Real
effectiveStrain(const SymmTensor & symm_strain)
{
return std::sqrt(2.0 / 3.0 * symm_strain.doubleContraction(symm_strain));
}
Real
equivalentPlasticStrain(const SymmTensor & symm_strain)
{
return std::sqrt(2.0 / 3.0 * symm_strain.doubleContraction(symm_strain));
}
Real
MaterialTensorAux::getTensorQuantity(const SymmTensor & tensor,
const MTA_ENUM quantity,
const MooseEnum & quantity_moose_enum,
const int index,
const Point * curr_point,
const Point * p1,
const Point * p2)
{
Real value(0);
if (quantity == MTA_COMPONENT)
{
value = tensor.component(index);
}
else if ( quantity == MTA_VONMISES )
{
value = std::sqrt(0.5*(
std::pow(tensor.xx() - tensor.yy(), 2) +
std::pow(tensor.yy() - tensor.zz(), 2) +
std::pow(tensor.zz() - tensor.xx(), 2) + 6 * (
std::pow(tensor.xy(), 2) +
std::pow(tensor.yz(), 2) +
std::pow(tensor.zx(), 2))));
}
else if ( quantity == MTA_PLASTICSTRAINMAG )
{
value = std::sqrt(2.0/3.0 * tensor.doubleContraction(tensor));
}
else if ( quantity == MTA_HYDROSTATIC )
{
value = tensor.trace()/3.0;
}
else if ( quantity == MTA_HOOP )
{
// This is the location of the stress. A vector from the cylindrical axis to this point will define the x' axis.
Point p0( *curr_point );
// The vector p1 + t*(p2-p1) defines the cylindrical axis. The point along this
// axis closest to p0 is found by the following for t:
const Point p2p1( *p2 - *p1 );
const Point p2p0( *p2 - p0 );
const Point p1p0( *p1 - p0 );
const Real t( -(p1p0*p2p1)/p2p1.size_sq() );
// The nearest point on the cylindrical axis to p0 is p.
const Point p( *p1 + t * p2p1 );
Point xp( p0 - p );
xp /= xp.size();
Point yp( p2p1/p2p1.size() );
Point zp( xp.cross( yp ));
//
// The following works but does more than we need
//
// // Rotation matrix R
// ColumnMajorMatrix R(3,3);
// // Fill with direction cosines
// R(0,0) = xp(0);
// R(1,0) = xp(1);
// R(2,0) = xp(2);
// R(0,1) = yp(0);
// R(1,1) = yp(1);
// R(2,1) = yp(2);
// R(0,2) = zp(0);
// R(1,2) = zp(1);
// R(2,2) = zp(2);
// // Rotate
// ColumnMajorMatrix tensor( _tensor[_qp].columnMajorMatrix() );
// ColumnMajorMatrix tensorp( R.transpose() * ( tensor * R ));
// // Hoop stress is the zz stress
// value = tensorp(2,2);
//
// Instead, tensorp(2,2) = R^T(2,:)*tensor*R(:,2)
//
const Real zp0( zp(0) );
const Real zp1( zp(1) );
const Real zp2( zp(2) );
value = (zp0*tensor(0,0)+zp1*tensor(1,0)+zp2*tensor(2,0))*zp0 +
(zp0*tensor(0,1)+zp1*tensor(1,1)+zp2*tensor(2,1))*zp1 +
(zp0*tensor(0,2)+zp1*tensor(1,2)+zp2*tensor(2,2))*zp2;
}
else if ( quantity == MTA_RADIAL )
{
// This is the location of the stress. A vector from the cylindrical axis to this point will define the x' axis
// which is the radial direction in which we want the stress.
Point p0( *curr_point );
// The vector p1 + t*(p2-p1) defines the cylindrical axis. The point along this
// axis closest to p0 is found by the following for t:
const Point p2p1( *p2 - *p1 );
const Point p2p0( *p2 - p0 );
const Point p1p0( *p1 - p0 );
const Real t( -(p1p0*p2p1)/p2p1.size_sq() );
// The nearest point on the cylindrical axis to p0 is p.
const Point p( *p1 + t * p2p1 );
Point xp( p0 - p );
xp /= xp.size();
const Real xp0( xp(0) );
const Real xp1( xp(1) );
const Real xp2( xp(2) );
value = (xp0*tensor(0,0)+xp1*tensor(1,0)+xp2*tensor(2,0))*xp0 +
(xp0*tensor(0,1)+xp1*tensor(1,1)+xp2*tensor(2,1))*xp1 +
(xp0*tensor(0,2)+xp1*tensor(1,2)+xp2*tensor(2,2))*xp2;
}
else if ( quantity == MTA_AXIAL )
{
// The vector p2p1=(p2-p1) defines the axis, which is the direction in which we want the stress.
Point p2p1( *p2 - *p1 );
p2p1 /= p2p1.size();
const Real axis0( p2p1(0) );
const Real axis1( p2p1(1) );
const Real axis2( p2p1(2) );
value = (axis0*tensor(0,0)+axis1*tensor(1,0)+axis2*tensor(2,0))*axis0 +
(axis0*tensor(0,1)+axis1*tensor(1,1)+axis2*tensor(2,1))*axis1 +
(axis0*tensor(0,2)+axis1*tensor(1,2)+axis2*tensor(2,2))*axis2;
}
else if ( quantity == MTA_MAXPRINCIPAL )
{
value = principalValue( tensor, 0 );
}
else if ( quantity == MTA_MEDPRINCIPAL )
{
value = principalValue( tensor, 1 );
}
else if ( quantity == MTA_MINPRINCIPAL )
{
value = principalValue( tensor, 2 );
}
else if ( quantity == MTA_FIRSTINVARIANT )
{
value = tensor.trace();
}
else if ( quantity == MTA_SECONDINVARIANT )
{
value =
tensor.xx()*tensor.yy() +
tensor.yy()*tensor.zz() +
tensor.zz()*tensor.xx() -
tensor.xy()*tensor.xy() -
tensor.yz()*tensor.yz() -
tensor.zx()*tensor.zx();
}
else if ( quantity == MTA_THIRDINVARIANT )
{
value =
tensor.xx()*tensor.yy()*tensor.zz() -
tensor.xx()*tensor.yz()*tensor.yz() +
tensor.xy()*tensor.zx()*tensor.yz() -
tensor.xy()*tensor.xy()*tensor.zz() +
tensor.zx()*tensor.xy()*tensor.yz() -
tensor.zx()*tensor.zx()*tensor.yy();
}
else if ( quantity == MTA_TRIAXIALITY )
{
Real hydrostatic = tensor.trace()/3.0;
Real von_mises = std::sqrt(0.5*(
std::pow(tensor.xx() - tensor.yy(), 2) +
std::pow(tensor.yy() - tensor.zz(), 2) +
std::pow(tensor.zz() - tensor.xx(), 2) + 6 * (
std::pow(tensor.xy(), 2) +
std::pow(tensor.yz(), 2) +
std::pow(tensor.zx(), 2))));
value = std::abs(hydrostatic / von_mises);
}
else if ( quantity == MTA_VOLUMETRICSTRAIN )
{
value =
tensor.trace() +
tensor.xx()*tensor.yy() +
tensor.yy()*tensor.zz() +
tensor.zz()*tensor.xx() +
tensor.xx()*tensor.yy()*tensor.zz();
}
else
{
mooseError("Unknown quantity in MaterialTensorAux: " + quantity_moose_enum.operator std::string());
}
return value;
}