In this presentation we will discuss a continuum multiscale framework which combines the Bridging Domain Method (BDM) of Xiao and Belytschko [1] with the eXtended Finite Element Method (XFEM) of of Moës et al. [2]. The BDM is a hierarchical overlapping domain decomposition scheme. Material in the coarse-scale domain is modelled as a continuum using XFEM and in the fine-scale domain by Molecular...

• The variable-node multiscale extended finite element method (V-XFEM) is elaborated for the dynamic crack analysis of linearly uncoupled and coupled physical phenomena in a compact formula. numerical results elastic piezoelectric problems considered as illustrated examples show that V-XFEM has higher accuracy more efficiency than standard XFEM. For structures, normalized intensity factors have...

We introduce a new, efficient approach for modelling the deformation of organs following surgical cuts, retractions, and resections. It uses the extended finite element method (XFEM), recently developed in ”fracture mechanics” for dealing with cracks in mechanical parts. XFEM eliminates the computationally-expensive remeshing that would be required if the standard finite element method (FEM) wa...

This paper presents a fracture mapping (FM) approach combined with the extended finite element method (XFEM) to simulate coupled deformation and fluid flow in fractured porous media. Specifically, the method accurately represents the impact of discrete fractures on flow and deformation, although the individual fractures are not part of the finite element mesh. A key feature of FM-XFEM is its ab...

This paper develops the extended finite element method (XFEM) to evolve patterns of multiple cracks, in a brittle thin film bonded to an elastic substrate, with a relatively coarse mesh, and without remeshing during evolution. A shear lag model describes the deformation in three dimensions with approximate field equations in two-dimensions. The film is susceptible to subcritical cracking, obeyi...

Healing large bone defects, especially in weight-bearing locations, remains a challenge using available synthetic ceramic scaffolds. Manufactured as a scaffold using 3D printing technology, Sr-HT-Gahnite at high porosity (66%) had demonstrated significantly improved compressive strength (53 ± 9 MPa) and toughness. Nevertheless, the main concern of ceramic scaffolds in general remains to be thei...

This paper presents and studies a residual a posteriori error estimator for Laplace’s equation in two space dimensions approximated by the eXtended Finite Element Method (XFEM). The XFEM allows to perform finite element computations on multi-cracked domains by using meshes of the non-cracked domain. The main idea consists of adding supplementary basis functions of Heaviside type and singular fu...