An extended boundary element method formulation for the direct calculation of the stress intensity factors in fully anisotropic materials

Abstract

(2017) 'An extended boundary element method formulation for the direct calculation of the stress intensity factors in fully anisotropic materials.', International journal for numerical methods in engineering., 109 (7). pp. 965-981. Further information on publisher's website:https://doi.org/10.1002/nme.5311Publisher's copyright statement: This is the accepted version of the following article: Hattori, G., Alatawi, I.A. Trevelyan, J. (2017). An extended boundary element method formulation for the direct calculation of stress intensity factors in fully anisotropic materials. International Journal for Numerical Methods in Engineering, 109(7): 965-981, which has been published in nal form at https://doi.org/10.1002/nme.5311. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. ABSTRACTWe propose a formulation for linear elastic fracture mechanics (LEFM) in which the stress intensity factors (SIF) are found directly from the solution vector of an extended boundary element method (XBEM) formulation. The enrichment is embedded in the BEM formulation, rather than adding new degrees of freedom for each enriched node. Therefore, a very limited number of new degrees of freedom is added to the problem, which contributes to preserving the conditioning of the linear system of equations. The Stroh formalism is used to provide BEM fundamental solutions for any degree of anisotropy, and these are used for both conventional and enriched degrees of freedom. Several numerical examples are shown with benchmark solutions to validate the proposed method.

A non-ordinary state-based peridynamics framework for anisotropic materials

“…The dynamic stress intensity factors (DSIF) are calculated and compared with converged FEM solutions. We have employed the extrapolation method in order to calculate the DSIF as follows [16,49]…”

“…where K I (t) and K II (t) are the dynamic mode I and mode II at time t, respectively; ∆u 1 (t) and ∆u 2 (t) are the crack opening displacement at time t in the x and y-direction, respectively; A, B come from the material properties and are obtained from the Stroh formalism [16,44]; (•) represents the real part of (•) while i is the imaginary component; and r is the distance where the crack opening displacements are measured to the crack tip.…”

“…Fracture mechanics have been studied for nearly a century, from the first work of Griffith [15] for brittle materials. Over the years a number of researchers have modelled fracture mechanics analytically [28,36] for simple problems and geometries, and more commonly using numerical frameworks, such as the extended finite element method (XFEM) [4,27] and the extended boundary element method (XBEM) [16], among many others. Nevertheless, these methods suffer when crack branching or coalescence are involved.…”

“…Several numerical examples have been used to validate the approach, and compared to other benchmark solution from the finite element method (FEM) and experimental results when available.Fracture mechanics have been studied for nearly a century, from the first work of Griffith [15] for brittle materials. Over the years a number of researchers have modelled fracture mechanics analytically [28,36] for simple problems and geometries, and more commonly using numerical frameworks, such as the extended finite element method (XFEM) [4,27] and the extended boundary element method (XBEM) [16], among many others. Nevertheless, these methods suffer when crack branching or coalescence are involved.The phase-field method has been shown to model crack branching behaviour [1,18].…”

Mixed Finite Element Computation of Energy Release Rate in Anisotropic Materials Based on Virtual Crack Closure-Integral Method

“…In nature, most materials are anisotropic and in the recent works on industrial fields tends to focus on those type of materials [1][2][3][4][5]. I Several works on the crack propagation in anisotropic material made their reliability, where it is investigated with the linear elastic fracture mechanics [6] and the J-Integral [7] but the phase-field modeling developed for the anisotropic surface energy [8] is getting popular for brittle anisotropic material [9,10] and in crystalline material [11,12]. The finite element method is also known for treating the fracture mechanics problems, the Stroh formalism is used with an enriched boundary element method to offer better results for any degrees of anisotropy [6].…”