A multiscale flaw detection algorithm based on XFEM

We present a novel multiscale algorithm for nondestructive detection of multiple flaws in structures, within an inverse problem type setting. The key idea is to apply a two‐step optimization scheme, where first rough flaw locations are quickly determined, and then, fine tuning is applied in these localized subdomains to obtain global convergence to the true flaws. The two‐step framework combines the strengths of heuristic and gradient‐based optimization methods. The first phase employs a discrete‐type optimization in which the optimizer is limited to specific flaw locations and shapes, thus converting a continuous optimization problem in the entire domain into a coarse discrete optimization problem with limited number of choices. To this end, we develop a special algorithm called discrete artificial bee colony. The second phase employs a gradient‐based optimization of the Broyden–Fletcher–Goldfarb–Shanno type on local well‐defined and bounded subdomains determined in the previous phase. A semi‐analytical approach is developed to compute the stiffness derivative associated with the evaluation of objective function gradients. The eXtended FEM (XFEM), with both circular and elliptical void enrichment functions, is used to solve the forward problem and alleviate the costly remeshing of every candidate flaw, in both optimization steps. The multiscale algorithm is tested on several benchmark examples to identify various numbers and types of flaws with arbitrary shapes and sizes (e.g., cracks, voids, and their combination), without knowing the number of flaws beforehand. We study the size effect of the pseudo grids in the first optimization step and consider the effect of modeling error and measurement noise. The results are compared with the previous work that employed a single continuous optimization scheme (XFEM–genetic algorithm and XFEM–artificial bee colony methods). We illustrate that the proposed methodology is robust, yields accurate flaw detection results, and in particular leads to significant improvements in convergence rates compared with the previous work. Copyright © 2014 John Wiley & Sons, Ltd.     

除冰盐环境下水泥混凝土路面传力杆的锈蚀机理与传荷失效过程分析

传力杆锈蚀所引起的混凝土保护层开裂是影响水泥混凝土路面结构使用寿命的重要因素。该文基于扩展有限元方法,建立了传力杆锈蚀产物-混凝土保护层耦合作用开裂力学分析模型。使用此模型模拟了混凝土保护层锈胀开裂过程中的弥散分布裂纹起裂及扩展演化行为,研究了除冰盐环境下传力杆因锈蚀引起传荷失效的过程。设计传力杆试件的除冰盐环境室外暴露试验对数值模拟结果进行验证,发现两者在锈胀开裂模式方面符合较好。根据已验证的模型分析发现：传力杆的松动是促使其快速脱钝,并发生严重锈蚀的初始条件,松动量对传力杆表面锈蚀产物的物相组成比例无明显影响;锈蚀产物体积膨胀造成混凝土保护层出现龟裂,降低了混凝土为传力杆提供支承的能力,是传力杆因锈蚀导致传荷失效的主要原因。     

水平井水力压裂的三维有限元数值模拟研究

对水平井进行水力压裂,一口井可以形成多条横向裂缝,增产效果比直井更明显,因此近年来水平井压裂应用越来越广泛.该文以ABAQUS软件为平台,采用流固耦合单元模拟岩石的应力渗流耦合行为,采用带有孔隙压力自由度的粘结单元模拟油层和隔层的破裂和扩展,射孔连接微环隙和横向裂缝,即假设了双向同时起裂和扩展的可能性.对大庆油田某水平...     

Computing stress intensity factors for curvilinear cracks

The use of the interaction integral to compute stress intensity factors around a crack tip requires selecting an auxiliary field and a material variation field. We formulate a family of these fields accounting for the curvilinear nature of cracks that, in conjunction with a discrete formulation of the interaction integral, yield optimally convergent stress intensity factors. In particular, we formulate three pairs of auxiliary and material variation fields chosen to yield a simple expression of the interaction integral for different classes of problems. The formulation accounts for crack face tractions and body forces. Distinct features of the fields are their ease of construction and implementation. The resulting stress intensity factors are observed converging at a rate that doubles that of the stress field. We provide a sketch of the theoretical justification for the observed convergence rates and discuss issues such as quadratures and domain approximations needed to attain such convergent behavior. Through two representative examples, a circular arc crack and a loaded power function crack, we illustrate the convergence rates of the computed stress intensity factors. The numerical results also show the independence of the method from the size of the domain of integration. Copyright © 2015 John Wiley & Sons, Ltd.     

Finite strain fracture analysis using the extended finite element method with new set of enrichment functions

Nonlinear fracture analysis of rubber‐like materials is computationally challenging due to a number of complicated numerical problems. The aim of this paper is to study finite strain fracture problems based on appropriate enrichment functions within the extended finite element method. Two‐dimensional static and quasi‐static crack propagation problems are solved to demonstrate the efficiency of the proposed method. Complex mixed‐mode problems under extreme large deformation regimes are solved to evaluate the performance of the proposed extended finite element analysis based on different tip enrichment functions. Finally, it is demonstrated that the logarithmic set of enrichment functions provides the most accurate and efficient solution for finite strain fracture analysis. Copyright © 2015 John Wiley & Sons, Ltd.     

汽车动力总成液压悬置橡胶主簧静特性有限元分析

以某一型号轿车发动机液压悬置为研究对象,应用大型通用有限元分析软件ABAQUS分析了橡胶主簧在垂直方向的静态特性。介绍了橡胶材料本构关系的基本理论,论述了橡胶有限元模型的建立过程,计算分析了橡胶主簧各结构参数对主簧静态特性的影响程度,并讨论了橡胶主簧静态特性有限元分析结果与单元特性的关系。     

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

New 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. Copyright © 2006 John Wiley & Sons, Ltd.     

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

An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented. This method enables the accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non‐smooth features within elements. This is achieved by enriching the polynomial approximation space of the classical finite element method. The GEFM/XFEM has shown its potential in a variety of applications that involve non‐smooth solutions near interfaces: Among them are the simulation of cracks, shear bands, dislocations, solidification, and multi‐field problems. Copyright © 2010 John Wiley & Sons, Ltd.     

Stress intensity factor evaluations for a curved crack in orthotropic particulate composites using an interaction integral method

This paper develops a domain-independent interaction integral (DII-integral) for extracting mixed-mode stress intensity factors (SIFs) for orthotropic materials with complex interfaces. The DII-integral does not require material property gradients, and moreover its validity is not affected by material interfaces. Combined with the extended finite element method (XFEM), the DII-integral is employed to investigate a straight crack in an orthotropic functionally graded plate and a curved crack in orthotropic particulate composites.     

水力压裂过程的扩展有限元数值模拟方法

建立了基于扩展有限元法的水力压裂数值模拟方法,使水力裂缝独立于网格存在,无需预设裂缝扩展方位。在扩展有限元计算框架下,将裂缝面处理为求解域内边界,将缝内水压力转化为相关单元等效节点力;运用考虑缝内水压力作用的相互积分法来数值求解缝尖应力强度因子;采用最大能量释放率准则确定裂缝是否继续扩展及扩展方位;最终编制了计算机程序。利用该方法数值模拟了单条水力裂缝在恒定水压力作用下作非平面扩展,所得结果分别与室内试验和解析模型相对比。结果表明,数值结果与室内试验和解析解吻合较好,缝尖应力强度因子最大相对误差不高于0.45%,验证了该方法的可行性和准确性。     

A spline‐based enrichment function for arbitrary inclusions in extended finite element method with applications to finite deformations

A novel enrichment function, which can model arbitrarily shaped inclusions within the framework of the extended finite element method, is proposed. The internal boundary of an arbitrary‐shaped inclusion is first discretized, and a numerical enrichment function is constructed ‘on the fly’ using spline interpolation. We consider a piecewise cubic spline which is constructed from seven localized discrete boundary points. The enrichment function is then determined by solving numerically a nonlinear equation which determines the distance from any point to the spline curve. Parametric convergence studies are carried out to show the accuracy of this approach compared with pointwise and linear segmentation of points for the construction of the enrichment function in the case of simple inclusions and arbitrarily shaped inclusions in linear elasticity. Moreover, the viability of this approach is illustrated on a neo‐Hookean hyperelastic material with a hole undergoing large deformation. In this case, the enrichment is able to adapt to the deformation and effectively capture the correct response without remeshing. Copyright © 2013 John Wiley & Sons, Ltd.     

On the construction of blending elements for local partition of unity enriched finite elements

For computational efficiency, partition of unity enrichments are preferably localized to the sub‐domains where they are needed. It is shown that an appropriate construction of the elements in the blending area, the region where the enriched elements blend to unenriched elements, is often crucial for good performance of local partition of unity enrichments. An enhanced strain formulation is developed which leads to good performance; the optimal rate of convergence is achieved. For polynomial enrichments, it is shown that a proper choice of the finite element shape functions and partition of unity shape functions also improves the accuracy and convergence. The methods are illustrated by several examples. The examples deal primarily with the signed distance function enrichment for treating discontinuous derivatives inside an element, but other enrichments are also considered. Results show that both methods provide optimal rates of convergence. Copyright © 2003 John Wiley & Sons, Ltd.     

A domain-independent interaction integral for linear elastic fracture analysis of micropolar materials

This paper establishes a domain-independent interaction integral (DII-integral) for linear elastic fracture mechanics of micropolar elastic solids. The DII-integral has three amazing features that make it effective for solving the fracture parameters of complex micropolar materials. The first one is that the DII-integral can decouple the stress intensity factors (SIFs) and couple stress intensity factors (CSIFs) both of which are the key fracture parameters charactering the crack-tip asymptotic singular fields. In details, the DII-integral is derived from the J-integral by superimposing an actual field and an auxiliary field. By assigning the fracture parameters in the auxiliary field with different values, the SIFs and CSIFs of different crack opening modes can be obtained separately through the DII-integral. The second important feature is that the DII-integral is domain-independent for material nonhomogeneity and discontinuity. Thanks to this feature, the DII-integral becomes extremely effective for the micropolar materials with arbitrary nonhomogeneous properties or complex interfaces. The third feature is that the DII-integral does not contain any derivatives of material properties, which feature facilitate the practical implementation of the DII-integral on complex micropolar materials. Finally, the DII-integral combined with the extended finite element method (XFEM) is employed to solve four representative crack problems and the results show good validity of the DII-integral for complex micropolar materials.     

Embedded interfaces by polytope FEM

In this paper, the Polytope Finite Element Method is employed to model an embedded interface through the body, independent of the background FEM mesh. The elements that are crossed by the embedded interface are decomposed into new polytope elements which have some nodes on the interface line. The interface introduces discontinuity into the primary variable (strong) or into its derivatives (weak). Both strong and weak discontinuities are studied by the proposed method through different numerical examples including fracture problems with traction‐free and cohesive cracks, and heat conduction problems with Dirichlet and Dirichlet–Neumann types of boundary conditions on the embedded interface. For traction‐free cracks which have tip singularity, the nodes near the crack tip are enriched with the singular functions through the eXtended Finite Element Method. The concept of Natural Element Coordinates (NECs) is invoked to drive shape functions for the produced polytopes. A simple treatment is proposed for concave polytopes produced by a kinked interface and also for locating crack tip inside an element prior to using the singularity enrichment. The proposed method pursues some implementational details of eXtended/Generalized Finite Element Methods for interfaces. But here the additional DOFs are constructed on the interface lines in contrast to X/G‐FEM, which attach enriched DOFs to the previously existed nodes. Copyright © 2011 John Wiley & Sons, Ltd.     

Nondestructive identification of multiple flaws using XFEM and a topologically adapting artificial bee colony algorithm

We present a novel algorithm based on the extended finite element method (XFEM) and an enhanced artificial bee colony (EABC) algorithm to detect and quantify multiple flaws in structures. The concept is based on recent work that have shown the excellent synergy between XFEM, used to model the forward problem, and a genetic‐type algorithm to solve an inverse identification problem and converge to the ‘best’ flaw parameters. In this paper, an adaptive algorithm that can detect multiple flaws without any knowledge on the number of flaws beforehand is proposed. The algorithm is based on the introduction of topological variables into the search space, used to adaptively activate/deactivate flaws during run time until convergence is reached. The identification is based on a limited number of strain sensors assumed to be attached to the structure surface boundaries. Each flaw is approximated by a circular void with the following three variables: center coordinates (x_c, y_c) and radius (r_c), within the XFEM framework. In addition, the proposed EABC scheme is improved by a guided‐to‐best solution updating strategy and a local search (LS) operator of the Nelder–Mead simplex type that show fast convergence and superior global/LS abilities compared with the standard ABC or classic genetic algorithms. Several numerical examples, with increasing level of difficulty, are studied in order to evaluate the proposed algorithm. In particular, we consider identification of multiple flaws with unknown a priori information on the number of flaws (which makes the inverse problem harder), the proximity of flaws, flaws having irregular shapes (similar to artificial noise), and the effect of structured/unstructured meshes. The results show that the proposed XFEM–EABC algorithm is able to converge on all test problems and accurately identify flaws. Hence, this methodology is found to be robust and efficient for nondestructive detection and quantification of multiple flaws in structures. Copyright © 2013 John Wiley & Sons, Ltd.     

T‐stress evaluations for nonhomogeneous materials using an interaction integral method

A new equivalent domain integral of the interaction integral is derived for the computation of the T‐stress in nonhomogeneous materials with continuous or discontinuous properties. It can be found that the derived expression does not involve any derivatives of material properties. Moreover, the formulation can be proved valid even when the integral domain contains material interfaces. Therefore, the present method can be used to extract the T‐stress of nonhomogeneous materials with complex interfaces effectively. The interaction integral method in conjunction with the extended FEM is used to solve several representative examples to show its validity. Finally, using this method, the influences of material properties on the T‐stress are investigated. Numerical results show that the mechanical properties and their first‐order derivatives affect the T‐stress greatly, while the higher‐order derivatives affect the T‐stress slightly. Copyright © 2012 John Wiley & Sons, Ltd.     

基于有限元与边界元耦合法的波浪力分析

利用有限元与边界元耦合法对三维无界区域中直立圆柱所受的波浪力进行进行计算,把整个求解区域分成内域或外域两部分,在内域采用有限元法,对外域采用边界元法,数值计算的结果与理论解吻合良好,表明该方法有效。     

Ductile failure analysis and crack behavior of X65 buried pipes using extended finite element method

This paper aims to study the ductile fracture mechanism of API X65 buried pipes including crack initiation and propagation using the extended finite element method (XFEM). First, the crack evolution histories of X65 specimens with initial crack-like flaws during tensile and three-point bending tests are illustrated, and the numerical results are compared with experimental data. In addition, effects of different crack configurations, damage initiation and evolution criteria are investigated. Second, the burst processes of straight pipes with initial gouge flaws are presented, and the FE results are compared with assessment in related standards and experiments. Finally, the crack onset and growth of buried pipes due to deflection arising from landslide movements are predicted, and the numerical results are compared with previous study. Particularly, the internal pressure, wall thickness, and soil properties on crack behavior and limit load-bearing ability are investigated. This paper provides a fundamental support for the integrity assessment and safety evaluation of buried pipes.