A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM.

*(English)* Zbl 1144.74043
Summary: We present a comparative study on finite elements for capturing strong discontinuities by means of elemental (E-FEM) or nodal enrichments (X-FEM). Based on the same constitutive model (continuum damage) and linear elements (triangles and tetrahedra), optimized implementations of both types of enrichments in the same nonlinear code are tested for a representative set of 2D and 3D crack propagation examples. It is shown that both methods provide the same qualitative and quantitative results for enough refined meshes. For the performed tests, E-FEM exhibited, in general, a higher accuracy, mostly for coarse meshes, whereas, convergence rate with mesh refinement, which is super-linear, showed slightly higher for X-FEM. As for the computational costs for single crack modelling X-FEM showed, depending on the case, from 1.1 to about 2.5 times more expensive than E-FEM. For multiple cracks, the computational cost of E-FEM keeps constant, whereas the cost associated to X-FEM increases linearly with the number of modelled cracks.

##### MSC:

74S05 | Finite element methods in solid mechanics |

74R10 | Brittle fracture |