A hybrid boundary element method for three-dimensional fracture analysis

At first, a hybrid boundary element method used for three-dimensional linear elastic fracture analysis is established by introducing the relative displacement fundamental function into the first and the second kind of boundary integral equations. Then the numerical approaches are presented in detail. Finally, several numerical examples are given out to check the proposed method. The numerical results show that the hybrid boundary element method has a very high accuracy for analysis of a three-dimensional stress intensity factor.     

Time dependent principal stress analysis by the hybrid method of photoviscoelasticity and boundary element

In this paper the basic relations in linear isotropic photoviscoelasticity have been discussed theoretically in detail. A new routine to solve the time dependent principal stress without the measurement of isoclinics has been found. As a proof of the method, examples are illustrated at the end of this paper.     

Determination of stress intensity factors for bimaterial interface stationary rigid line inclusions by boundary element method

The stress intensity factors for a rigid line inclusion lying along a bimaterial interface are calculated by the boundary element method with the multiregion and the discontinuous traction singular elements. The relationships between the stress intensity factors and the inclusion surface stresses are derived. The numerically computed stress intensity factors for the bimaterial interface rigid line inclusion in the infinite body are proved to be in good agreement within 3% when compared with the previous exact solutions. In the finite bimaterial models, the stress intensity factors for the center and edge rigid line inclusions at the interface are computed with the variation of the rigid line inclusion length and the shear modulus ratio under the uniaxial and biaxial loading conditions.     

Explicit determination of element stiffness matrices in the hybrid stress method

The hybrid stress method has demonstrated many improvements over conventional displacement-based formulations. A main detraction from the method, however, has been the higher computatational cost in forming element stiffness coefficients due to matrix inversions and manipulations as required by the technique. By utilizing permissible field transformations of initially assumed stresses, a spanning set of orthonormalized stress modes can be generated which simplify the matrix equations and allow explicit expressions for element stiffness coefficients to be derived. The developed methodology is demonstrated using several selected 2-D quadrilateral and 3-D hexahedral elements.     

An indirect boundary element method for three-dimensional dynamic fracture mechanics

Indirect boundary element methods (fictitious load and displacement discontinuity) have been developed for the analysis of three-dimensional elastostatic and elastodynamic fracture mechanics problems. A set of boundary integral equations for fictitious loads and displacement discontinuities have been derived. The stress intensity factors were obtained by the stress equivalent method for static loading. For dynamic loading the problem was studied in Laplace transform space where the numerical calculation procedure, for the stress intensity factor K_I(p), is the same: as that for the static problem. The Durbin inversion method for Laplace transforms was used to obtain the stress intensity factors in the time domain K_I(t). Results of this analysis are presented for a square bar, with either a rectangular or a circular crack, under static and dynamic loads.     

Dual boundary element method for anisotropic dynamic fracture mechanics

In this work, the dual boundary element method formulation is developed for effective modelling of dynamic crack problems. The static fundamental solutions are used and the domain integral, which comes from the inertial term, is transformed into boundary integrals using the dual reciprocity technique. Dynamic stress intensity factors are computed from crack opening displacements. Comparisons are made with quasi‐isotropic as well as anisotropic results, using the sub‐region technique. Several examples are presented to assess the accuracy and efficiency of the proposed method. Copyright © 2004 John Wiley & Sons, Ltd.     

Dual boundary element method for three-dimensional thermoelastic crack problems

This paper describes the formulation and numerical implementation of the three-dimensional dual boundary element method (DBEM) for the thermoelastic analysis of mixed-mode crack problems in linear elastic fracture mechanics. The DBEM incorporates two pairs of independent boundary integral equations; namely the temperature and displacement, and the flux and traction equations. In this technique, one pair is applied on one of the crack faces and the other pair on the opposite one. On non-crack boundaries, the temperature and displacement equations are applied. This revised version was published online in July 2006 with corrections to the Cover Date.     

Simulating three-dimensional stress intensity factors by the least-squares method

The main purpose of this paper is to investigate the accuracy of the least-squares method incorporating the finite element method for finding three-dimensional (3-D) Stress Intensity Factors (SIFs). Numerical simulations in this paper indicate that the least-squares method can be used to calculate 3-D SIFs accurately, if three or more than three displacement or stress terms are included. The calculated SIFs of this method are independent of the maximum radius of the area from which data is included; furthermore, a very fine mesh is not necessary. © 1998 John Wiley & Sons, Ltd.     

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

We propose a formulation for linear elastic fracture mechanics in which the stress intensity factors are found directly from the solution vector of an extended boundary element method formulation. The enrichment is embedded in the boundary element method 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 boundary element method 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. Copyright © 2016 John Wiley & Sons, Ltd.     

Modelling dynamic crack propagation using the scaled boundary finite element method

This study presents a novel application of the scaled boundary finite element method (SBFEM) to model dynamic crack propagation problems. Accurate dynamic stress intensity factors are extracted directly from the semi‐analytical solutions of SBFEM. They are then used in the dynamic fracture criteria to determine the crack‐tip position, velocity and propagation direction. A simple, yet flexible remeshing algorithm is used to accommodate crack propagation. Three dynamic crack propagation problems that include mode‐I and mix‐mode fracture are modelled. The results show good agreement with experimental and numerical results available in the literature. It is found that the developed method offers some advantages over conventional FEM in terms of accuracy, efficiency and ease of implementation. Copyright © 2011 John Wiley & Sons, Ltd.     

Computation of the stress intensity factors of sharp notched plates by the fractal‐like finite element method

The fractal‐like finite element method (FFEM) is an accurate and efficient method to compute the stress intensity factors (SIFs) of different crack configurations. In the FFEM, the cracked/notched body is divided into singular and regular regions; both regions are modelled using conventional finite elements. A self‐similar fractal mesh of an ‘infinite’ number of conventional finite elements is used to model the singular region. The corresponding large number of local variables in the singular region around the crack tip is transformed to a small set of global co‐ordinates after performing a global transformation by using global interpolation functions. In this paper, we extend this method to analyse the singularity problems of sharp notched plates. The exact stress and displacement fields of a plate with a notch of general angle are derived for plane‐stress/strain conditions. These exact analytical solutions which are eigenfunction expansion series are used to perform the global transformation and to determine the SIFs. The use of the global interpolation functions reduces the computational cost significantly and neither post‐processing technique to extract SIFs nor special singular elements to model the singular region are needed. The numerical examples demonstrate the accuracy and efficiency of the FFEM for sharp notched problems. Copyright © 2008 John Wiley & Sons, Ltd.     

Analysis of cracked plates using an iterative hybrid technique of boundary element method and distributed dislocation method

An iterative hybrid technique of boundary element method (BEM) and distributed dislocation method (DDM) is introduced for solving two dimensional crack problems. The technique decomposes the problem into (n + 1) subsidiary problems where n is the number of crack branches. The required solution will be the sum of these (n + 1) solutions. The first subsidiary problem is to find the stress distribution induced in the plate in the absence of the crack using BEM. All of the remaining subsidiary problems, are stress disturbance ones that will be solved using DDM. The results will be added and compared with the boundary conditions of the original problem. Iteration will be performed between the plate boundaries and crack faces until all of the boundary conditions are satisfied.     

A new variable‐order singular boundary element for two‐dimensional stress analysis

A new variable‐order singular boundary element for two‐dimensional stress analysis is developed. This element is an extension of the basic three‐node quadratic boundary element with the shape functions enriched with variable‐order singular displacement and traction fields which are obtained from an asymptotic singularity analysis. Both the variable order of the singularity and the polar profile of the singular fields are incorporated into the singular element to enhance its accuracy. The enriched shape functions are also formulated such that the stress intensity factors appear as nodal unknowns at the singular node thereby enabling direct calculation instead of through indirect extrapolation or contour‐integral methods. Numerical examples involving crack, notch and corner problems in homogeneous materials and bimaterial systems show the singular element's great versatility and accuracy in solving a wide range of problems with various orders of singularities. The stress intensity factors which are obtained agree very well with those reported in the literature. Copyright © 2002 John Wiley & Sons, Ltd.     

Rapid evaluation of notch stress intensity factors using the peak stress method: Comparison of commercial finite element codes for a range of mesh patterns

The peak stress method (PSM) is an engineering, finite element (FE)‐oriented method to rapidly estimate the notch stress intensity factors by using the singular linear elastic peak stresses calculated from coarse FE analyses. The average element size adopted to generate the mesh pattern can be chosen arbitrarily within a given range. Originally, the PSM has been calibrated under pure mode I and pure mode II loadings by means of Ansys FE software. In the present contribution, a round robin between 10 Italian universities has been carried out to calibrate the PSM with 7 different commercial FE codes. To this aim, several two‐dimensional mode I and mode II problems have been analysed independently by the participants. The obtained results have been used to calibrate the PSM for given stress analysis conditions in (i) FE software, (ii) element type and element formulation, (iii) mesh pattern, and (iv) criteria for stress extrapolation and principal stress analysis at FE nodes.     

Calculation of stress intensity factors by the force method

The force method is a simple and accurate technique for calculating stress intensity factors (SIFs) from finite element (FE) models, but it has been scarcely used. This paper shows three important advantages of the force method, which make it particularly attractive for designers and researchers. First, it can be employed without special singular quadratic finite elements at the crack tip. Actually, linear reduced integration elements may be used. Second, the force method can be applied to highly anisotropic materials without requiring knowledge of complicated elasticity relations for the stress field around the crack tip. Third, it can handle mixed-mode fracture problems.     

h-Hierarchical adaptive boundary element method using local reanalysis

An adaptive boundary element scheme is developed using the concept of local reanalysis and h-hierarchical functions for the construction of near-optimal computational models. The use of local reanalysis in the error estimation guarantees the reliability of the modelling process while the use of quadratic and quartic h-hieararchical elements guarantees the efficiency of the adaptive algorithm. The technique is developed for the elastic analysis of two-dimensional models. Numerical examples show the rapid convergence of the results with a few refinement steps.     

Finite element evaluation of mixed mode stress intensity factors in functionally graded materials

This paper is directed towards finite element computation of fracture parameters in functionally graded material (FGM) assemblages of arbitrary geometry with stationary cracks. Graded finite elements are developed where the elastic moduli are smooth functions of spatial co‐ordinates which are integrated into the element stiffness matrix. In particular, stress intensity factors for mode I and mixed‐mode two‐dimensional problems are evaluated and compared through three different approaches tailored for FGMs: path‐independent J^*_k‐integral, modified crack‐closure integral method, and displacement correlation technique. The accuracy of these methods is discussed based on comparison with available theoretical, experimental or numerical solutions. Copyright © 2001 John Wiley & Sons, Ltd.     

Evaluating stress intensity factors of a surface crack in lubricated rolling contacts

The three-dimensional finite element method and the least-squares method were used to find the stress intensity factors (SIFs) of a surface crack in a lubricated roller. A steel roller on a rigid plane was modeled, in which a semi-elliptical surface crack is inclined at an angle ψ to the vertical axis. A distance c is set between the crack base and the roller edge. The results indicate that the mode-I SIF reaches the maximum value when the angle θ is equal to 0° (on the roller surface), and the mode-II SIF reaches the absolute maximum value when the angle θ is near or equal to 90° (inside the roller), where θ is the angle of the semi-ellipse from 0° to 180°. The influence of mode-III SIFs in this model is minor since they are much smaller than the mode-I and mode-II SIFs. The SIFs increase greatly when the crack location approaches the uncrowned edge. At this time, a crowned profile can be used to significantly reduce the SIFs near the roller edge. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the calculation of boundary stresses with the Somigliana stress identity

The computation of boundary stresses by Boundary Element Method (BEM) is usually performed either by expressing the boundary tractions in a local co-ordinate system, calculating the remaining stresses by shape function differentiation and inserting into Hooke's law or recently also by solving the hypersingular integral equation for the stresses. While direct solution of the hypersingular integral equation, the so-called Somigliana stress identity, has been shown to be more reliable, the interpretation and numerical treatment of the hypersingularity causes a number of problems. In this paper, the limiting procedure in taking the load point to the boundary is carried out by leaving the boundary smooth and the contributions of all different types of singularities to the boundary integral equation are studied in detail. The hypersingular integral in the arising boundary integral equation is then reduced to a strongly singular one by considering a traction free rigid body motion. For the numerical treatment, an algorithm for multidimensional Cauchy Principal Value (CPV) integrals is extended that is applicable for the calculation of boundary stresses. Moreover, the shape of the surrounding of the singular point is studied in detail. A numerical example of elastostatics confirms the validity of the proposed method.     

A time‐dependent formulation of dual boundary element method for 3D dynamic crack problems

In this paper, the dual boundary element method in time domain is developed for three‐dimensional dynamic crack problems. The boundary integral equations for displacement and traction in time domain are presented. By using the displacement equation and traction equation on crack surfaces, the discontinuity displacement on the crack can be determined. The integral equations are solved numerically by a time‐stepping technique with quadratic boundary elements. The dynamic stress intensity factors are calculated from the crack opening displacement. Several examples are presented to demonstrate the accuracy of this method. Copyright © 1999 John Wiley & Sons, Ltd