Embedded interfaces by polytope FEM

Abstract

SUMMARYIn this paper, the Polytope Finite Element Method is employed to model an embedded interface through the body, independent of the background FEM mesh. The elements that are crossed by the embedded interface are decomposed into new polytope elements which have some nodes on the interface line. The interface introduces discontinuity into the primary variable (strong) or into its derivatives (weak). Both strong and weak discontinuities are studied by the proposed method through different numerical examples including fracture problems with traction-free and cohesive cracks, and heat conduction problems with Dirichlet and Dirichlet-Neumann types of boundary conditions on the embedded interface. For tractionfree cracks which have tip singularity, the nodes near the crack tip are enriched with the singular functions through the eXtended Finite Element Method.The concept of Natural Element Coordinates (NECs) is invoked to drive shape functions for the produced polytopes. A simple treatment is proposed for concave polytopes produced by a kinked interface and also for locating crack tip inside an element prior to using the singularity enrichment. The proposed method pursues some implementational details of eXtended/Generalized Finite Element Methods for interfaces. But here the additional DOFs are constructed on the interface lines in contrast to X/G-FEM, which attach enriched DOFs to the previously existed nodes.

Cohesive and non‐cohesive fracture by higher‐order enrichment of XFEM

“…We wish to solve (17) for X and˛subject to the constraint of satisfying the crack propagation criterion denoted in the general form as P D 0. The residual of the Newton-Raphson method is defined as…”

Polygon scaled boundary finite elements for crack propagation modelling

“…Compared with the polygon elements developed in , classical finite element shape functions can be used for an arbitrary polygon. A simple and flexible local remeshing procedure that is augmented from Ref.…”

“…This coupled method retains the advantages of both XFEM and HCE. It can model a crack independent of the finite element mesh yet still able to compute accurate stress intensity factors (SIF) and coefficients of higher order terms of the crack tip asymptotic field.Nodal enrichment has also been recently implemented with polygon-based finite elements by Tabarraei and Sukumar [21] and Zamani and Eslami [22] in polygon finite elements based on barycentric coordinates shape function, Li and Ghosh [23,24] in the Voronoi cell FEM and by in the SFEM to model crack propagation. Therein, the salient features of the proposed methods were demonstrated for various crack propagation problems.This paper presents an automatic crack propagation modelling technique using polygon elements that are formulated using the scaled boundary finite element method (SBFEM).…”

“…Once a domain has been discretised using polygons, each polygon can simply be treated by the SBFEM as a subdomain. This method retains the attractive feature of the SBFEM in that it does not require any nodal enrichment or special integration techniques such as in [13][14][15][16][17][18][19][21][22][23][24][25]] and yet, still captures the singular stress field at the crack tip Compared with the polygon elements developed in [1-3, 21, 22], classical finite element shape functions can be used for an arbitrary polygon. A simple and flexible local remeshing procedure that is augmented from Ref.[30] is used to accommodate crack propagation.…”

“…Nodal enrichment has also been recently implemented with polygon-based finite elements by Tabarraei and Sukumar [21] and Zamani and Eslami [22] in polygon finite elements based on barycentric coordinates shape function, Li and Ghosh [23,24] in the Voronoi cell FEM and by in the SFEM to model crack propagation. Therein, the salient features of the proposed methods were demonstrated for various crack propagation problems.…”