void
RotationMatrixTest::rotVtoU(RealVectorValue v, RealVectorValue u)
{
RealTensorValue ident(1,0,0, 0,1,0, 0,0,1);
RealVectorValue vhat = v/v.size();
RealVectorValue uhat = u/u.size();
RealTensorValue r = RotationMatrix::rotVec1ToVec2(v, u);
RealVectorValue rotated_v = r*vhat;
for (unsigned i = 0 ; i < LIBMESH_DIM ; ++i)
CPPUNIT_ASSERT_DOUBLES_EQUAL( rotated_v(i), uhat(i), 0.0001);
CPPUNIT_ASSERT( r*r.transpose() == ident);
CPPUNIT_ASSERT( r.transpose()*r == ident);
}
ContactState
FrictionalContactProblem::calculateInteractionSlip(RealVectorValue &slip,
Real &slip_residual,
const RealVectorValue &normal,
const RealVectorValue &residual,
const RealVectorValue &incremental_slip,
const RealVectorValue &stiffness,
const Real friction_coefficient,
const Real slip_factor,
const Real slip_too_far_factor,
const int dim)
{
ContactState state = STICKING;
RealVectorValue normal_residual = normal * (normal * residual);
Real normal_force = normal_residual.size();
// _console<<"normal="<<info._normal<<std::endl;
// _console<<"normal_force="<<normal_force<<std::endl;
// _console<<"residual="<<residual<<std::endl;
// _console<<"stiffness="<<stiff_vec<<std::endl;
RealVectorValue tangential_force = normal_residual - residual ; // swap sign to make the code more manageable
Real tangential_force_magnitude = tangential_force.size();
Real capacity = normal_force * friction_coefficient;
if (capacity < 0.0)
capacity = 0.0;
Real slip_inc = incremental_slip.size();
slip(0)=0.0;
slip(1)=0.0;
slip(2)=0.0;
if (slip_inc > 0)
{
state = SLIPPING;
Real slip_dot_tang_force = incremental_slip*tangential_force / slip_inc;
if (slip_dot_tang_force < capacity)
{
state = SLIPPED_TOO_FAR;
// _console<<"STF slip_dot_force: "<<slip_dot_tang_force<<" capacity: "<<capacity<<std::endl;
}
}
Real excess_force = tangential_force_magnitude - capacity;
if (excess_force < 0.0)
excess_force = 0;
if (state == SLIPPED_TOO_FAR)
{
RealVectorValue slip_inc_direction = incremental_slip / slip_inc;
Real tangential_force_in_slip_dir = slip_inc_direction*tangential_force;
slip_residual = capacity - tangential_force_in_slip_dir;
RealVectorValue force_from_unit_slip(0.0,0.0,0.0);
for (int i=0; i<dim; ++i)
{
force_from_unit_slip(i) = stiffness(i) * slip_inc_direction(i);
}
Real stiffness_slipdir = force_from_unit_slip * slip_inc_direction; //k=f resolved to slip dir because f=kd and d is a unit vector
Real slip_distance = slip_too_far_factor*(capacity - tangential_force_in_slip_dir) / stiffness_slipdir;
// _console<<"STF dist: "<<slip_distance<<" inc: "<<slip_inc<<std::endl;
// _console<<"STF cap: "<<capacity<<" tfs: "<<tangential_force_in_slip_dir<<std::endl;
if (slip_distance < slip_inc)
{
// _console<<"STF"<<std::endl;
slip = slip_inc_direction * -slip_distance;
}
else
{
// _console<<"STF max"<<std::endl;
slip = -incremental_slip;
}
}
else if (excess_force > 0)
{
state = SLIPPING;
Real tangential_force_magnitude = tangential_force.size();
slip_residual = excess_force;
RealVectorValue tangential_direction = tangential_force / tangential_force_magnitude;
RealVectorValue excess_force_vector = tangential_direction * excess_force;
for (int i=0; i<dim; ++i)
{
slip(i) = slip_factor * excess_force_vector(i) / stiffness(i);
}
//zero out component of slip in normal direction
RealVectorValue slip_normal_dir = normal * (normal * slip);
slip = slip - slip_normal_dir;
}
return state;
}