ClosestPoint is the most commonly-used option and accounts for most of the mapping scenarios targeted by the Envyo application. Beginning with the target mesh, the next element or integration point is identified and its data transferred to the target mesh.

The ElementSizeSearchRadius option supports mapping of results from mesoscale process simulations using shell elements onto a target mesh. The target mesh element size is therefore used as a search radius, whereas the source mesh elements are projected onto the target mesh along the source-mesh normal and a check is performed to see if the intersection is within the target element. The element size can be scaled using Scale_SearchRadius (below).

The ConsiderOndulation option considers the through-thickness position of the identified fiber orientation. This information is therefore not considered as provided by user input, but by the position in the source mesh related to the target mesh. This option does not account for the ordering of the input parts - it first maps those that are closest to the target part, then the second closest and so on. No resinuous areas can be assigned with this option. If the MapThickness option (below) is enabled, the offset between the source layers is also considered, which usually leads to varying thicknesses throughout the part.

With RVE Detection, you can define specific criteria which allows the Envyo application to decide if a specific combination of fibers has been identified and therefore assigns a specific, user-defined material ID to the dedicated integration point.

CP - directly activates the closest point algorithm to transfer everything stored in the *INITIAL STRESS OPTION fields on the source side. This is the default algorithm.

AVG - the euclidean average is taken from the values found within a specific search radius. By default, the search radius is based on the average target mesh element length.

SHEPARD NO1 - activates the general Shepard's inverse distance weighting function. You may specify the exponent using the SHEPARD EXPONENT option.

SHEPARD NO2 - activates the Shepard's inverse distance weighting function, with a minimum of four and a maximum of ten points considered for the interpolation function. You may also specify the exponent using the SHEPARD EXPONENT option.

SHEPARD NO3 - activates the Shepard's inverse distance weighting function, with a minimum of four and a maximum of ten points considered for the interpolation function, including direction. You may also specify the exponent using the SHEPARD EXPONENT option.

SHEPARD NO4 - activates the Shepard's inverse distance weighting function, with a minimum of four and a maximum of ten points considered for the interpolation function, including direction and the slope. You may also specify the exponent using the SHEPARD EXPONENT option.

The search radius for the four options listed above is adjusted based on Shepard's proposal, see [22].

FE - activates the interpolation of values found in the *INITIAL STRESS OPTION fields based on finite element shape functions and point projection of the considered integration points into the plane of the source shells. If the source and target through-thickness integration rules are different, through-thickness interpolation is performed based on the method proposed in [24], minimizing the difference in the areas underneath the through-thickness integration rules on source- and target side for all values being transferred. This interpolation result can be visualized using the WriteTTInterpolationFile and TTInterpolationFile options.

FE NODAL AVG - activates the interpolation of values found in the *INITIAL STRESS OPTION fields based on finite element shape functions and point projection of the considered integration points into the plane of the source shells. In addition to the described method above, values of the connected elements on the source side are also considered through extrapolation of the integration point values onto the element nodes, taking the euclidean average and performing a value recovery on the target integration point.

Besides using the standard euclidean average (AVG), which is the default and recommended value, further interpolation methods based on tensor invariants have been investigated due to the fact that swelling effects are often seen when performing standard euclidean average of tensorial data (the tensor shape changes).

Based on the work of [9], several invariant sets have been implemented for the interpolation functions available in MapStress, and linear interpolation is performed for these invariant sets instead of the single tensorial values. These interpolated invariants allow you to recover the eigenvalues based on a closed form solution of the cubic function and together with the eigenvectors determined through linear interpolation of the originating tensors, the resulting tensor can be recovered.

Due to the boundaries of the recovery function, which is based on the arccosine defined between -1.0 ≤ x ≤ 1.0, this might lead to unexpected behavior with the current implementation.

INV-K refers to an orthogonal invariant set based the tensor trace, the Frobenius norm of the tensor's deviatoric (fractional anisotropy of the tensor), and the mode of the deviatoric.

INV-R refers to an orthogonal invariant set based the tensor norm, the relative anisotropy of the tensor, and the mode of the deviatoric as in INV-K.

INV-N is a non-orthogonal invariant set based on the tensor trace, the fractional anisotropy, and the tensor mode.

INV-U is a uniform invariant set based on the tensor trace, the scaled relative anisotropy of the tensor, and the scaled angular mode AM.

These invariant sets have been proposed in [9] for positive definite tensors gained in DT-MRI measurements. Generally, stress tensors are not positive definite. The Cauchy stress tensor invariant set INV-C is therefore added to the interpolation options, even though this might not solve the issue regarding the arccos in the recovery function.

For cases where the target mesh does not contain any information regarding the integration rules being used, such as element formulation and through-thickness integration points, you must define these manually. The input for this is as follows: