Developing new enrichment functions for crack simulation in orthotropic media by the extended finite element method

Abstract

SUMMARYNew enrichment functions are proposed for crack modelling in orthotropic media using the extended finite element method (XFEM). In this method, Heaviside and near-tip functions are utilized in the framework of the partition of unity method for modelling discontinuities in the classical finite element method. In this procedure, by using meshless based ideas, elements containing a crack are not required to conform to crack edges. Therefore, mesh generation is directly performed ignoring the existence of any crack while the method remains capable of extending the crack without any remeshing requirement. Furthermore, the type of elements around the crack-tip remains the same as other parts of the finite element model and the number of nodes and consequently degrees of freedom are reduced considerably in comparison to the classical finite element method. Mixed-mode stress intensity factors (SIFs) are evaluated to determine the fracture properties of domain and to compare the proposed approach with other available methods. In this paper, the interaction integral (M-integral) is adopted, which is considered as one of the most accurate numerical methods for calculating stress intensity factors.

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

“…Recently enrichments for orthotropic materials have been given in [4] and a further discussion of their application can be found in [77]. The four enrichment functions for orthotropic materials are only a little more complicated than the branch functions (6) and are given by…”

An experimental/numerical investigation into the main driving force for crack propagation in uni-directional fibre-reinforced composite laminae

“…These branch functions span the first order terms of the Williams' expansion [34] of the asymptotic displacement field around a crack tip in a linear elastic material. For orthotropic materials, attempts have been made to derive the crack tip enrichment functions by [19] (See also Menk and Bordas [28] where those are computed numerically). The asymptotic fields for orthotropic materials are given in [19] as,…”

“…For orthotropic materials, attempts have been made to derive the crack tip enrichment functions by [19] (See also Menk and Bordas [28] where those are computed numerically). The asymptotic fields for orthotropic materials are given in [19] as,…”

“…This is despite the fact that such a method, which has been shown to perform efficiently for damage tolerance assessment of complex structures [16], [17], [18] and also holds promise for the analysis of the durability of composite materials by virtue of its ability to describe arbitrary crack growth without remeshing and with relatively coarse meshes. The most significant contributions in the area of orthotropic materials have come from [19], [20], [21] who developed new crack tip enrichment functions to effectively capture the crack tip displacement fields within linear elastic orthotropic materials. Further developments in dynamics allowed the study of propagation in orthotropic materials using XFEM [22].…”

“…In this paper, a new tool based on the extended finite element method (XFEM) which allows to simulate the growth of arbitrary cracks in orthotropic materials is devised, analysed and validated experimentally. The technique builds on recent work of Asadpoure and Mohammadi [19], which concentrates on the calculation of stress intensity factors (SIFs) and extends it to allow the accurate simulation of crack growth through an orthotropic material. The model is thoroughly validated by a bespoke test series and further applied to more complex problems to study the driving factors for crack propagation in orthotropic laminae.…”