On the use of effective properties for the fracture analysis of microstructured materials

Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation

“…In Wagner et al (2001), a computational model for rigid particles in Stokes flow was proposed, whereas moving phase boundary problems have been modeled using the coupled extended finite element and level set methods (Merle and Dolbow, 2002;Ji et al, 2002;Chessa et al, 2002). Dolbow and Nadeau (2002) investigated the use of effective properties for fracture analysis in functionally-graded systems, whereas Sukumar et al (2003b) adopted the X-FEM as a fracture tool to study the competition between intergranular and transgranular modes of crack growth through a material microstructure. In other related studies, Wells and Sluys (2001) used the Heaviside step function to model the displacement discontinuity within a finite-element based cohesive crack model, whereas Wells et al (2002) used partition of unity enrichment to alleviate volumetric locking during plastic flow.…”

Crack analysis in orthotropic media using the extended finite element method

“…In this method a discontinuous function and the near-tip asymptotic displacement fields are added to the finite element approximation by means of partition of unity. Belytschko and Black [12], Moe¨s et al [13], Dolbow et al [14][15][16][17], Dolbow and Nadeau [18], Daux et al [19], reported 2-D isotropic modelings, while Sukumar et al [20] conducted 3-D modeling.…”

A survey of the extended finite element

“…The X-FEM has been utilized to model computational phenomena in areas such as fluid mechanics, phase transformations, and materials science: Solidification problems [130][131][132], multi-phase flow [133], functionally graded materials FGMs [134,135], powder forming problems [136,137], and bio-film growth [138].…”