13th International Conference on Fracture June 16–21, 2013, Beijing, China Refined volume mesh Surface mesh Cutting algorithm Cut surface mesh Figure 1. Cutting surface input/output. The second stage of the a algorithm is related to a volumetric mesh adaption of the uncracked structure closely to the crack geometry. This operation is done using an iterative process. For each point of the actual volumetric mesh, the closest point of the crack surface will be searched (using a binary tree with a log(n) complexity for n points on the crack surface). Let d be the distance between any those two points. Thus an explicit refinement function is applied to specify the required element size on the volumetric mesh: (1) where hmin is a minimal edge length, N is the number of minimal size element layers that must be imposed closely to the crack surface, is a refinement factor (usually chosen within 0.1<) and h is the actual mesh size (meaning that only a refinement operation is done). Figure 2. Operation on a near surface cut element. The volumetric remeshing operation is then carried out on the complete mesh (or only a subdomain close enough to the crack surface - while the interface with the rest of the mesh must be exactly preserved). This stage is done using the meshadapt software from Distene/Inria where the imposed isotropic refinement map is imposed. Another required distance map is finally rebuilt (using the same refinement function) on the output mesh and compared to the actual edges size. If the size maps are close enough, convergence is assumed to be reached, in the other case another remeshing -3Initial volume element Cutting surface element Local crack surface Edge intersections with the crack surface Element faces intersection with crack front Inserted crack front
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