A vector level set method and new discontinuity approximations for crack growth by EFG.

*(English)* Zbl 1034.74053
Summary: We present a new vector level set method for modelling propagating cracks in the element-free Galerkin (EFG) method. With this approach only nodal data are used to describe the crack; no geometrical entity is introduced for the crack trajectory, and no partial differential equations need to be solved to update the level sets. The nodal description is updated as the crack propagates by geometric equations. The advantages of this approach, here introduced and analysed for the two-dimensional case, are particularly promising in three-dimensional applications, where the geometric description and evolution of an arbitrary crack surface in a complex solid is very awkward. In addition, new methods for crack approximations in EFG are introduced, using a jump function accounting for the displacement discontinuity along crack faces, and the Westergard’s solution enrichment near crack tips. These enrichments, being extrinsic, can be limited only to the nodes surrounding the crack, and are naturally coupled to the level set crack representation.

##### MSC:

74S30 | Other numerical methods in solid mechanics |

74R10 | Brittle fracture |