Partition of unity enrichment for bimaterial interface cracks

Abstract

SUMMARYPartition of unity enrichment techniques are developed for bimaterial interface cracks. A discontinuous function and the two-dimensional near-tip asymptotic displacement functions are added to the finite element approximation using the framework of partition of unity. This enables the domain to be modelled by finite elements without explicitly meshing the crack surfaces. The crack-tip enrichment functions are chosen as those that span the asymptotic displacement fields for an interfacial crack. The concept of partition of unity facilitates the incorporation of the oscillatory nature of the singularity within a conforming finite element approximation. The mixed-mode (complex) stress intensity factors for bimaterial interfacial cracks are numerically evaluated using the domain form of the interaction integral. Good agreement between the numerical results and the reference solutions for benchmark interfacial crack problems is realized.

The extended/generalized finite element method: An overview of the method and its applications

“…XFEM has been applied to bimaterial problems by Sukumar et al [100], Hettich et al [54] and Huynh and Belytschko [56]. In the latter, both the crack and the interface were described by level sets.…”

Finite element-based model for crack propagation in polycrystalline materials

“…In [17], the linear elastic near-tip asymptotic fields were used as enrichment functions, whereas in [26], the asymptotic near-tip fields for a bimaterial interface crack were adopted. We summarize some of the essential concepts related to 2-d crack modeling in isotropic media [17].…”

A Reduced Basis Enrichment for the eXtended Finite Element Method

“…The classical Xfem may become very expensive to model bi-material interface cracks ( [28]) because the number of nonsmooth functions generating the exact opening mode and the shear mode increases significantly compared to the homogeneous case ( [14], [13]). In RB-Xfem, the number of pre-computed functions will be the same than in the homogeneous case, i.e.…”

“…When the fracture propagates along the interface between two different materials, the asymptotic displacement u s can be also written as in (2.5) with more intricate expressions of the two modes u I and u II than in the homogeneous case [10,28]. Let T h be a regular family of triangulations (in the sense of Ciarlet [8]) of the non-cracked domain Ω * (h being the mesh parameter).…”