This study aimed at using eXtended finite element method (XFEM) to characterize crack growth through bone's intra-cortical pores. Two techniques were compared using Abaqus: (1) void material properties were assigned to pores; (2) multiple enrichment regions with independent crack-growth possibilities were employed. Both were applied to 2D models of transverse images of mouse bone with differing...

The paper shows an inf-sup stability property for several well-known 2D and 3D Stokes elements on triangulations which are not fitted to a given smooth or polygonal domain. The property implies stability and optimal error estimates for a class of unfitted finite element methods for the Stokes and Stokes interface problems, such as Nitsche-XFEM or cutFEM. The error analysis is presented for the ...

We consider a standard model for mass transport across an evolving interface. The solution has to satisfy a jump condition across an evolving interface. We present and analyze a finite element discretization method for this mass transport problem. This method is based on a space-time approach in which a discontinuous Galerkin (DG) technique is combined with an extended finite element method (XF...

In this work, XFEM is employed to obtain the stress intensity factors (SIFs) of a semi elliptical part through thickness axial crack. In XFEM, additional functions are employed to enrich the displacement approximation using partition of unity approach. Level set functions are approximated using higher order shape functions in the crack front elements to ensure the accurate modeling of the crack...

In this paper, and its companion Part 2 [Dong and Atluri (2013b)], the Symmetric Galerkin Boundary Element Method (SGBEM), and the SGBEMFEM alternating/coupling methods, are compared with the recently popularized Extended Finite Element Method (XFEM), for analyzing fracture and fatigue crack propagation in complex structural geometries. The historical development, and the theoretical/algorithmi...

Fatigue failure of strucutres is normally caused by cracks that extend beyond a safe size. Flaws are present to some extend in all structural parts, either as a result of manufacturing fabrication defects or damage in service. Crack growth is a complex phenomenon to model and simplifications are assumed. In recent years, there has been an increasing realisation that advanced computational metho...

this paper focuses on using the recently developed extended finite element model for buckling analysis of edge cracked columns under concentric axial load. the effect of crack depth and its location on the carrying capacity of columns is studied. the effect of different boundary conditions is also investigated. numerical examples are offered to show the efficiency and effectiveness of the propo...

Deformable fractured porous media appear in many geoscience applications. While the extended finite element (XFEM) has been successfully developed within computational mechanics community for accurate modeling of deformation, its application natural geoscientific applications is not straightforward. This mainly due to fact that subsurface formations are heterogeneous and span large length scale...

This paper presents a novel framework for probabilistic crack size quantification using fiber Bragg grating (FBG) sensors. The key idea is to use a high-order extended finite element method (XFEM) together with a transfer (T)-matrix method to analyze the reflection intensity spectra of FBG sensors, for various crack sizes. Compared with the standard FEM, the XFEM offers two superior capabilitie...