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Elasticity.C
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// $Id$
//==============================================================================
//!
//! \file Elasticity.C
//!
//! \date Nov 12 2009
//!
//! \author Knut Morten Okstad / SINTEF
//!
//! \brief Base class for linear and nonlinear elasticity problems.
//!
//==============================================================================
#include "Elasticity.h"
#include "GlobalIntegral.h"
#include "IsotropicTextureMat.h"
#include "FiniteElement.h"
#include "HHTMats.h"
#include "BDFMats.h"
#include "ElmNorm.h"
#include "AnaSol.h"
#include "TensorFunction.h"
#include "Vec3Oper.h"
#include "Utilities.h"
#include "VTF.h"
#include "IFEM.h"
#include "tinyxml2.h"
#include <iomanip>
#ifndef epsR
//! \brief Zero tolerance for the radial coordinate.
#define epsR 1.0e-16
#endif
bool Elasticity::wantStrain = false;
bool Elasticity::wantPrincipalStress = false;
bool Elasticity::asolProject = false;
Elasticity::Elasticity (unsigned short int n, bool ax) : axiSymmetry(ax)
{
nsd = axiSymmetry ? 2 : n;
nDF = axiSymmetry ? 3 : nsd;
npv = nsd; // Number of primary unknowns per node
// Assign default material properties, in case of no user-input
static LinIsotropic defaultMat;
material = &defaultMat;
locSys = nullptr;
tracFld = nullptr;
fluxFld = nullptr;
bodyFld = nullptr;
pDirBuf = nullptr;
dualRHS = nullptr;
myReacI = nullptr;
gamma = 1.0;
calcMaxVal = true;
}
Elasticity::~Elasticity ()
{
if (locSys) delete locSys;
if (pDirBuf) delete pDirBuf;
}
bool Elasticity::parse (const tinyxml2::XMLElement* elem)
{
if (this->ElasticBase::parse(elem))
return true;
else if (!strcasecmp(elem->Value(),"stabilization"))
{
utl::getAttribute(elem,"gamma",gamma);
IFEM::cout <<"\tStabilization parameter "<< gamma << std::endl;
}
else if (!strcasecmp(elem->Value(),"localsystem"))
this->parseLocalSystem(elem);
else
return false;
return true;
}
Material* Elasticity::parseMatProp (char* cline, bool planeStrain)
{
double E = atof(strtok(cline," "));
double nu = atof(strtok(nullptr," "));
double rho = atof(strtok(nullptr," "));
IFEM::cout << E <<" "<< nu <<" "<< rho << std::endl;
material = new LinIsotropic(E,nu,rho,!planeStrain,axiSymmetry);
return material;
}
Material* Elasticity::parseMatProp (const tinyxml2::XMLElement* elem, bool planeStrain)
{
if (!strcasecmp(elem->Value(),"texturematerial"))
material = new IsotropicTextureMat(!planeStrain,axiSymmetry);
else
material = new LinIsotropic(!planeStrain,axiSymmetry);
material->parse(elem);
return material;
}
void Elasticity::printLog () const
{
utl::LogStream& os = IFEM::cout;
if (axiSymmetry)
os <<"Axial-symmetric Elasticity problem\n";
os <<"Elasticity: "<< nsd <<"D, gravity =";
for (unsigned short int d = 0; d < nsd; d++)
os <<" "<< gravity[d];
os << std::endl;
material->printLog();
}
void Elasticity::setMaterial (Material* mat)
{
if (mat == material) return;
#ifdef INT_DEBUG
if (mat && material)
{
IFEM::cout <<"\nElasticity::setMaterial: Switching material properties:\n";
mat->printLog();
}
#endif
material = mat;
}
void Elasticity::addExtrFunction (FunctionBase* extr)
{
if (dynamic_cast<VecFunc*>(extr))
{
dualFld.push_back(extr);
this->setNoSolutions(1+dualFld.size(),true);
if (!dualRHS) dualRHS = extr;
}
else
{
dualFld.clear();
dualRHS = nullptr;
}
}
LocalIntegral* Elasticity::getLocalIntegral (size_t nen, size_t iEl,
bool neumann) const
{
ElmMats* result = nullptr;
if (this->inActive(iEl))
return result; // element is not in current material group
if (m_mode != SIM::DYNAMIC) // linear or nonlinear (quasi-)static analysis
result = new ElmMats();
else if (bdf)
result = new BDFMats(*bdf);
else if (intPrm[3] > 0.0) // linear dynamic analysis
result = new NewmarkMats(intPrm[0], intPrm[1], intPrm[2], intPrm[3],
intPrm[4] == 2.0);
else // nonlinear dynamic analysis
result = new HHTMats(intPrm[2], intPrm[0], intPrm[1], intPrm[4] != 1.0);
switch (m_mode)
{
case SIM::STATIC:
case SIM::MASS_ONLY:
result->rhsOnly = neumann;
result->withLHS = !neumann;
result->resize(neumann ? 0 : 1, neumann || dS == 0 ? 1 : dS, nsd);
break;
case SIM::ARCLEN:
result->rhsOnly = neumann;
result->withLHS = !neumann;
result->resize(neumann ? 0 : 1, 2, nsd);
break;
case SIM::DYNAMIC:
result->rhsOnly = neumann;
result->withLHS = !neumann;
result->resize(neumann ? 0 : (intPrm[3] >= 0.0 ? 3 : 4),
intPrm[4] == 1.0 ? 3 : (neumann || intPrm[3] > 0.0 ? 1:2), nsd);
break;
case SIM::VIBRATION:
case SIM::BUCKLING:
result->resize(2,0);
break;
case SIM::STIFF_ONLY:
result->resize(1,0);
break;
case SIM::RHS_ONLY:
case SIM::INT_FORCES:
result->resize(neumann ? 0 : 1, 1, nsd);
case SIM::RECOVERY:
result->rhsOnly = true;
result->withLHS = false;
break;
default:
;
}
result->redim(nsd*nen);
result->Aname = matNames;
result->Bname = vecNames;
return result;
}
bool Elasticity::hasBoundaryTerms () const
{
return (m_mode >= SIM::STATIC && m_mode <= SIM::DYNAMIC) ||
(m_mode >= SIM::RHS_ONLY && m_mode <= SIM::INT_FORCES) ||
m_mode == SIM::NORMS;
}
void Elasticity::setSecondaryInt (GlobalIntegral* gq)
{
delete myReacI;
myReacI = gq;
}
GlobalIntegral& Elasticity::getGlobalInt (GlobalIntegral* gq) const
{
if (m_mode == SIM::RHS_ONLY && myReacI)
return *myReacI;
return this->ElasticBase::getGlobalInt(gq);
}
Vec3 Elasticity::getTraction (const Vec3& X, const Vec3& n, bool grd) const
{
if (fluxFld)
return grd ? fluxFld->timeDerivative(X) : (*fluxFld)(X);
else if (tracFld)
return grd ? tracFld->timeDerivative(X,n) : (*tracFld)(X,n);
else
return Vec3();
}
Vec3 Elasticity::getBodyforce (const Vec3& X, bool grd) const
{
if (grd)
return bodyFld ? bodyFld->deriv(X,4) : Vec3();
Vec3 f(gravity);
f *= material->getMassDensity(X);
if (bodyFld)
f += (*bodyFld)(X);
return f;
}
bool Elasticity::haveLoads () const
{
if (tracFld) return true;
if (fluxFld) return true;
if (bodyFld) return true;
for (unsigned short int i = 0; i < nsd; i++)
if (gravity[i] != 0.0)
return material->getMassDensity(Vec3()) != 0.0;
return false;
}
void Elasticity::initIntegration (size_t, size_t nBp)
{
tracVal.clear();
tracVal.resize(nBp,std::make_pair(Vec3(),Vec3()));
}
void Elasticity::initResultPoints (double, bool prinDir)
{
if (wantPrincipalStress && prinDir)
{
if (!pDirBuf) pDirBuf = new Vec3Vec();
pDirBuf->clear();
}
else if (pDirBuf)
{
delete pDirBuf;
pDirBuf = nullptr;
}
}
bool Elasticity::writeGlvT (VTF* vtf, int iStep, int& geoBlk, int& nBlock) const
{
if (tracVal.empty())
return true;
else if (!vtf)
return false;
// Write boundary tractions as discrete point vectors to the VTF-file
return vtf->writeVectors(tracVal,geoBlk,++nBlock,"Tractions",iStep);
}
/*!
The strain-displacement matrix for a continuum element is formally defined as:
\f[ \mbox{In 3D,~~}
[B] = \left[\begin{array}{ccc}
\frac{\partial}{\partial x} & 0 & 0 \\
0 & \frac{\partial}{\partial y} & 0 \\
0 & 0 & \frac{\partial}{\partial z} \\
\frac{\partial}{\partial y} & \frac{\partial}{\partial x} & 0 \\
0 & \frac{\partial}{\partial z} & \frac{\partial}{\partial y} \\
\frac{\partial}{\partial z} & 0 & \frac{\partial}{\partial x}
\end{array}\right] [N] \hskip 5mm\mbox{and in 2D,~~}
[B] = \left[\begin{array}{ccc}
\frac{\partial}{\partial x} & 0 \\
0 & \frac{\partial}{\partial y} \\
\frac{\partial}{\partial y} & \frac{\partial}{\partial x}
\end{array}\right] [N]
\f]
where
[\a N ] is the element basis functions arranged in a [nsd][nsd*NENOD] matrix.
*/
bool Elasticity::formBmatrix (Matrix& Bmat, const Matrix& dNdX) const
{
const size_t nenod = dNdX.rows();
const size_t nstrc = nsd*(nsd+1)/2;
Bmat.resize(nstrc*nsd,nenod,true);
if (dNdX.cols() < nsd)
{
std::cerr <<" *** Elasticity::formBmatrix: Invalid dimension on dNdX, "
<< dNdX.rows() <<"x"<< dNdX.cols() <<"."<< std::endl;
return false;
}
#define INDEX(i,j) i+nstrc*(j-1)
switch (nsd) {
case 1:
// Strain-displacement matrix for 1D elements:
//
// [B] = | d/dx | * [N]
for (size_t i = 1; i <= nenod; i++)
Bmat(1,i) = dNdX(i,1);
break;
case 2:
// Strain-displacement matrix for 2D elements:
//
// | d/dx 0 |
// [B] = | 0 d/dy | * [N]
// | d/dy d/dx |
for (size_t i = 1; i <= nenod; i++)
{
// Normal strain part
Bmat(INDEX(1,1),i) = dNdX(i,1);
Bmat(INDEX(2,2),i) = dNdX(i,2);
// Shear strain part
Bmat(INDEX(3,1),i) = dNdX(i,2);
Bmat(INDEX(3,2),i) = dNdX(i,1);
}
break;
case 3:
// Strain-displacement matrix for 3D elements:
//
// | d/dx 0 0 |
// | 0 d/dy 0 |
// [B] = | 0 0 d/dz | * [N]
// | d/dy d/dx 0 |
// | 0 d/dz d/dy |
// | d/dz 0 d/dx |
for (size_t i = 1; i <= nenod; i++)
{
// Normal strain part
Bmat(INDEX(1,1),i) = dNdX(i,1);
Bmat(INDEX(2,2),i) = dNdX(i,2);
Bmat(INDEX(3,3),i) = dNdX(i,3);
// Shear strain part
Bmat(INDEX(4,1),i) = dNdX(i,2);
Bmat(INDEX(4,2),i) = dNdX(i,1);
Bmat(INDEX(5,2),i) = dNdX(i,3);
Bmat(INDEX(5,3),i) = dNdX(i,2);
Bmat(INDEX(6,1),i) = dNdX(i,3);
Bmat(INDEX(6,3),i) = dNdX(i,1);
}
break;
default:
std::cerr <<" *** Elasticity::formBmatrix: nsd="<< nsd << std::endl;
return false;
}
#undef INDEX
Bmat.resize(nstrc,nsd*nenod);
return true;
}
/*!
The strain-displacement matrix for an axially symmetric 3D continuum element
is formally defined as:
\f[
[B] = \left[\begin{array}{cc}
\frac{\partial}{\partial r} & 0 \\
0 & \frac{\partial}{\partial z} \\
\frac{1}{r} & 0 \\
\frac{\partial}{\partial z} & \frac{\partial}{\partial r}
\end{array}\right] [N]
\f]
where
[\a N ] is the element basis functions arranged in a [2][2*NENOD] matrix.
*/
bool Elasticity::formBmatrix (Matrix& Bmat, const Vector& N, const Matrix& dNdX,
const double r) const
{
const size_t nenod = N.size();
Bmat.resize(8,nenod,true);
if (dNdX.cols() < 2)
{
std::cerr <<" *** Elasticity::formBmatrix: Invalid dimension on dNdX, "
<< dNdX.rows() <<"x"<< dNdX.cols() <<"."<< std::endl;
return false;
}
else if (r < -epsR)
{
std::cerr <<" *** Elasticity::formBmatrix: Invalid point r < 0, "
<< r << std::endl;
return false;
}
#define INDEX(i,j) i+4*(j-1)
// Strain-displacement matrix for 3D axisymmetric elements:
//
// | d/dr 0 |
// [B] = | 0 d/dz | * [N]
// | 1/r 0 |
// | d/dz d/dr |
for (size_t i = 1; i <= nenod; i++)
{
// Normal strain part
Bmat(INDEX(1,1),i) = dNdX(i,1);
Bmat(INDEX(2,2),i) = dNdX(i,2);
// Hoop strain part
Bmat(INDEX(3,1),i) = r <= epsR ? dNdX(i,1) : N(i)/r;
// Shear strain part
Bmat(INDEX(4,1),i) = dNdX(i,2);
Bmat(INDEX(4,2),i) = dNdX(i,1);
}
#undef INDEX
Bmat.resize(4,2*nenod);
return true;
}
bool Elasticity::formDefGradient (const Vector& eV, const Vector& N,
const Matrix& dNdX, double r, Tensor& F,
bool gradOnly) const
{
F = gradOnly ? 0.0 : 1.0;
if (eV.empty())
return true; // Initial state, deformation gradient is identity tensor
const size_t nenod = dNdX.rows();
if (eV.size() != nsd*nenod || dNdX.cols() < nsd)
{
std::cerr <<" *** Elasticity::formDefGradient: Invalid dimension,"
<<" dNdX("<< nenod <<","<< dNdX.cols() <<")"<< std::endl;
return false;
}
// Compute the deformation gradient, [F] = [I] + [dudX] = [I] + [dNdX]*[u].
// Notice that the matrix multiplication method used here treats the element
// displacement vector, *eV, as a matrix whose number of columns equals the
// number of rows in the matrix dNdX.
Matrix dUdX;
if (!dUdX.multiplyMat(eV,dNdX)) // dUdX = Grad{u} = eV*dNdX
return false;
// Cannot use operator= here, in case F is of higher dimension than dUdX
for (size_t i = 1; i <= dUdX.rows(); i++)
for (size_t j = 1; j <= dUdX.cols(); j++)
F(i,j) += dUdX(i,j);
// Add the dU/r term to the F(3,3)-term for axisymmetric problems
if (axiSymmetry && r > epsR && !gradOnly)
F(3,3) += eV.dot(N,0,nsd)/r;
#if INT_DEBUG > 0
std::cout <<"Elasticity::eV ="<< eV
<<"Elasticity::F =\n"<< F;
#endif
return true;
}
bool Elasticity::kinematics (const Vector& eV,
const Vector& N, const Matrix& dNdX, double r,
Matrix& B, Tensor&, SymmTensor& eps) const
{
// Evaluate the strain-displacement matrix, B
if (axiSymmetry)
{
if (!this->formBmatrix(B,N,dNdX,r))
return false;
}
else
{
if (!this->formBmatrix(B,dNdX))
return false;
}
if (eV.empty() || eps.dim() == 0)
return true;
// Evaluate the strains
return B.multiply(eV,eps); // eps = B*eV
}
void Elasticity::formKG (Matrix& EM, const Vector& N, const Matrix& dNdX,
double r, const Tensor& sigma, double detJW) const
{
#if INT_DEBUG > 3
std::cout <<"Elasticity::sigma =\n"<< sigma
<<"Elasticity::kg =";
#endif
unsigned short int i, j;
double kgrr = axiSymmetry && r > 0.0 ? sigma(3,3)/(r*r) : 0.0;
for (size_t a = 1; a <= dNdX.rows(); a++)
for (size_t b = 1; b <= dNdX.rows(); b++)
{
double kg = 0.0;
for (i = 1; i <= nsd; i++)
for (j = 1; j <= nsd; j++)
kg += dNdX(a,i)*sigma(i,j)*dNdX(b,j);
#if INT_DEBUG > 3
std::cout << (b == 1 ? '\n' : ' ') << kg;
#endif
for (i = 1; i <= nsd; i++)
EM(nsd*(a-1)+i,nsd*(b-1)+i) += kg*detJW;
if (kgrr > 0.0)
EM(nsd*(a-1)+1,nsd*(b-1)+1) += N(a)*kgrr*N(b)*detJW;
}
#if INT_DEBUG > 3
std::cout << std::endl;
#endif
}
void Elasticity::formMassMatrix (Matrix& EM, const Vector& N,
const Vec3& X, double detJW) const
{
double rhow = material->getMassDensity(X)*detJW;
if (rhow == 0.0) return;
for (size_t a = 1; a <= N.size(); a++)
for (size_t b = 1; b <= N.size(); b++)
for (unsigned short int i = 1; i <= nsd; i++)
EM(nsd*(a-1)+i,nsd*(b-1)+i) += rhow*N(a)*N(b);
}
void Elasticity::formBodyForce (Vector& ES, RealArray& sumLoad, const Vector& N,
const Vec3& X, double detJW, bool grd) const
{
Vec3 f = this->getBodyforce(X,grd);
if (f.isZero()) return;
f *= detJW;
for (size_t a = 1; a <= N.size(); a++)
for (unsigned short int i = 1; i <= nsd; i++)
ES(nsd*(a-1)+i) += f[i-1]*N(a);
if (grd) return;
// Integrate total external load
for (unsigned short int i = 0; i < nsd && i < sumLoad.size(); i++)
sumLoad[i] += f[i];
}
bool Elasticity::evalBou (LocalIntegral& elmInt, const FiniteElement& fe,
const Vec3& X, const Vec3& normal) const
{
if (!tracFld && !fluxFld)
{
std::cerr <<" *** Elasticity::evalBou: No tractions."<< std::endl;
return false;
}
else if (!eS)
{
std::cerr <<" *** Elasticity::evalBou: No load vector."<< std::endl;
return false;
}
// Axi-symmetric integration point volume; 2*pi*r*|J|*w
const double detJW = axiSymmetry ? 2.0*M_PI*X.x*fe.detJxW : fe.detJxW;
// Evaluate the surface traction
Vec3 T = this->getTraction(X,normal);
// Store traction value for visualization
if (fe.iGP < tracVal.size())
{
tracVal[fe.iGP].first = X;
tracVal[fe.iGP].second += T;
}
// Pull-back traction to reference configuration
if (!this->pullBackTraction(T))
return false;
// Integrate the force vector
Vector& ES = static_cast<ElmMats&>(elmInt).b[eS-1];
for (size_t a = 1; a <= fe.N.size(); a++)
for (unsigned short int i = 1; i <= nsd; i++)
ES(nsd*(a-1)+i) += T[i-1]*fe.N(a)*detJW;
// Integrate total external load
RealArray& sumLoad = static_cast<ElmMats&>(elmInt).c;
for (unsigned short int i = 0; i < nsd && i < sumLoad.size(); i++)
sumLoad[i] += T[i]*fe.detJxW;
if (gS)
{
// Evaluate the surface traction gradient
T = this->getTraction(X,normal,true);
// Pull-back traction to reference configuration
if (!this->pullBackTraction(T))
return false;
// Integrate the force gradient vector
Vector& GS = static_cast<ElmMats&>(elmInt).b[gS-1];
for (size_t a = 1; a <= fe.N.size(); a++)
for (unsigned short int i = 1; i <= nsd; i++)
GS(nsd*(a-1)+i) += T[i-1]*fe.N(a)*detJW;
}
return true;
}
Vec3 Elasticity::evalSol (const Vector& eV, const Vector& N) const
{
Vec3 u;
if (eV.size() == nsd*N.size())
for (unsigned short int i = 0; i < nsd; i++)
u[i] = eV.dot(N,i,nsd);
return u;
}
bool Elasticity::formCmat (Matrix& C, const FiniteElement& fe,
const Vec3& X, bool inverted) const
{
SymmTensor dummy(nsd,axiSymmetry); double U;
return material->evaluate(C,dummy,U,fe,X,dummy,dummy, inverted ? -1 : 0);
}
bool Elasticity::evalSol2 (Vector& s, const Vectors& eV,
const FiniteElement& fe, const Vec3& X) const
{
Vec3* pBuf = nullptr;
if (pDirBuf)
{
// Store principal stress directions in the internal buffer
size_t ifirst = pDirBuf->size();
pDirBuf->resize(ifirst+2);
pBuf = pDirBuf->data() + ifirst;
}
// Evaluate the stress tensor
if (fe.detJxW == 0.0)
{
// Singular point, just return an empty vector for now
s.clear();
return true;
}
else if (!this->evalSol(s,eV,fe,X,true,pBuf))
return false;
#if INT_DEBUG > 2
else if (pBuf)
std::cout <<"Elasticity::evalSol2("<< X <<"): "
<<" Pdir1 = "<< pBuf[0] <<", Pdir2 = "<< pBuf[1] << std::endl;
#endif
// Additional result variables?
for (int i = 1; i <= material->getNoIntVariables(); i++)
s.push_back(material->getInternalVariable(i,nullptr,fe.iGP));
if (!calcMaxVal || maxVal.empty())
return true; // Avoid thread sync if no max value calculation
// Find the maximum values for each quantity. This block must be performed
// serially on multi-threaded runs too, due to the update of the maxVal array
// which is a member of the Elasticity class. Therefore the critical pragma.
#pragma omp critical
for (size_t j = 0; j < s.size() && j < maxVal.size(); j++)
{
size_t pidx = maxVal[j].size() > 1 ? LocalSystem::patch : 0;
if (pidx < maxVal[j].size() && fabs(s[j]) > fabs(maxVal[j][pidx].second))
maxVal[j][pidx] = std::make_pair(X,s[j]);
}
return true;
}
bool Elasticity::evalSol (Vector& s, const Vectors& eV, const FiniteElement& fe,
const Vec3& X, bool toLocal, Vec3* pdir) const
{
if (eV.empty())
{
std::cerr <<" *** Elasticity::evalSol: No solutions vector."<< std::endl;
return false;
}
else if (!eV.front().empty() && eV.front().size() != nsd*fe.dNdX.rows())
{
std::cerr <<" *** Elasticity::evalSol: Invalid displacement vector."
<<"\n size(eV) = "<< eV.front().size() <<" size(dNdX) = "
<< fe.dNdX.rows() <<","<< fe.dNdX.cols() << std::endl;
return false;
}
// Evaluate the deformation gradient, dUdX, and/or the strain tensor, eps
Matrix Bmat;
Tensor dUdX(nDF);
SymmTensor eps(nsd,axiSymmetry);
if (!this->kinematics(eV.front(),fe.N,fe.dNdX,X.x,Bmat,dUdX,eps))
return false;
// Add strains due to temperature expansion, if any
double epsT = this->getThermalStrain(eV.back(),fe.N,X);
if (epsT != 0.0) eps -= epsT;
SymmTensor sigma(nsd, axiSymmetry || material->isPlaneStrain());
if (wantStrain)
sigma.copy(eps);
else
{
// Calculate the stress tensor through the constitutive relation
Matrix Cmat;
double U = 0.0;
if (!material->evaluate(Cmat,sigma,U,fe,X,dUdX,eps))
return false;
else if (epsT != 0.0 && nsd == 2 && material->isPlaneStrain())
sigma(3,3) -= material->getStiffness(X)*epsT;
}
Vec3 p;
bool havePval = false;
if (toLocal && wantPrincipalStress)
{
// Calculate principal stresses and associated direction vectors
if (sigma.size() == 4)
{
SymmTensor tmp(2); tmp = sigma; // discard the sigma_zz component
havePval = pdir ? tmp.principal(p,pdir,2) : tmp.principal(p);
}
else
havePval = pdir ? sigma.principal(p,pdir,2) : sigma.principal(p);
// Congruence transformation to local coordinate system at current point
if (locSys) sigma.transform(locSys->getTmat(X));
}
s = sigma;
if (toLocal)
s.push_back(sigma.vonMises());
if (havePval)
{
s.push_back(p.x);
s.push_back(p.y);
if (sigma.dim() == 3)
s.push_back(p.z);
}
return true;
}
bool Elasticity::evalSol (Vector& s, const STensorFunc& asol,
const Vec3& X) const
{
s = asol(X);
SymmTensor sigma(s);
s = sigma;
s.push_back(sigma.vonMises());
if (wantPrincipalStress)
{
Vec3 p;
sigma.principal(p);
s.resize(s.size()+material->getNoIntVariables());
s.push_back(p.x);
s.push_back(p.y);
if (nsd == 3)
s.push_back(p.z);
}
return true;
}
bool Elasticity::evalEps (Vector& s, const Vector& eV, const FiniteElement& fe,
const Vec3& X) const
{
if (eV.size() != fe.dNdX.rows()*nsd)
{
std::cerr <<" *** Elasticity::evalEps: Invalid displacement vector."
<<"\n size(eV) = "<< eV.size() <<" size(dNdX) = "
<< fe.dNdX.rows() <<","<< fe.dNdX.cols() << std::endl;
return false;
}
// Evaluate the strain tensor
Matrix Bmat;
SymmTensor eps(nsd,axiSymmetry);
if (!this->kinematics(eV,fe.N,fe.dNdX,X.x,Bmat,eps,eps))
return false;
s = eps;
return true;
}
Vector* Elasticity::getExtractionField (size_t ifield)
{
return dS && ifield < primsol.size() ? &primsol[ifield] : nullptr;
}
bool Elasticity::getPrincipalDir (Matrix& pdir, size_t nPt, size_t idx) const
{
if (!pDirBuf || idx < 1 || idx > 2) return false;
if (pDirBuf->size() != nPt*2)
{
std::cerr <<" *** Elasticity::getPrincipalDir: Result point mismatch, nPt="
<< nPt <<", pDirBuf->size()="<< pDirBuf->size() << std::endl;
return false;
}
pdir.resize(nsd,nPt);
for (size_t i = 0; i < nPt; i++)
pdir.fillColumn(1+i,(*pDirBuf)[2*i+idx-1].ptr());
return true;
}
size_t Elasticity::getNoFields (int fld) const
{
if (fld < 2)
return nsd; // Displacement components
size_t nf = nsd*(nsd+1)/2; // Symmetric stress tensor components
if (nsd == 2 && (axiSymmetry || material->isPlaneStrain()))
++nf; // Include Hoop or normal stress
if (fld == 2)
{
// Include von Mises stress and internal variables
nf += 1 + material->getNoIntVariables();
if (wantPrincipalStress)
nf += nsd; // Include principal stress components
}
#if INT_DEBUG > 1
std::cout <<"Elasticity::getNoFields: "<< nf << std::endl;
#endif
return nf;
}
std::string Elasticity::getField1Name (size_t i, const char* prefix) const
{
if (i > nsd) i = 4;
static const char* s[5] = { "u_x", "u_y", "u_z", "u_r", "displacement" };
if (!prefix) return s[i];
return prefix + std::string(" ") + s[axiSymmetry ? 3-i : i];
}
std::string Elasticity::getField2Name (size_t i, const char* prefix) const
{
size_t nVars = this->getNoFields(2);
if (i >= nVars) return "";
static const char* r[4] = { "s_rr", "s_zz", "s_tt", "s_zr" };
static const char* s[6] = { "s_xx", "s_yy", "s_zz", "s_xy", "s_yz", "s_xz" };
std::string name;
if (prefix)
name = std::string(prefix) + " ";
else
name.clear();
// Number of components in the stress vector of this problem
size_t nStress = this->getNoFields(3);
if (nsd == 1)
name += "Axial stress";
else if (i == 2 && nStress == 3)
name += s[3]; // No s_zz when plane stress
else if (i < nStress)
{
size_t j = name.size();
name += axiSymmetry ? r[i] : s[i];
if (wantStrain) name[j] = 'e';
}
else if (i == nStress)
name += "von Mises " + std::string(wantStrain ? "strain" : "stress");
else if ((int)(i -= nStress) <= material->getNoIntVariables())
{
char varName[32];
material->getInternalVariable(i,varName);
name += varName;
}
else if ((i -= material->getNoIntVariables()) <= nsd)
name += "P" + std::to_string(i);
return name;
}
void Elasticity::initMaxVals (size_t nP)
{
#ifdef INT_DEBUG
std::cout <<"Elasticity::initMaxVals: "<< maxVal.size()
<<" --> "<< nP << std::endl;
#endif
if (maxVal.empty() && nP > 0)
maxVal.resize(this->getNoFields(2),PointValues(nP,PointValue(Vec3(),0.0)));
else for (PointValues& pval : maxVal)
std::fill(pval.begin(),pval.end(),PointValue(Vec3(),0.0));
}
void Elasticity::printMaxVals (std::streamsize precision, size_t comp) const
{
size_t i1 = 1, i2 = maxVal.size();
if (comp > i2)
return;
else if (comp > 0)
i1 = i2 = comp;
std::streamsize fldWidth = 8 + precision;
utl::LogStream& os = IFEM::cout;
for (size_t i = i1-1; i < i2; i++)
{
if (maxVal[i].empty())
continue;
else if (maxVal[i].size() == 1 && maxVal[i].front().second == 0.0)
continue; // no value
std::string name = this->getField2Name(i,nullptr);