void
RankTwoTensorTest::dthirdInvariantTest()
{
// this derivative is less trivial
// so let's check with a finite-difference approximation
Real ep = 1E-5; // small finite-difference parameter
Real thirdInvariant; // thirdInvariant provided by RankTwoTensor
RankTwoTensor deriv; // derivative of thirdInvariant provided by RankTwoTensor
RankTwoTensor mep; // the RankTwoTensor with successive entries shifted by ep
thirdInvariant = _m3.thirdInvariant();
deriv = _m3.dthirdInvariant();
mep = _m3;
for (unsigned i = 0 ; i < 3 ; ++i)
for (unsigned j = 0 ; j < 3 ; ++j)
{
mep(i, j) += ep;
CPPUNIT_ASSERT_DOUBLES_EQUAL((mep.thirdInvariant() - thirdInvariant)/ep, deriv(i, j), 10*ep);
mep(i, j) -= ep;
}
thirdInvariant = _unsymmetric1.thirdInvariant();
deriv = _unsymmetric1.dthirdInvariant();
mep = _unsymmetric1;
for (unsigned i = 0 ; i < 3 ; ++i)
for (unsigned j = 0 ; j < 3 ; ++j)
{
mep(i, j) += ep;
CPPUNIT_ASSERT_DOUBLES_EQUAL((mep.thirdInvariant() - thirdInvariant)/ep, deriv(i, j), 10*ep);
mep(i, j) -= ep;
// since thirdInvariant is explicitly symmeterised, we can also do
mep(i, j) += 0.5*ep;
mep(j, i) += 0.5*ep;
CPPUNIT_ASSERT_DOUBLES_EQUAL((mep.thirdInvariant() - thirdInvariant)/ep, deriv(i, j), 10*ep);
mep(i, j) -= 0.5*ep;
mep(j, i) -= 0.5*ep;
}
}
