void beam_PK1_stress_function(TensorValue<double>& PP,
const TensorValue<double>& FF,
const libMesh::Point& /*X*/,
const libMesh::Point& s,
Elem* const /*elem*/,
const vector<NumericVector<double>*>& /*system_data*/,
double /*time*/,
void* /*ctx*/)
{ const double dist2root = sqrt((s(0) - 0) * (s(0) - 0));
if (dist2root <= fixed_L) // we use penalty method to fix the root
{
PP = 0.0 * FF; // so we no longer compute stress here
return ;
}
// 1) compute the radius r(x) : r_x
double arc_s = get_arc_length(s(0));
const double r_x = slope * arc_s + r0;
// 2) compute ratio_moduli;
const double ratio_radius = r_x /r0;
const double ratio_moduli = ratio_radius * ratio_radius* ratio_radius* ratio_radius;
const TensorValue<double> CC = FF.transpose() * FF;
const TensorValue<double> EE = 0.5 * (CC - II);
const TensorValue<double> SS = lambda_s * EE.tr() * II + 2.0 * mu_s * EE;
PP = ratio_moduli * FF * SS;
return;
} // beam_PK1_stress_function
void
beam_PK1_stress_function(TensorValue<double>& PP,
const TensorValue<double>& FF,
const libMesh::Point& /*X*/,
const libMesh::Point& s,
Elem* const /*elem*/,
const vector<NumericVector<double>*>& /*system_data*/,
double /*time*/,
void* /*ctx*/)
{
const double r = sqrt((s(0) - 0.2) * (s(0) - 0.2) + (s(1) - 0.2) * (s(1) - 0.2));
if (r > 0.05)
{
static const TensorValue<double> II(1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0);
const TensorValue<double> CC = FF.transpose() * FF;
const TensorValue<double> EE = 0.5 * (CC - II);
const TensorValue<double> SS = lambda_s * EE.tr() * II + 2.0 * mu_s * EE;
PP = FF * SS;
}
else
{
PP.zero();
}
return;
} // beam_PK1_stress_function
void
upper_PK1_stress_function(
TensorValue<double>& PP,
const TensorValue<double>& FF,
const libMesh::Point& /*X*/,
const libMesh::Point& s,
Elem* const /*elem*/,
const vector<NumericVector<double>*>& /*system_data*/,
double /*time*/,
void* /*ctx*/)
{
if (s(0) > 5.0 && s(0) < 10.0)
{
static const TensorValue<double> II(1.0,0.0,0.0,
0.0,1.0,0.0,
0.0,0.0,1.0);
const TensorValue<double> CC = FF.transpose()*FF;
const TensorValue<double> EE = 0.5*(CC - II);
const TensorValue<double> SS = lambda_s*EE.tr()*II + 2.0*mu_s*EE;
PP = FF*SS;
}
else
{
PP.zero();
}
return;
}// upper_PK1_stress_function
void PK1_stress_function(TensorValue<double>& PP,
const TensorValue<double>& FF,
const libMesh::Point& /*x*/,
const libMesh::Point& /*X*/,
subdomain_id_type /*subdomain_id*/,
std::vector<double>& /*internal_vars*/,
double /*time*/,
void* /*ctx*/)
{
const TensorValue<double> FF_inv_trans = tensor_inverse_transpose(FF, NDIM);
const TensorValue<double> CC = FF.transpose() * FF;
PP = 2.0 * c1_s * FF;
if (!MathUtilities<double>::equalEps(p0_s, 0.0))
{
PP -= 2.0 * p0_s * FF_inv_trans;
}
if (!MathUtilities<double>::equalEps(beta_s, 0.0))
{
PP += beta_s * log(CC.det()) * FF_inv_trans;
}
return;
} // PK1_stress_function