void
CrackFrontDefinition::calculateRThetaToCrackFront(const Point qp, const unsigned int node_index, Real & r, Real & theta) const
{
unsigned int num_nodes(_ordered_crack_front_nodes.size());
Point p = qp;
// Loop over nodes to find the two crack front nodes closest to the point qp
Real mindist1(1.0e30);
Real mindist2(1.0e30);
Point closest_node1(0.0);
Point closest_node2(0.0);
for (unsigned int nit = 0; nit != num_nodes; ++nit)
{
Node & crack_front_node = _mesh.node(_ordered_crack_front_nodes[nit]);
RealVectorValue crack_node_to_current_node = p - crack_front_node;
Real dist = crack_node_to_current_node.size();
if (dist < mindist1)
{
mindist2 = mindist1;
closest_node2 = closest_node1;
mindist1 = dist;
closest_node1 = crack_front_node;
}
else if (dist < mindist2 && dist != mindist1)
{
mindist2 = dist;
closest_node2 = crack_front_node;
}
}
//Rotate coordinates to crack front coordinate system
closest_node1 = rotateToCrackFrontCoords(closest_node1,node_index);
closest_node2 = rotateToCrackFrontCoords(closest_node2,node_index);
if (closest_node1(2) > closest_node2(2))
{
RealVectorValue tmp = closest_node2;
closest_node2 = closest_node1;
closest_node1 = tmp;
}
p = rotateToCrackFrontCoords(p,node_index);
//Find r, the distance between the qp and the crack front
RealVectorValue crack_front_edge = closest_node2 - closest_node1;
Real edge_length_sq = crack_front_edge.size_sq();
RealVectorValue closest_node1_to_p = p - closest_node1;
Real perp = crack_front_edge * closest_node1_to_p;
Real dist_along_edge = perp / edge_length_sq;
RealVectorValue point_on_edge = closest_node1 + crack_front_edge * dist_along_edge;
RealVectorValue r_vec = p - point_on_edge;
r = r_vec.size();
//Find theta, the angle between r and the crack front plane
RealVectorValue crack_plane_normal = rotateToCrackFrontCoords(_crack_plane_normal,node_index);
Real p_to_plane_dist = std::abs(closest_node1_to_p*crack_plane_normal);
//Determine if p is above or below the crack plane
Real y_local = p(1) - closest_node1(1);
//Determine if p is in front of or behind the crack front
RealVectorValue p2(p);
p2(1) = 0;
RealVectorValue p2_vec = p2 - closest_node1;
Real ahead = crack_front_edge(2) * p2_vec(0) - crack_front_edge(0) * p2_vec(2);
Real x_local(0);
if (ahead >= 0)
x_local = 1;
else
x_local = -1;
//Calculate theta based on in which quadrant in the crack front coordinate
//system the qp is located
if (x_local >= 0 && y_local >= 0)
theta = std::asin(p_to_plane_dist/r);
else if (x_local < 0 && y_local >= 0)
theta = libMesh::pi - std::asin(p_to_plane_dist/r);
else if (x_local < 0 && y_local < 0)
theta = -(libMesh::pi - std::asin(p_to_plane_dist/r));
else if (x_local >= 0 && y_local < 0)
theta = -std::asin(p_to_plane_dist/r);
}
void
CrackFrontDefinition::calculateRThetaToCrackFront(const Point qp, const unsigned int node_index, Real & r, Real & theta) const
{
unsigned int num_nodes(_ordered_crack_front_nodes.size());
Point p = qp;
Point closest_node(0.0);
RealVectorValue closest_node_to_p;
Node & crack_tip_node = _mesh.node(_ordered_crack_front_nodes[node_index]);
RealVectorValue crack_tip_node_rot = rotateToCrackFrontCoords(crack_tip_node,node_index);
RealVectorValue crack_front_edge = rotateToCrackFrontCoords(_tangent_directions[node_index],node_index);
Point p_rot = rotateToCrackFrontCoords(p,node_index);
p_rot = p_rot - crack_tip_node_rot;
if (_treat_as_2d)
{
closest_node = crack_tip_node_rot;
closest_node_to_p = p_rot;
//Find r, the distance between the qp and the crack front
RealVectorValue r_vec = p_rot;
r = r_vec.size();
}
else
{
// Loop over crack front nodes to find the one closest to the point qp
Real min_dist = std::numeric_limits<Real>::max();
for (unsigned int nit = 0; nit != num_nodes; ++nit)
{
Node & crack_front_node = _mesh.node(_ordered_crack_front_nodes[nit]);
RealVectorValue crack_node_to_current_node = p - crack_front_node;
Real dist = crack_node_to_current_node.size();
if (dist < min_dist)
{
min_dist = dist;
closest_node = crack_front_node;
}
}
//Rotate coordinates to crack front coordinate system
closest_node = rotateToCrackFrontCoords(closest_node,node_index);
closest_node = closest_node - crack_tip_node_rot;
//Find r, the distance between the qp and the crack front
Real edge_length_sq = crack_front_edge.size_sq();
closest_node_to_p = p_rot - closest_node;
Real perp = crack_front_edge * closest_node_to_p;
Real dist_along_edge = perp / edge_length_sq;
RealVectorValue point_on_edge = closest_node + crack_front_edge * dist_along_edge;
RealVectorValue r_vec = p_rot - point_on_edge;
r = r_vec.size();
}
//Find theta, the angle between r and the crack front plane
RealVectorValue crack_plane_normal = rotateToCrackFrontCoords(_crack_plane_normal,node_index);
Real p_to_plane_dist = std::abs(closest_node_to_p*crack_plane_normal);
//Determine if p is above or below the crack plane
Real y_local = p_rot(1) - closest_node(1);
//Determine if p is in front of or behind the crack front
RealVectorValue p2(p_rot);
p2(1) = 0;
RealVectorValue p2_vec = p2 - closest_node;
Real ahead = crack_front_edge(2) * p2_vec(0) - crack_front_edge(0) * p2_vec(2);
Real x_local(0);
if (ahead >= 0)
x_local = 1;
else
x_local = -1;
//Calculate theta based on in which quadrant in the crack front coordinate
//system the qp is located
if (x_local >= 0 && y_local >= 0)
theta = std::asin(p_to_plane_dist/r);
else if (x_local < 0 && y_local >= 0)
theta = libMesh::pi - std::asin(p_to_plane_dist/r);
else if (x_local < 0 && y_local < 0)
theta = -(libMesh::pi - std::asin(p_to_plane_dist/r));
else if (x_local >= 0 && y_local < 0)
theta = -std::asin(p_to_plane_dist/r);
}
