Hello,
I have two questions when studying Step-18.
1) Should there be a factor 1/2 when calculating the rotation matrix angle
(code in tutorial: angle
<https://www.dealii.org/current/doxygen/deal.II/grid__tools__nontemplates_8cc.html#a1b9d6e95246f7a6b7ecc7430631dd0b6>
= std::atan
<https://www.dealii.org/current/doxygen/deal.II/namespaceDifferentiation_1_1SD.html#a803fcea270d7a523a91e3b7c173059f9>(curl)
) ? This is a mathematical problem. Can anyone give some material for the
formula to clear out my doubt?
2) In the introduction, it says "we will consider a model in which we
produce *a small deformation*, deform the physical coordinates of the body
by this deformation, and then consider the next loading step again as a
linear problem. *This isn't consistent*, since the assumption of *linearity
*implies that *deformations are infinitesimal* and so moving around the
vertices of our mesh by *a finite amount* before solving the next linear
problem is an inconsistent approach." My question is how to make it
consistent. Can I just add the nonlinear part of the strain tensor like the
following (of course in both get_strain functions)? I just want to consider
the geometrical nonlinearity.
template <int dim>
inline SymmetricTensor<2, dim>
*get_strain*(const std::vector<Tensor<1, dim>> &grad)
{
Assert(grad.size() == dim, ExcInternalError());
SymmetricTensor<2, dim> strain;
for (unsigned int i = 0; i < dim; ++i)
strain[i][i] = grad[i][i];
for (unsigned int i = 0; i < dim; ++i)
for (unsigned int j = i + 1; j < dim; ++j)
strain[i][j] = (grad[i][j] + grad[j][i] *+ * // linear part
*grad[i][0] * grad[j][0]* *+ //nonlinear
part*
* grad[i][1] * grad[j][1] + *
* grad[i][2] * grad[j][2]*) / 2;
return strain;
}
Thanks,
Michael
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