void ArmSideView::configDraw(std::string name, int w, int h)
{
// create an image of the specified size
// able to represent the arm in 3 directions (up, down and right)
// with isotropic scaling (same scale in all directions)
setIsotropic(true);
initPlot(w, h, name);
// only positive x ranges
setRanges(0, maxLen, -maxLen, maxLen);
}
bool FractureElasticityVoigt::evalStress (double lambda, double mu, double Gc,
const SymmTensor& epsil, double* Phi,
SymmTensor* sigma, Matrix* dSdE,
bool postProc, bool printElm) const
{
PROFILE3("FractureEl::evalStress");
unsigned short int a = 0, b = 0;
// Define a Lambda-function to set up the isotropic constitutive matrix
auto&& setIsotropic = [this,a,b](Matrix& C, double lambda, double mu) mutable
{
for (a = 1; a <= C.rows(); a++)
if (a > nsd)
C(a,a) = mu;
else
{
C(a,a) = 2.0*mu;
for (b = 1; b <= nsd; b++)
C(a,b) += lambda;
}
};
// Define some material constants
double trEps = epsil.trace();
double C0 = trEps >= -epsZ ? Gc*lambda : lambda;
double Cp = Gc*mu;
if (trEps >= -epsZ && trEps <= epsZ)
{
// No strains, stress free configuration
Phi[0] = 0.0;
if (postProc)
Phi[1] = Phi[2] = Phi[3] = 0.0;
if (sigma)
*sigma = 0.0;
if (dSdE)
setIsotropic(*dSdE,C0,Cp);
return true;
}
// Calculate principal strains and the associated directions
Vec3 eps;
std::vector<SymmTensor> M(nsd,SymmTensor(nsd));
{
PROFILE4("Tensor::principal");
if (!epsil.principal(eps,M.data()))
return false;
}
// Split the strain tensor into positive and negative parts
SymmTensor ePos(nsd), eNeg(nsd);
for (a = 0; a < nsd; a++)
if (eps[a] > 0.0)
ePos += eps[a]*M[a];
else if (eps[a] < 0.0)
eNeg += eps[a]*M[a];
if (sigma)
{
// Evaluate the stress tensor
*sigma = C0*trEps;
*sigma += 2.0*mu*(Gc*ePos + eNeg);
}
// Evaluate the tensile energy
Phi[0] = mu*(ePos*ePos).trace();
if (trEps > 0.0) Phi[0] += 0.5*lambda*trEps*trEps;
if (postProc)
{
// Evaluate the compressive energy
Phi[1] = mu*(eNeg*eNeg).trace();
if (trEps < 0.0) Phi[1] += 0.5*lambda*trEps*trEps;
// Evaluate the total strain energy
Phi[2] = Gc*Phi[0] + Phi[1];
// Evaluate the bulk energy
Phi[3] = Gc*(Phi[0] + Phi[1]);
}
else if (sigmaC > 0.0) // Evaluate the crack driving function
Phi[0] = this->MieheCrit56(eps,lambda,mu);
#if INT_DEBUG > 4
std::cout <<"eps_p = "<< eps <<"\n";
for (a = 0; a < nsd; a++)
std::cout <<"M("<< 1+a <<") =\n"<< M[a];
std::cout <<"ePos =\n"<< ePos <<"eNeg =\n"<< eNeg;
if (sigma) std::cout <<"sigma =\n"<< *sigma;
std::cout <<"Phi = "<< Phi[0];
if (postProc) std::cout <<" "<< Phi[1] <<" "<< Phi[2] <<" "<< Phi[3];
std::cout << std::endl;
#else
if (printElm)
{
std::cout <<"g(c) = "<< Gc
<<"\nepsilon =\n"<< epsil <<"eps_p = "<< eps
<<"\nePos =\n"<< ePos <<"eNeg =\n"<< eNeg;
if (sigma) std::cout <<"sigma =\n"<< *sigma;
std::cout <<"Phi = "<< Phi[0];
if (postProc) std::cout <<" "<< Phi[1] <<" "<< Phi[2] <<" "<< Phi[3];
std::cout << std::endl;
}
#endif
if (!dSdE)
return true;
else if (eps[0] == eps[nsd-1])
{
// Hydrostatic pressure
setIsotropic(*dSdE, C0, eps.x > 0.0 ? Cp : mu);
return true;
}
typedef unsigned short int s_ind; // Convenience type definition
// Define a Lambda-function to calculate (lower triangle of) the matrix Qa
auto&& getQ = [this](Matrix& Q, const SymmTensor& Ma, double C)
{
if (C == 0.0) return;
auto&& Mult = [Ma](s_ind i, s_ind j, s_ind k, s_ind l)
{
return Ma(i,j)*Ma(k,l);
};
s_ind i, j, k, l, is, js;
// Normal stresses and strains
for (i = 1; i <= nsd; i++)
for (j = 1; j <= i; j++)
Q(i,j) += C*Mult(i,i,j,j);
is = nsd+1;
for (i = 1; i < nsd; i++)
for (j = i+1; j <= nsd; j++, is++)
{
// Shear stress coupled to normal strain
for (k = 1; k <= nsd; k++)
Q(is,k) += C*Mult(i,j,k,k);
// Shear stress coupled to shear strain
js = nsd+1;
for (k = 1; k < nsd; k++)
for (l = k+1; js <= is; l++, js++)
Q(is,js) += C*Mult(i,j,k,l);
}
};
// Define a Lambda-function to calculate (lower triangle of) the matrix Gab
auto&& getG = [this](Matrix& G, const SymmTensor& Ma,
const SymmTensor& Mb, double C)
{
if (C == 0.0) return;
auto&& Mult = [Ma,Mb](s_ind i, s_ind j, s_ind k, s_ind l)
{
return Ma(i,k)*Mb(j,l) + Ma(i,l)*Mb(j,k) +
Mb(i,k)*Ma(j,l) + Mb(i,l)*Ma(j,k);
};
s_ind i, j, k, l, is, js;
// Normal stresses and strains
for (i = 1; i <= nsd; i++)
for (j = 1; j <= i; j++)
G(i,j) += C*Mult(i,i,j,j);
is = nsd+1;
for (i = 1; i < nsd; i++)
for (j = i+1; j <= nsd; j++, is++)
{
// Shear stress coupled to normal strain
for (k = 1; k <= nsd; k++)
G(is,k) += C*Mult(i,j,k,k);
// Shear stress coupled to shear strain
js = nsd+1;
for (k = 1; k < nsd; k++)
for (l = k+1; js <= is; l++, js++)
G(is,js) += C*Mult(i,j,k,l);
}
};
// Evaluate the stress tangent assuming Voigt notation and symmetry
for (a = 1; a <= nsd; a++)
for (b = 1; b <= a; b++)
(*dSdE)(a,b) = C0;
for (a = 0; a < nsd; a++)
{
double C1 = eps[a] >= 0.0 ? Cp : mu;
getQ(*dSdE, M[a], 2.0*C1);
if (eps[a] != 0.0)
for (b = 0; b < nsd; b++)
if (a != b && eps[a] != eps[b])
getG(*dSdE,M[a],M[b],C1/(1.0-eps[b]/eps[a]));
}
// Account for symmetry
for (b = 2; b <= dSdE->rows(); b++)
for (a = 1; a < b; a++)
(*dSdE)(a,b) = (*dSdE)(b,a);
return true;
}