void NeoHookeanMaterialNonLinear<Mesh>::computeStiffness ( const vector_Type& sol,
Real /*factor*/,
const dataPtr_Type& dataMaterial,
const mapMarkerVolumesPtr_Type mapsMarkerVolumes,
const displayerPtr_Type& displayer )
{
this->M_stiff.reset (new vector_Type (*this->M_localMap) );
displayer->leaderPrint (" \n******************************************************************\n ");
displayer->leaderPrint (" Non-Linear S- Computing the Neo-Hookean nonlinear stiffness vector" );
displayer->leaderPrint (" \n******************************************************************\n ");
UInt totalDof = this->M_FESpace->dof().numTotalDof();
UInt dim = this->M_FESpace->dim();
VectorElemental dk_loc ( this->M_FESpace->fe().nbFEDof(), nDimensions );
//vector_Type disp(sol);
vector_Type dRep (sol, Repeated);
mapIterator_Type it;
for ( it = (*mapsMarkerVolumes).begin(); it != (*mapsMarkerVolumes).end(); it++ )
{
//Given the marker pointed by the iterator, let's extract the material parameters
UInt marker = it->first;
Real mu = dataMaterial->mu (marker);
Real bulk = dataMaterial->bulk (marker);
for ( UInt j (0); j < it->second.size(); j++ )
{
this->M_FESpace->fe().updateFirstDerivQuadPt ( * (it->second[j]) );
UInt eleID = this->M_FESpace->fe().currentLocalId();
for ( UInt iNode = 0 ; iNode < ( UInt ) this->M_FESpace->fe().nbFEDof() ; iNode++ )
{
UInt iloc = this->M_FESpace->fe().patternFirst ( iNode );
for ( UInt iComp = 0; iComp < nDimensions; ++iComp )
{
UInt ig = this->M_FESpace->dof().localToGlobalMap ( eleID, iloc ) + iComp * dim + this->M_offset;
dk_loc[ iloc + iComp * this->M_FESpace->fe().nbFEDof() ] = dRep[ig];
}
}
this->M_elvecK->zero();
computeKinematicsVariables ( dk_loc );
//! Stiffness for non-linear terms of the Neo-Hookean model
/*!
The results of the integrals are stored at each step into elvecK, until to build K matrix of the bilinear form
*/
//! Volumetric part
/*!
Source term Pvol: int { bulk /2* (J1^2 - J1 + log(J1) ) * 1/J1 * (CofF1 : \nabla v) }
*/
AssemblyElementalStructure::source_Pvol ( 0.5 * bulk, (*M_CofFk), (*M_Jack),
*this->M_elvecK, this->M_FESpace->fe() );
//! Isochoric part
/*!
Source term P1iso_NH
*/
AssemblyElementalStructure::source_P1iso_NH ( mu, (*M_CofFk) , (*M_Fk), (*M_Jack), (*M_trCisok) ,
*this->M_elvecK, this->M_FESpace->fe() );
for ( UInt ic = 0; ic < nDimensions; ++ic )
{
/*!
M_elvecK is assemble into *vec_stiff vector that is recall
from updateSystem(matrix_ptrtype& mat_stiff, vector_ptr_type& vec_stiff)
*/
assembleVector ( *this->M_stiff,
*this->M_elvecK,
this->M_FESpace->fe(),
this->M_FESpace->dof(),
ic, this->M_offset + ic * totalDof );
}
}
}
this->M_stiff->globalAssemble();
}
void NeoHookeanMaterialNonLinear<Mesh>::updateNonLinearJacobianTerms ( matrixPtr_Type& jacobian,
const vector_Type& disp,
const dataPtr_Type& dataMaterial,
const mapMarkerVolumesPtr_Type mapsMarkerVolumes,
const displayerPtr_Type& displayer )
{
displayer->leaderPrint (" Non-Linear S- updating non linear terms in the Jacobian Matrix (Neo-Hookean)");
UInt totalDof = this->M_FESpace->dof().numTotalDof();
VectorElemental dk_loc (this->M_FESpace->fe().nbFEDof(), nDimensions);
vector_Type dRep (disp, Repeated);
//! Number of displacement components
UInt nc = nDimensions;
//! Nonlinear part of jacobian
//! loop on volumes: assembling source term
mapIterator_Type it;
for ( it = (*mapsMarkerVolumes).begin(); it != (*mapsMarkerVolumes).end(); it++ )
{
//Given the marker pointed by the iterator, let's extract the material parameters
UInt marker = it->first;
Real mu = dataMaterial->mu (marker);
Real bulk = dataMaterial->bulk (marker);
for ( UInt j (0); j < it->second.size(); j++ )
{
this->M_FESpace->fe().updateFirstDerivQuadPt ( * (it->second[j]) );
UInt eleID = this->M_FESpace->fe().currentLocalId();
for ( UInt iNode = 0; iNode < ( UInt ) this->M_FESpace->fe().nbFEDof(); iNode++ )
{
UInt iloc = this->M_FESpace->fe().patternFirst ( iNode );
for ( UInt iComp = 0; iComp < nDimensions; ++iComp )
{
UInt ig = this->M_FESpace->dof().localToGlobalMap ( eleID, iloc ) + iComp * this->M_FESpace->dim() + this->M_offset;
dk_loc[iloc + iComp * this->M_FESpace->fe().nbFEDof()] = dRep[ig];
}
}
this->M_elmatK->zero();
//! Computes F, Cof(F), J = det(F), Tr(C)
computeKinematicsVariables ( dk_loc );
//! Stiffness for non-linear terms of the Neo-Hookean model
/*!
The results of the integrals are stored at each step into elmatK, until to build K matrix of the bilinear form
*/
//! VOLUMETRIC PART
//! 1. Stiffness matrix: int { 1/2 * bulk * ( 2 - 1/J + 1/J^2 ) * ( CofF : \nabla \delta ) (CofF : \nabla v) }
AssemblyElementalStructure::stiff_Jac_Pvol_1term ( 0.5 * bulk, (*M_CofFk), (*M_Jack),
*this->M_elmatK, this->M_FESpace->fe() );
//! 2. Stiffness matrix: int { 1/2 * bulk * ( 1/J- 1 - log(J)/J^2 ) * ( CofF [\nabla \delta]^t CofF ) : \nabla v }
AssemblyElementalStructure::stiff_Jac_Pvol_2term ( 0.5 * bulk, (*M_CofFk), (*M_Jack),
*this->M_elmatK, this->M_FESpace->fe() );
//! ISOCHORIC PART
//! 1. Stiffness matrix : int { -2/3 * mu * J^(-5/3) *( CofF : \nabla \delta ) ( F : \nabla \v ) }
AssemblyElementalStructure::stiff_Jac_P1iso_NH_1term ( (-2.0 / 3.0) * mu, (*M_CofFk), (*M_Fk), (*M_Jack),
*this->M_elmatK, this->M_FESpace->fe() );
//! 2. Stiffness matrix : int { 2/9 * mu * ( Ic_iso / J^2 )( CofF : \nabla \delta ) ( CofF : \nabla \v ) }
AssemblyElementalStructure::stiff_Jac_P1iso_NH_2term ( (2.0 / 9.0) * mu, (*M_CofFk), (*M_Jack), (*M_trCisok),
*this->M_elmatK, this->M_FESpace->fe() );
//! 3. Stiffness matrix : int { mu * J^(-2/3) (\nabla \delta : \nabla \v)}
AssemblyElementalStructure::stiff_Jac_P1iso_NH_3term ( mu, (*M_Jack), *this->M_elmatK, this->M_FESpace->fe() );
//! 4. Stiffness matrix : int { -2/3 * mu * J^(-5/3) ( F : \nabla \delta ) ( CofF : \nabla \v ) }
AssemblyElementalStructure::stiff_Jac_P1iso_NH_4term ( (-2.0 / 3.0) * mu, (*M_CofFk), (*M_Fk), (*M_Jack),
*this->M_elmatK, this->M_FESpace->fe() );
//! 5. Stiffness matrix : int { 1/3 * mu * J^(-2) * Ic_iso * (CofF [\nabla \delta]^t CofF ) : \nabla \v }
AssemblyElementalStructure::stiff_Jac_P1iso_NH_5term ( (1.0 / 3.0) * mu, (*M_CofFk), (*M_Jack), (*M_trCisok),
*this->M_elmatK, this->M_FESpace->fe() );
//! assembling
for ( UInt ic = 0; ic < nc; ++ic )
{
for ( UInt jc = 0; jc < nc; jc++ )
{
assembleMatrix ( *jacobian,
*this->M_elmatK,
this->M_FESpace->fe(),
this->M_FESpace->dof(),
ic, jc,
this->M_offset + ic * totalDof, this->M_offset + jc * totalDof );
}
}
}
}
}