJtD[3]+*/J[ 5][4]*KJtD[4]+ J[ 5][5]*KJtD[5] ;
F[ 6] = J[ 6][0]*KJtD[0]+/*J[ 6][1]*KJtD[1]+ J[ 6][2]*KJtD[2]+*/
J[ 6][3]*KJtD[3]+/*J[ 6][4]*KJtD[4]+*/J[ 6][5]*KJtD[5] ;
F[ 7] = /*J[ 7][0]*KJtD[0]+*/J[ 7][1]*KJtD[1]+/*J[ 7][2]*KJtD[2]+*/
J[ 7][3]*KJtD[3]+ J[ 7][4]*KJtD[4] /*J[ 7][5]*KJtD[5]*/;
F[ 8] = /*J[ 8][0]*KJtD[0]+ J[ 8][1]*KJtD[1]+*/J[ 8][2]*KJtD[2]+
/*J[ 8][3]*KJtD[3]+*/J[ 8][4]*KJtD[4]+ J[ 8][5]*KJtD[5] ;
F[ 9] = J[ 9][0]*KJtD[0]+/*J[ 9][1]*KJtD[1]+ J[ 9][2]*KJtD[2]+*/
J[ 9][3]*KJtD[3]+/*J[ 9][4]*KJtD[4]+*/J[ 9][5]*KJtD[5] ;
F[10] = /*J[10][0]*KJtD[0]+*/J[10][1]*KJtD[1]+/*J[10][2]*KJtD[2]+*/
J[10][3]*KJtD[3]+ J[10][4]*KJtD[4] /*J[10][5]*KJtD[5]*/;
F[11] = /*J[11][0]*KJtD[0]+ J[11][1]*KJtD[1]+*/J[11][2]*KJtD[2]+
/*J[11][3]*KJtD[3]+*/J[11][4]*KJtD[4]+ J[11][5]*KJtD[5] ;
}
template<class DataTypes>
inline void TetrahedralCorotationalFEMForceField<DataTypes>::computeForce( Displacement &F, const Displacement &Depl, const MaterialStiffness &K, const StrainDisplacementTransposed &J, SReal fact )
{
// Unit of K = unit of youngModulus / unit of volume = Pa / m^3 = kg m^-4 s^-2
// Unit of J = m^2
// Unit of JKJt = kg s^-2
// Unit of displacement = m
// Unit of force = kg m s^-2
/* We have these zeros
K[0][3] K[0][4] K[0][5]
K[1][3] K[1][4] K[1][5]
K[2][3] K[2][4] K[2][5]
K[3][0] K[3][1] K[3][2] K[3][4] K[3][5]
K[4][0] K[4][1] K[4][2] K[4][3] K[4][5]
K[5][0] K[5][1] K[5][2] K[5][3] K[5][4]
J[0][1] J[0][2] J[0][4]
J[1][0] J[1][2] J[1][5]
J[2][0] J[2][1] J[2][3]
J[3][1] J[3][2] J[3][4]
J[4][0] J[4][2] J[4][5]
J[5][0] J[5][1] J[5][3]
J[6][1] J[6][2] J[6][4]
J[7][0] J[7][2] J[7][5]
J[8][0] J[8][1] J[8][3]
J[9][1] J[9][2] J[9][4]
J[10][0] J[10][2] J[10][5]
J[11][0] J[11][1] J[11][3]
*/
type::VecNoInit<6,Real> JtD;
JtD[0] = J[ 0][0]*Depl[ 0]+/*J[ 1][0]*Depl[ 1]+ J[ 2][0]*Depl[ 2]+*/
J[ 3][0]*Depl[ 3]+/*J[ 4][0]*Depl[ 4]+ J[ 5][0]*Depl[ 5]+*/
J[ 6][0]*Depl[ 6]+/*J[ 7][0]*Depl[ 7]+ J[ 8][0]*Depl[ 8]+*/
J[ 9][0]*Depl[ 9] /*J[10][0]*Depl[10]+ J[11][0]*Depl[11]*/;
JtD[1] = /*J[ 0][1]*Depl[ 0]+*/J[ 1][1]*Depl[ 1]+/*J[ 2][1]*Depl[ 2]+*/
/*J[ 3][1]*Depl[ 3]+*/J[ 4][1]*Depl[ 4]+/*J[ 5][1]*Depl[ 5]+*/
/*J[ 6][1]*Depl[ 6]+*/J[ 7][1]*Depl[ 7]+/*J[ 8][1]*Depl[ 8]+*/
/*J[ 9][1]*Depl[ 9]+*/J[10][1]*Depl[10] /*J[11][1]*Depl[11]*/;
JtD[2] = /*J[ 0][2]*Depl[ 0]+ J[ 1][2]*Depl[ 1]+*/J[ 2][2]*Depl[ 2]+
/*J[ 3][2]*Depl[ 3]+ J[ 4][2]*Depl[ 4]+*/J[ 5][2]*Depl[ 5]+
/*J[ 6][2]*Depl[ 6]+ J[ 7][2]*Depl[ 7]+*/J[ 8][2]*Depl[ 8]+
/*J[ 9][2]*Depl[ 9]+ J[10][2]*Depl[10]+*/J[11][2]*Depl[11] ;
JtD[3] = J[ 0][3]*Depl[ 0]+ J[ 1][3]*Depl[ 1]+/*J[ 2][3]*Depl[ 2]+*/
J[ 3][3]*Depl[ 3]+ J[ 4][3]*Depl[ 4]+/*J[ 5][3]*Depl[ 5]+*/
J[ 6][3]*Depl[ 6]+ J[ 7][3]*Depl[ 7]+/*J[ 8][3]*Depl[ 8]+*/
J[ 9][3]*Depl[ 9]+ J[10][3]*Depl[10] /*J[11][3]*Depl[11]*/;
JtD[4] = /*J[ 0][4]*Depl[ 0]+*/J[ 1][4]*Depl[ 1]+ J[ 2][4]*Depl[ 2]+
/*J[ 3][4]*Depl[ 3]+*/J[ 4][4]*Depl[ 4]+ J[ 5][4]*Depl[ 5]+
/*J[ 6][4]*Depl[ 6]+*/J[ 7][4]*Depl[ 7]+ J[ 8][4]*Depl[ 8]+
/*J[ 9][4]*Depl[ 9]+*/J[10][4]*Depl[10]+ J[11][4]*Depl[11] ;
JtD[5] = J[ 0][5]*Depl[ 0]+/*J[ 1][5]*Depl[ 1]*/ J[ 2][5]*Depl[ 2]+
J[ 3][5]*Depl[ 3]+/*J[ 4][5]*Depl[ 4]*/ J[ 5][5]*Depl[ 5]+
J[ 6][5]*Depl[ 6]+/*J[ 7][5]*Depl[ 7]*/ J[ 8][5]*Depl[ 8]+
J[ 9][5]*Depl[ 9]+/*J[10][5]*Depl[10]*/ J[11][5]*Depl[11];
type::VecNoInit<6,Real> KJtD;
KJtD[0] = K[0][0]*JtD[0]+ K[0][1]*JtD[1]+ K[0][2]*JtD[2]
/*K[0][3]*JtD[3]+ K[0][4]*JtD[4]+ K[0][5]*JtD[5]*/;
KJtD[1] = K[1][0]*JtD[0]+ K[1][1]*JtD[1]+ K[1][2]*JtD[2]
/*K[1][3]*JtD[3]+ K[1][4]*JtD[4]+ K[1][5]*JtD[5]*/;
KJtD[2] = K[2][0]*JtD[0]+ K[2][1]*JtD[1]+ K[2][2]*JtD[2]
/*K[2][3]*JtD[3]+ K[2][4]*JtD[4]+ K[2][5]*JtD[5]*/;
KJtD[3] = /*K[3][0]*JtD[0]+ K[3][1]*JtD[1]+ K[3][2]*JtD[2]+*/
K[3][3]*JtD[3] /*K[3][4]*JtD[4]+ K[3][5]*JtD[5]*/;
KJtD[4] = /*K[4][0]*JtD[0]+ K[4][1]*JtD[1]+ K[4][2]*JtD[2]+*/
/*K[4][3]*JtD[3]+*/K[4][4]*JtD[4] /*K[4][5]*JtD[5]*/;
KJtD[5] = /*K[5][0]*JtD[0]+ K[5][1]*JtD[1]+ K[5][2]*JtD[2]+*/
/*K[5][3]*JtD[3]+ K[5][4]*JtD[4]+*/K[5][5]*JtD[5] ;
KJtD *= fact;
F[ 0] = J[ 0][0]*KJtD[0]+/*J[ 0][1]*KJtD[1]+ J[ 0][2]*KJtD[2]+*/
J[ 0][3]*KJtD[3]+/*J[ 0][4]*KJtD[4]+*/J[ 0][5]*KJtD[5] ;
F[ 1] = /*J[ 1][0]*KJtD[0]+*/J[ 1][1]*KJtD[1]+/*J[ 1][2]*KJtD[2]+*/
J[ 1][3]*KJtD[3]+ J[ 1][4]*KJtD[4] /*J[ 1][5]*KJtD[5]*/;
F[ 2] = /*J[ 2][0]*KJtD[0]+ J[ 2][1]*KJtD[1]+*/J[ 2][2]*KJtD[2]+
/*J[ 2][3]*KJtD[3]+*/J[ 2][4]*KJtD[4]+ J[ 2][5]*KJtD[5] ;
F[ 3] = J[ 3][0]*KJtD[0]+/*J[ 3][1]*KJtD[1]+ J[ 3][2]*KJtD[2]+*/
J[ 3][3]*KJtD[3]+/*J[ 3][4]*KJtD[4]+*/J[ 3][5]*KJtD[5] ;
F[ 4] = /*J[ 4][0]*KJtD[0]+*/J[ 4][1]*KJtD[1]+/*J[ 4][2]*KJtD[2]+*/
J[ 4][3]*KJtD[3]+ J[ 4][4]*KJtD[4] /*J[ 4][5]*KJtD[5]*/;
F[ 5] = /*J[ 5][0]*KJtD[0]+ J[ 5][1]*KJtD[1]+*/J[ 5][2]*KJtD[2]+
/*J[ 5][3]*KJtD[3]+*/J[ 5][4]*KJtD[4]+ J[ 5][5]*KJtD[5] ;
F[ 6] = J[ 6][0]*KJtD[0]+/*J[ 6][1]*KJtD[1]+ J[ 6][2]*KJtD[2]+*/
J[ 6][3]*KJtD[3]+/*J[ 6][4]*KJtD[4]+*/J[ 6][5]*KJtD[5] ;
F[ 7] = /*J[ 7][0]*KJtD[0]+*/J[ 7][1]*KJtD[1]+/*J[ 7][2]*KJtD[2]+*/
J[ 7][3]*KJtD[3]+ J[ 7][4]*KJtD[4] /*J[ 7][5]*KJtD[5]*/;
F[ 8] = /*J[ 8][0]*KJtD[0]+ J[ 8][1]*KJtD[1]+*/J[ 8][2]*KJtD[2]+
/*J[ 8][3]*KJtD[3]+*/J[ 8][4]*KJtD[4]+ J[ 8][5]*KJtD[5] ;
F[ 9] = J[ 9][0]*KJtD[0]+/*J[ 9][1]*KJtD[1]+ J[ 9][2]*KJtD[2]+*/
J[ 9][3]*KJtD[3]+/*J[ 9][4]*KJtD[4]+*/J[ 9][5]*KJtD[5] ;
F[10] = /*J[10][0]*KJtD[0]+*/J[10][1]*KJtD[1]+/*J[10][2]*KJtD[2]+*/
J[10][3]*KJtD[3]+ J[10][4]*KJtD[4] /*J[10][5]*KJtD[5]*/;
F[11] = /*J[11][0]*KJtD[0]+ J[11][1]*KJtD[1]+*/J[11][2]*KJtD[2]+
/*J[11][3]*KJtD[3]+*/J[11][4]*KJtD[4]+ J[11][5]*KJtD[5] ;
}
//////////////////////////////////////////////////////////////////////
//////////////////// small displacements method ////////////////////
//////////////////////////////////////////////////////////////////////
template<class DataTypes>
void TetrahedralCorotationalFEMForceField<DataTypes>::initSmall(int i, Index&a, Index&b, Index&c, Index&d)
{
const VecCoord X0=this->mstate->read(core::ConstVecCoordId::restPosition())->getValue();
type::vector<typename TetrahedralCorotationalFEMForceField<DataTypes>::TetrahedronInformation>& tetrahedronInf = *(tetrahedronInfo.beginEdit());
computeStrainDisplacement(tetrahedronInf[i].strainDisplacementTransposedMatrix, (X0)[a], (X0)[b], (X0)[c], (X0)[d] );
tetrahedronInfo.endEdit();
this->printStiffnessMatrix(i);////////////////////////////////////////////////////////////////
}
template<class DataTypes>
void TetrahedralCorotationalFEMForceField<DataTypes>::accumulateForceSmall( Vector& f, const Vector & p,Index elementIndex )
{
const core::topology::BaseMeshTopology::Tetrahedron t=m_topology->getTetrahedron(elementIndex);
const VecCoord& X0=this->mstate->read(core::ConstVecCoordId::restPosition())->getValue();
Index a = t[0];
Index b = t[1];
Index c = t[2];
Index d = t[3];
// displacements
Displacement D;
D[0] = 0;
D[1] = 0;
D[2] = 0;
D[3] = (X0)[b][0] - (X0)[a][0] - p[b][0]+p[a][0];
D[4] = (X0)[b][1] - (X0)[a][1] - p[b][1]+p[a][1];
D[5] = (X0)[b][2] - (X0)[a][2] - p[b][2]+p[a][2];
D[6] = (X0)[c][0] - (X0)[a][0] - p[c][0]+p[a][0];
D[7] = (X0)[c][1] - (X0)[a][1] - p[c][1]+p[a][1];
D[8] = (X0)[c][2] - (X0)[a][2] - p[c][2]+p[a][2];
D[9] = (X0)[d][0] - (X0)[a][0] - p[d][0]+p[a][0];
D[10] = (X0)[d][1] - (X0)[a][1] - p[d][1]+p[a][1];
D[11] = (X0)[d][2] - (X0)[a][2] - p[d][2]+p[a][2];
// compute force on element
Displacement F;
const type::vector<typename TetrahedralCorotationalFEMForceField<DataTypes>::TetrahedronInformation>& tetrahedronInf = tetrahedronInfo.getValue();
if(!_assembling.getValue())
{
computeForce( F, D,tetrahedronInf[elementIndex].materialMatrix,tetrahedronInf[elementIndex].strainDisplacementTransposedMatrix );
}
else
{
Transformation Rot;
Rot[0][0]=Rot[1][1]=Rot[2][2]=1;
Rot[0][1]=Rot[0][2]=0;
Rot[1][0]=Rot[1][2]=0;
Rot[2][0]=Rot[2][1]=0;
StiffnessMatrix JKJt,tmp;
computeStiffnessMatrix(JKJt,tmp,tetrahedronInf[elementIndex].materialMatrix,tetrahedronInf[elementIndex].strainDisplacementTransposedMatrix,Rot);
//erase the stiffness matrix at each time step
if(elementIndex==0)
{
for(Size i=0; i<_stiffnesses.size(); ++i)
{
_stiffnesses[i].resize(0);
}
}
for(int i=0; i<12; ++i)
{
int row = t[i/3]*3+i%3;
for(int j=0; j<12; ++j)
{
if(JKJt[i][j]!=0)
{
int col = t[j/3]*3+j%3;
// search if the vertex is already take into account by another element
typename CompressedValue::iterator result = _stiffnesses[row].end();
for(typename CompressedValue::iterator it=_stiffnesses[row].begin(); it!=_stiffnesses[row].end()&&result==_stiffnesses[row].end(); ++it)
{
if( (*it).first == col )
result = it;
}
if( result==_stiffnesses[row].end() )
_stiffnesses[row].push_back( Col_Value(col,JKJt[i][j] ) );
else
(*result).second += JKJt[i][j];
}
}
}
F = JKJt * D;
}
f[a] += Deriv( F[0], F[1], F[2] );
f[b] += Deriv( F[3], F[4], F[5] );
f[c] += Deriv( F[6], F[7], F[8] );
f[d] += Deriv( F[9], F[10], F[11] );
}
template<class DataTypes>
void TetrahedralCorotationalFEMForceField<DataTypes>::applyStiffnessSmall( Vector& f, const Vector& x, int i, Index a, Index b, Index c, Index d, SReal fact )
{
Displacement X;
X[0] = x[a][0];
X[1] = x[a][1];
X[2] = x[a][2];
X[3] = x[b][0];
X[4] = x[b][1];
X[5] = x[b][2];
X[6] = x[c][0];
X[7] = x[c][1];
X[8] = x[c][2];
X[9] = x[d][0];
X[10] = x[d][1];
X[11] = x[d][2];
Displacement F;
const type::vector<typename TetrahedralCorotationalFEMForceField<DataTypes>::TetrahedronInformation>& tetrahedronInf = tetrahedronInfo.getValue();
computeForce( F, X,tetrahedronInf[i].materialMatrix,tetrahedronInf[i].strainDisplacementTransposedMatrix, fact);
f[a] += Deriv( -F[0], -F[1], -F[2] );
f[b] += Deriv( -F[3], -F[4], -F[5] );
f[c] += Deriv( -F[6], -F[7], -F[8] );
f[d] += Deriv( -F[9], -F[10], -F[11] );
}
//////////////////////////////////////////////////////////////////////
//////////////////// large displacements method ////////////////////
//////////////////////////////////////////////////////////////////////
template<class DataTypes>
inline void TetrahedralCorotationalFEMForceField<DataTypes>::computeRotationLarge( Transformation &r, const Vector &p, const Index &a, const Index &b, const Index &c)
{
// first vector on first edge
// second vector in the plane of the two first edges
// third vector orthogonal to first and second
const Coord edgex = (p[b]-p[a]).normalized();
Coord edgey = p[c]-p[a];
const Coord edgez = cross( edgex, edgey ).normalized();
edgey = cross( edgez, edgex ); //edgey is unit vector because edgez and edgex are orthogonal unit vectors
r[0][0] = edgex[0];
r[0][1] = edgex[1];
r[0][2] = edgex[2];
r[1][0] = edgey[0];
r[1][1] = edgey[1];
r[1][2] = edgey[2];
r[2][0] = edgez[0];
r[2][1] = edgez[1];
r[2][2] = edgez[2];
}
template <class DataTypes>
inline void TetrahedralCorotationalFEMForceField<DataTypes>::getElementRotation(Transformation& R, Index elementIdx)
{
type::vector<TetrahedronInformation>& tetraInf = *(tetrahedronInfo.beginEdit());
TetrahedronInformation *tinfo = &tetraInf[elementIdx];
Transformation r01,r21;
r01=tinfo->initialTransformation;
r21=tinfo->rotation*r01;
R=r21;
}
template <class DataTypes>
inline void TetrahedralCorotationalFEMForceField<DataTypes>::getRotation(Transformation& R, Index nodeIdx)
{
const type::vector<typename TetrahedralCorotationalFEMForceField<DataTypes>::TetrahedronInformation>& tetraInf = tetrahedronInfo.getValue();
const int numNeiTetra=m_topology->getTetrahedraAroundVertex(nodeIdx).size();
Transformation r;
r.clear();
for(int i=0; i<numNeiTetra; i++)
{
int tetraIdx=m_topology->getTetrahedraAroundVertex(nodeIdx)[i];
const TetrahedronInformation *tinfo = &tetraInf[tetraIdx];
Transformation r01,r21;
r01=tinfo->initialTransformation;
r21=tinfo->rotation*r01;
r+=r21;
}
R=r*(1.0f/numNeiTetra);
//orthogonalization
Coord ex,ey,ez;
for(int i=0; i<3; i++)
{
ex[i]=R[0][i];
ey[i]=R[1][i];
}
ex.normalize();
ey.normalize();
ez=cross(ex,ey);
ez.normalize();
ey=cross(ez,ex);
ey.normalize();
for(int i=0; i<3; i++)
{
R[0][i]=ex[i];
R[1][i]=ey[i];
R[2][i]=ez[i];
}
}
template <class DataTypes>
inline void TetrahedralCorotationalFEMForceField<DataTypes>::getElementStiffnessMatrix(Real* stiffness, Index elementIndex)
{
const type::vector<typename TetrahedralCorotationalFEMForceField<DataTypes>::TetrahedronInformation>& tetraInf = tetrahedronInfo.getValue();
Transformation Rot;
StiffnessMatrix JKJt,tmp;
Rot[0][0]=Rot[1][1]=Rot[2][2]=1;
Rot[0][1]=Rot[0][2]=0;
Rot[1][0]=Rot[1][2]=0;
Rot[2][0]=Rot[2][1]=0;
computeStiffnessMatrix(JKJt,tmp,tetraInf[elementIndex].materialMatrix, tetraInf[elementIndex].strainDisplacementTransposedMatrix,Rot);
for(int i=0; i<12; i++)
{
for(int j=0; j<12; j++)
stiffness[i*12+j]=JKJt(i,j);
}
}
template <class DataTypes>
inline void TetrahedralCorotationalFEMForceField<DataTypes>::getElementStiffnessMatrix(Real* stiffness, core::topology::BaseMeshTopology::Tetra& te)
{
const VecCoord X0=this->mstate->read(core::ConstVecCoordId::restPosition())->getValue();
Index a = te[0];
Index b = te[1];
Index c = te[2];
Index d = te[3];
Transformation R_0_1;
computeRotationLarge( R_0_1, (X0), a, b, c);
MaterialStiffness materialMatrix;
StrainDisplacementTransposed strainMatrix;
type::fixed_array<Coord,4> rotatedInitialElements;
rotatedInitialElements[0] = R_0_1*(X0)[a];
rotatedInitialElements[1] = R_0_1*(X0)[b];
rotatedInitialElements[2] = R_0_1*(X0)[c];
rotatedInitialElements[3] = R_0_1*(X0)[d];
rotatedInitialElements[1] -= rotatedInitialElements[0];
rotatedInitialElements[2] -= rotatedInitialElements[0];
rotatedInitialElements[3] -= rotatedInitialElements[0];
rotatedInitialElements[0] = Coord(0,0,0);
computeMaterialStiffness(materialMatrix,a,b,c,d);
computeStrainDisplacement(strainMatrix, rotatedInitialElements[0], rotatedInitialElements[1], rotatedInitialElements[2], rotatedInitialElements[3]);
Transformation Rot;
StiffnessMatrix JKJt,tmp;
Rot[0][0]=Rot[1][1]=Rot[2][2]=1;
Rot[0][1]=Rot[0][2]=0;
Rot[1][0]=Rot[1][2]=0;
Rot[2][0]=Rot[2][1]=0;
computeStiffnessMatrix(JKJt, tmp, materialMatrix, strainMatrix, Rot);
for(int i=0; i<12; i++)
{
for(int j=0; j<12; j++)
stiffness[i*12+j]=JKJt(i,j);
}
}
template<class DataTypes>
void TetrahedralCorotationalFEMForceField<DataTypes>::initLarge(int i, Index&a, Index&b, Index&c, Index&d)
{
// Rotation matrix (initial Tetrahedre/world)
// first vector on first edge
// second vector in the plane of the two first edges
// third vector orthogonal to first and second
const VecCoord& X0=this->mstate->read(core::ConstVecCoordId::restPosition())->getValue();
Transformation R_0_1;
computeRotationLarge( R_0_1, (X0), a, b, c);
type::vector<typename TetrahedralCorotationalFEMForceField<DataTypes>::TetrahedronInformation>& tetrahedronInf = *(tetrahedronInfo.beginEdit());
tetrahedronInf[i].rotatedInitialElements[0] = R_0_1*(X0)[a];
tetrahedronInf[i].rotatedInitialElements[1] = R_0_1*(X0)[b];
tetrahedronInf[i].rotatedInitialElements[2] = R_0_1*(X0)[c];
tetrahedronInf[i].rotatedInitialElements[3] = R_0_1*(X0)[d];
tetrahedronInf[i].initialTransformation = R_0_1;
tetrahedronInf[i].rotatedInitialElements[1] -= tetrahedronInf[i].rotatedInitialElements[0];
tetrahedronInf[i].rotatedInitialElements[2] -= tetrahedronInf[i].rotatedInitialElements[0];
tetrahedronInf[i].rotatedInitialElements[3] -= tetrahedronInf[i].rotatedInitialElements[0];
tetrahedronInf[i].rotatedInitialElements[0] = Coord(0,0,0);
computeStrainDisplacement( tetrahedronInf[i].strainDisplacementTransposedMatrix,tetrahedronInf[i].rotatedInitialElements[0], tetrahedronInf[i].rotatedInitialElements[1],tetrahedronInf[i].rotatedInitialElements[2],tetrahedronInf[i].rotatedInitialElements[3] );
tetrahedronInfo.endEdit();
}
template<class DataTypes>
void TetrahedralCorotationalFEMForceField<DataTypes>::accumulateForceLarge( Vector& f, const Vector & p, Index elementIndex )
{
const core::topology::BaseMeshTopology::Tetrahedron t=m_topology->getTetrahedron(elementIndex);
type::vector<typename TetrahedralCorotationalFEMForceField<DataTypes>::TetrahedronInformation>& tetrahedronInf = *(tetrahedronInfo.beginEdit());
// Rotation matrix (deformed and displaced Tetrahedron/world)
Transformation R_0_2;
computeRotationLarge( R_0_2, p, t[0],t[1],t[2]);
tetrahedronInf[elementIndex].rotation.transpose(R_0_2);
// positions of the deformed and displaced Tetrahedron in its frame
type::fixed_array<Coord,4> deforme;
for(int i=0; i<4; ++i)
deforme[i] = R_0_2*p[t[i]];
deforme[1][0] -= deforme[0][0];
deforme[2][0] -= deforme[0][0];
deforme[2][1] -= deforme[0][1];
deforme[3] -= deforme[0];
// displacement
Displacement D;
D[0] = 0;
D[1] = 0;
D[2] = 0;
D[3] = tetrahedronInf[elementIndex].rotatedInitialElements[1][0] - deforme[1][0];
D[4] = 0;
D[5] = 0;
D[6] = tetrahedronInf[elementIndex].rotatedInitialElements[2][0] - deforme[2][0];
D[7] = tetrahedronInf[elementIndex].rotatedInitialElements[2][1] - deforme[2][1];
D[8] = 0;
D[9] = tetrahedronInf[elementIndex].rotatedInitialElements[3][0] - deforme[3][0];
D[10] = tetrahedronInf[elementIndex].rotatedInitialElements[3][1] - deforme[3][1];
D[11] =tetrahedronInf[elementIndex].rotatedInitialElements[3][2] - deforme[3][2];
Displacement F;
if(_updateStiffnessMatrix.getValue())
{
StrainDisplacementTransposed& J = tetrahedronInf[elementIndex].strainDisplacementTransposedMatrix;
J[0][0] = J[1][3] = J[2][5] = ( - deforme[2][1]*deforme[3][2] );
J[1][1] = J[0][3] = J[2][4] = ( deforme[2][0]*deforme[3][2] - deforme[1][0]*deforme[3][2] );
J[2][2] = J[0][5] = J[1][4] = ( deforme[2][1]*deforme[3][0] - deforme[2][0]*deforme[3][1] + deforme[1][0]*deforme[3][1] - deforme[1][0]*deforme[2][1] );
J[3][0] = J[4][3] = J[5][5] = ( deforme[2][1]*deforme[3][2] );
J[4][1] = J[3][3] = J[5][4] = ( - deforme[2][0]*deforme[3][2] );
J[5][2] = J[3][5] = J[4][4] = ( - deforme[2][1]*deforme[3][0] + deforme[2][0]*deforme[3][1] );
J[7][1] = J[6][3] = J[8][4] = ( deforme[1][0]*deforme[3][2] );
J[8][2] = J[6][5] = J[7][4] = ( - deforme[1][0]*deforme[3][1] );
J[11][2] = J[9][5] = J[10][4] = ( deforme[1][0]*deforme[2][1] );
}
if(!_assembling.getValue())
{
// compute force on element
computeForce( F, D, tetrahedronInf[elementIndex].materialMatrix, tetrahedronInf[elementIndex].strainDisplacementTransposedMatrix);
for(int i=0; i<12; i+=3)
f[t[i/3]] += tetrahedronInf[elementIndex].rotation * Deriv( F[i], F[i+1], F[i+2] );
}
else
{
tetrahedronInf[elementIndex].strainDisplacementTransposedMatrix[6][0] = 0;
tetrahedronInf[elementIndex].strainDisplacementTransposedMatrix[9][0] = 0;
tetrahedronInf[elementIndex].strainDisplacementTransposedMatrix[10][1] = 0;
StiffnessMatrix RJKJt, RJKJtRt;
computeStiffnessMatrix(RJKJt,RJKJtRt,tetrahedronInf[elementIndex].materialMatrix, tetrahedronInf[elementIndex].strainDisplacementTransposedMatrix,tetrahedronInf[elementIndex].rotation);
//erase the stiffness matrix at each time step
if(elementIndex==0)
{
for(Size i=0; i<_stiffnesses.size(); ++i)
{