One of the options for adapting a mesh to the displacements of its boundary is based on an elastic material analogy. This remeshing technique belongs to the family of elliptic remeshing schemes and has the advantage of complete topological generality (in 2D and 3D), since no regular organization of the mesh is required. Its cost (in terms of CPU and memory) is comparable to that of the Thompson transformation described in Thompson Transformation.
In the interior of the domain, a nonlinear small displacement pseudo-elastic problem
is solved, stated in terms of displacement 
as
 | (16–15) |
where 
has the dimension of a Young’s modulus and the Poisson’s
ratio is equal to zero.
For the improved elastic remeshing, Equation 16–15 is modified as follows:
 | (16–16) |
where
 | (16–17) |
 | (16–18) |
In Equation 16–16,
is a torsion factor. If 
is equal to zero, Equation 16–15 and Equation 16–16 are identical. A nonzero value for 
adds a rotation stiffness with respect to the initial configuration.
This avoids deforming elements too much with respect to their initial shape. In
Ansys Polyflow, the value of 
is set to 5. Note that you cannot modify this parameter.
The improved elastic remeshing behaves in a similar way to the Optimesh technique. But whereas Optimesh cannot be used for meshes that require remeshing in all three dimensions, the improved elastic remeshing is applicable to any 3D mesh.
Equation 16–15 and Equation 16–16 are nonlinear because they are solved in the deformed configuration and not on the original domain. It corresponds, however, to the small displacement formulation.
Free-surface or interface positions act as Dirichlet boundary conditions on Equation 16–15 and Equation 16–16 More precisely, a prescribed displacement is imposed in the direction perpendicular to the domain boundary, while zero-traction conditions apply in the tangential directions, leaving to the system the possibility of adapting the mesh tangentially. In regions where no particular displacement applies, a zero-normal/zero-tangential-traction condition is applied, so that tangential remeshing coming from adjacent boundary displacements is allowed.
Examples include cases where the inherent topological complexity makes it difficult (or even impossible) to apply topologically regular methods, such as 2D and 3D extrusion and 3D parison extrusion modeling.
Moreover, the coupling between the remeshing and the kinematic condition (line or
surface) is treated differently. In the elastic remeshing, the physical dimension of the
pseudo-Young’s modulus 
matters, and should be small enough so that the remeshing equation
does not perturb the kinematic condition.
On the contrary, the improved elastic remeshing does not perturb the kinematic condition, and hence the pseudo-Young’s modulus value in Equation 16–16 has no importance.
Because the pseudo-Young’s modulus must be small so as not to perturb kinematic conditions, and because of its nonlinearity (to allow the proper application of tangential remeshing), the elastic method may have a lower radius of convergence than the spine or Optimesh methods, so you may need to use an evolution strategy to obtain convergence. See Evolution for details about evolution.
The improved elastic method suffers less from this drawback. Because the improved elastic remeshing does not require a sliceable mesh, if you want to add a constraint on the free jet (which does require a sliceable mesh), you have to provide the inlet and outlet sections of the remeshing region for the slicing. In order to do that, after the selection of the Improved Elastic remeshing menu item, Ansys Polydata displays the following question:
Is this remeshing defined on a free jet part and do you intend to stabilize
the free jet?
If you click the button, Ansys Polydata asks you to select the inlet and outlet sections and the Constraint on the free jet displacement option will be available. If you click the button, Ansys Polydata does not ask any further questions and the Constraint on the free jet displacement option will not be available.