Revisiting the topological enrichment pattern in the linear elastic fracture modeling via GFEM / XFEM

Resumo

The way of performing special enrichment to model crack tip singularities, in the linear elastic fracture
analysis via Partition of Unity (PoU) based methods, has been an issue of concern over the past two decades.
One aspect of significant importance is to alleviate the mesh dependences to assure convergence rates do not be
adversely affected by the discretization h-parameter reduction. The geometric enrichment pattern emerged as the
preferable strategy to reach such a goal. Additionally, the PoU regularity has been identified as a feature of great
impact in the ansatz’s capability of capturing the singularity of such especial enrichments, as shown in recent results
in the context of C
k
-GFEM. Thus, once lower dependence on the enrichment zone size has been found in the case
of using smooth PoU functions, the enrichment strategies which lead to a smaller increment in the amount of DOF
become attractive again. This work aims to study how the topological pattern of enrichment performs in the case
of the C
k
-GFEM if compared to the conventional XFEM / GFEM. Different schemes of polynomial enrichment
are also considered trying to enlighten some blending / transition effects. The approximations performances are
assessed by crack severity parameters computation using the material forces method.