A nonlocal fracture criterion and its effect on the mesh dependency of GraFEA

Remeshing-Free Graph-Based Finite Element Method for Ductile and Brittle Fracture

“…The advantage of using Gra-FEA is that it requires no remeshing, while adding little computational overhead on FEM and it still retains all the advantages of FEM. The dependency of Gra-FEA on the underlying mesh structure is thoroughly studied in another work [Khodabakhshi et al 2019]. Our work introduces Gra-FEA to the visual simulation of fracture for computer graphics.…”

“…While vector r refers to position of centroid of any tetrahedron in the mesh, r 0 denotes the position of centroid of the reference tetrahedron. As the support of kernel, 𝑅 𝑑 , increases, the cracks become more diffused i.e., they spread more inside the object [Khodabakhshi et al 2019]. For 𝑅 𝑑 = 0, the fracture criteria depends only on the reference tetrahedron, resembling a local fracture.…”

Fracture modelling of plain concrete using non-local fracture mechanics and a graph-based computational framework

“…The region meshed with a finer mesh density (where cracking is anticipated) has an average element size of le=1.5 mm. Therefore, dϕ=2rϕ=4le, and this condition is sufficient to produce a mesh-independent global force–displacement response [33,38]. …”

“…These non-local crack interactions are modelled using graph theoretic approaches in population dynamics [26]. Following [32,33], it is well known that the nodes and edges of a finite element discretization form a simplical complex [34,35]. Reddy & Srinivasa [36] have shown that (i) the strain energy function depends only on suitably defined graph edge distances and (b) the nodal forces maybe non-local but their directions are only along the edges.…”

A smoothed variable horizon peridynamics and its application to the fracture parameters evaluation

“…A coupling approach for extended multiscale FEM and PD was proposed for an efficient simulation of crack propagation in large scale solid structures [18]. Khodabakhshi et al [19] proposed a non-local fracture criterion for a special type of FEA for eliminating the mesh sensitivity in results caused by a local fracture criterion. The proposed criterion can also be utilized within the traditional FEM.…”