We consider an unsteady convection diffusion equation which models the transport of a dissolved species in two-phase incompressible flow problems. The so-called Henry interface condition leads to a jump condition for the concentration at the interface between the two phases. In [A. Hansbo, P. Hansbo, Comput. Methods Appl. Mech. Engrg. 191 (20002)], for the purely elliptic stationary case, exten...

In Part I [Int. J. Solids Struct., 2003], we described the implementation of the extended finite element method (XFEM) within Dynaflowe, a standard finite element package. In our implementation, we focused on two-dimensional crack modeling in linear elasticity. For crack modeling in the X-FEM, a discontinuous function and the near-tip asymptotic functions are added to the finite element approxi...

The modelization of bending plates with through the thickness cracks is investigated. We consider the Kirchhoff-Love plate model which is valid for very thin plates. We apply the eXtended Finite Element Method (XFEM) strategy: enrichment of the finite element space with the asymptotic bending and with the discontinuity across the crack. We present two variants and their numerical validations an...

A representative volume element (RVE) based multi-scale method is proposed to investigate the mechanism of fatigue crack propagation by molecular dynamics (MD) and extended finite methods(XFEM) in this study. An atomic model carbon steel plate built study behavior at micro scale MD method. Then RVE for should be fitting data which was obtained from result with Paris law model. Moreover, effect ...

The extended finite element method (XFEM) enables the representation of cracks in arbitrary locations of a mesh. We introduce here a variant of the XFEM rendering an optimally convergent scheme. Its distinguishing features are: a) the introduction of singular asymptotic crack tip fields with support on only a small region around the crack tip, the enrichment region, b) only one and two enrichme...

We consider a standard model for incompressible two-phase flows in which a localized force at the interface describes the effect of surface tension. If a level set method is applied then the approximation of the interface is in general not aligned with the triangulation. This causes severe difficulties w.r.t. the discretization and often results in large spurious velocities. In this paper we re...

Recently, a new strategy was proposed to solve stochastic partial differential equations on random domains. It is based on the extension to the stochastic framework of the eXtended Finite Element Method (X-FEM). This method leads by a “direct” calculus to an explicit solution in terms of the variables describing the randomness on the geometry. It relies on two major points: the implicit represe...

Dendritic solidification of pure materials from an undercooled melt is studied using the extended finite element method/level set method for modelling the thermal problem and a volume-averaged stabilized finite element formulation for modelling fluid flow. The extended finite element method using evolving enrichment functions allows accurate modelling of the discontinuous thermal conditions at ...

Abstract: The thermo-elastic fracture problem and equations are established for aluminium alloy Metal Inert Gas (MIG) welding, which include a moving heat source and a thermoelasticity equation with the initial and boundary conditions for a plate structure with a crack. The extended finite element method (XFEM) is implemented to solve the thermo-elastic fracture problem of a plate structure wit...

The use of temporary hip prosthesis made orthopedic cement (spacer) in conjunction with antibiotics became a widespread method used for treating prosthetic infections despite the fact that this makes bone (PMMA) more fragile. necessity to incorporate reinforcement is therefore crucial strengthen cement. In study, validated Finite Element Modelling (FEM) was analyze behavior spacers. This FEM mo...