摩擦接触裂纹问题的扩展有限元法

扩展有限元法(XFEM)是一种在常规有限元框架内求解强和弱不连续问题的新型数值方法。扩展有限元法分析闭合型裂纹时,必须考虑裂纹面间的接触问题。已有文献均采用迭代法求解裂纹面的接触问题。该文建立了闭合型摩擦裂纹问题的扩展有限元线性互补模型,将裂纹面非线性摩擦接触转化为一个线性互补问题求解,不需要迭代求解。算例分析说明了该方法的正确性和有效性,同时表明扩展有限元法结合线性互补法求解接触问题具有较好的前景。     

Finite element analysis of 3D elastic–plastic frictional contact problem for Cosserat materials

The objective of this paper is to develop a finite element model for 3D elastic–plastic frictional contact problem of Cosserat materials. Because 3D elastic–plastic frictional contact problems belong to the unspecified boundary problems with nonlinearities in both material and geometric forms, a large number of calculations are needed to obtain numerical results with high accuracy. Based on the parametric variational principle and the corresponding quadratic programming method for numerical simulation of frictional contact problems, a finite element model is developed for 3D elastic–plastic frictional contact analysis of Cosserat materials. The problems are finally reduced to linear complementarity problems (LCP). Numerical examples show the feasibility and importance of the developed model for analyzing the contact problems of structures with materials which have micro-polar characteristics.     

A computational procedure for flexible beams with frictional contact constraints

This paper deals with the application of a parametric quadratic programming (PQP) method to the numerical solution of large-deflection beams involving frictional contact constraints. The flexibility of the structure is modelled by an intrinsic spatial beam theory which is approximated by transverse-shear deformable linear beam elements. The linear complementary problem (LCP) without the penalty function resulting from PQP is made part of a Newton-Raphson search. The tool for solving the complementary equations is Lemke's algorithm, in which frictional contact conditions are enforced and new contact surfaces are updated during iteration. Applying the resulting contact element, a more accurate approximation of the contact point can be guaranteed, and the contact force can be directly computed by the adjacent beam elements. Three numerical examples are analysed to show the effectiveness and validity of the method.     

Variational boundary-integral-equation approach to unilateral contact problems in elasticity

On the basis of the boundary integral equation method, three variational principles for the frictionless unilateral contact problem in elasticity are presented. Two of them are saddle-point principles for the boundary unknowns (including the contact displacements); a third one is a maximum principle for the unknown contact displacements only. A discretization by boundary elements leads to algebraic formulations in the shape either of quadratic programming problems, or of linear complementarity problems, all characterized by symmetry and sign definiteness of the coefficient matrices. The method is also applicable to contact problems between two uncompenetrable elastic solids, as well as to the crack problem of fracture mechanics.     

Three-dimensional contact mechanics analysis of crack problems using the boundary element method

In this paper, a formulation based on the iterative-load incremental approach for the three-dimensional frictional contact mechanics analysis of fracture problems using the boundary element method (BEM), is presented. Special crack front elements are employed to provide a quick and direct means of obtaining the stress intensity factor. The veracity of the formulation is demonstrated with four crack problems. Three of these problems involve crack closure under bending loads, and the fourth is that of a pin-loaded rectangular plate with corner cracks at the pin-hole. The computed BEM solutions are compared, where possible, with those available in the literature, and there is generally good agreement between them. The numerical examples serve also to illustrate the need for a proper contact mechanics treatment to obtain accurate stress intensity factors for such problems.     

Frictional contact analysis of composite materials

In this paper, the highly non-linear frictional contact problems of composite materials are analysed. A proportional loading, the potential contact zone method and finite element analysis are used to solve the problems. A tree-like searching method is used to obtain the solution of the parametric linear complementary problem, which may overcome the anisotropic properties of contact equations caused by composite materials. In the frictional contact analysis of composite materials, the distributions of normal contact pressures, tangential contact stresses and relative tangential displacements are presented for different contact material systems and different coefficients of friction. The results show that the solutions in the paper have good agreement with Hertzian solutions. The influence of different contact material systems and different coefficients of friction on the contact stresses and displacements is large. As a numerical example, ball-indentation tests of composite materials are modelled by the three-dimensional finite element method.     

Symmetric‐Galerkin BEM simulation of fracture with frictional contact

A symmetric‐Galerkin boundary element framework for fracture analysis with frictional contact (crack friction) on the crack surfaces is presented. The algorithm employs a continuous interpolation on the crack surface (utilizing quadratic boundary elements) and enables the determination of two important quantities for the problem, namely the local normal tractions and sliding displacements on the crack surfaces. An effective iterative scheme for solving this non‐linear boundary value problem is proposed. The results of test examples are compared with available analytical solutions or with those obtained from the displacement discontinuity method (DDM) using linear elements and internal collocation. The results demonstrate that the method works well for difficult kinked/junction crack problems. Copyright © 2003 John Wiley & Sons, Ltd.     

A contact analysis approach based on linear complementarity formulation using smoothed finite element methods

Based on the subdomain parametric variational principle (SPVP), a contact analysis approach is formulated in the incremental form for 2D solid mechanics problems discretized using only triangular elements. The present approach is implemented for the newly developed node-based smoothed finite element method (NS-FEM), the edge-based smoothed finite element method (ES-FEM) as well as standard FEM models. In the approach, the contact interface equations are discretized by contact point-pairs using a modified Coulomb frictional contact model. For strictly imposing the contact constraints, the global discretized system equations are transformed into a standard linear complementarity problem (LCP), which can be readily solved using the Lemke method. This approach can simulate different contact behaviors including bonding/debonding, contacting/departing, and sticking/slipping. An intensive numerical study is conducted to investigate the effects of various parameters and validate the proposed method. The numerical results have demonstrated the validity and efficiency of the present contact analysis approach as well as the good performance of the ES-FEM method, which provides solutions of about 10 times better accuracy and higher convergence rate than the FEM and NS-FEM methods. The results also indicate that the NS-FEM provides upper-bound solutions in energy norm, relative to the fact that FEM provides lower-bound solutions.     

Modelling cohesive crack growth using a two-step finite element-scaled boundary finite element coupled method

A two-step method, coupling the finite element method (FEM) and the scaled boundary finite element method (SBFEM), is developed in this paper for modelling cohesive crack growth in quasi-brittle normal-sized structures such as concrete beams. In the first step, the crack trajectory is fully automatically predicted by a recently-developed simple remeshing procedure using the SBFEM based on the linear elastic fracture mechanics theory. In the second step, interfacial finite elements with tension-softening constitutive laws are inserted into the crack path to model gradual energy dissipation in the fracture process zone, while the elastic bulk material is modelled by the SBFEM. The resultant nonlinear equation system is solved by a local arc-length controlled solver. Two concrete beams subjected to mode-I and mixed-mode fracture respectively are modelled to validate the proposed method. The numerical results demonstrate that this two-step SBFEM-FEM coupled method can predict both satisfactory crack trajectories and accurate load-displacement relations with a small number of degrees of freedom, even for crack growth problems with strong snap-back phenomenon. The effects of the tensile strength, the mode-I and mode-II fracture energies on the predicted load-displacement relations are also discussed.     

Global Constitutive Behavior of Periodic Assemblies of Inelastic Bodies in Contact

This work attempts to capture the macroscopic behavior of inelastic bodies in contact by means of a numerical homogenized constitutive relation. The analysis is restricted to small strains, plane problems, and monotonic proportional loadings. An important feature of this work is the quasi-static frictional contact analysis of the microstructure composed of deformable inelastic bodies by means of a parametric quadratic programming principle and its corresponding algorithm in numerical analysis. Two numerical examples are given to demonstrate the efficiency of the algorithm presented in this article.     

An Abaqus implementation of the extended finite element method

In this paper, we introduce an implementation of the extended finite element method for fracture problems within the finite element software ABAQUS^TM. User subroutine (UEL) in Abaqus is used to enable the incorporation of extended finite element capabilities. We provide details on the data input format together with the proposed user element subroutine, which constitutes the core of the finite element analysis; however, pre-processing tools that are necessary for an X-FEM implementation, but not directly related to Abaqus, are not provided. In addition to problems in linear elastic fracture mechanics, non-linear frictional contact analyses are also realized. Several numerical examples in fracture mechanics are presented to demonstrate the benefits of the proposed implementation.     

弹性接触颗粒状周期性结构材料力学分析的均匀化方法(Ⅰ) ——局部RVE分析

研究工作目的是建立弹性接触颗粒状组成周期性结构材料力学分析的均匀化模型。首先对具有周期性构造的弹性接触颗粒材料力学的微观(小尺度)与宏观两级均匀化方法的研究现状进行了简要回顾,进而发展了问题局部RVE分析的有限元求解技术,该方法考虑了弹性接触体的粘着界面特性,并基于参变量变分原理提出了问题求解的参数二次规划算法,为宏观均匀化分析工作打下基础。      

Analysis of crack closure problem using the dual boundary element method

A numerical procedure of the crack closure problem solved by the dual boundary element method is developed in this paper. The dual boundary element method is used to allow for the solution to a general mixed-mode crack problem with a single regional formulation. The frictional contact problem on the crack surface is formulated with the complementary problem adapting the Coulomb's friction law. Several examples are shown to demonstrate the validity of the present procedure.     

Some recent fatigue and fracture mechanics research in BIAM

The paper presents a brief review of some of the major research activities on fatigue and fracture mechanics in recent years at the Beijing Institute of Aeronautical Materials. Attention is mainly given to the studies on weight function methods for analyses of two- and three-dimensional crack problems, fatigue crack growth under variable amplitude loading, small crack effects and a fracture-mechanics-based total fatigue life prediction method.Abbreviations 2(3)D two- (three-) dimensional - BIAM Institute of Aeronautical Materials, Beijing - CCT center cracked tension - COD crack opening displacement - CTOD crack tip opening displacement - FEM finite element method - LEFM linear elastic fracture mechanics - SENT single edge notched tension - SIF stress intensity factor - WFM weight function method     

A contact algorithm for frictional crack propagation with the extended finite element method

We present an incremental quasi‐static contact algorithm for path‐dependent frictional crack propagation in the framework of the extended finite element (FE) method. The discrete formulation allows for the modeling of frictional contact independent of the FE mesh. Standard Coulomb plasticity model is introduced to model the frictional contact on the surface of discontinuity. The contact constraint is borrowed from non‐linear contact mechanics and embedded within a localized element by penalty method. Newton–Raphson iteration with consistent linearization is used to advance the solution. We show the superior convergence performance of the proposed iterative method compared with a previously published algorithm called ‘LATIN’ for frictional crack propagation. Numerical examples include simulation of crack initiation and propagation in 2D plane strain with and without bulk plasticity. In the presence of bulk plasticity, the problem is also solved using an augmented Lagrangian procedure to demonstrate the efficacy and adequacy of the standard penalty solution. Copyright © 2008 John Wiley & Sons, Ltd.     

3D fracture analysis by the symmetric Galerkin BEM

 The subject of this paper is the formulation and the implementation of the symmetric Galerkin BEM for three-dimensional linear elastic fracture mechanics problems. A regularized version of the displacement and traction equations in weak form is adopted and the integration techniques utilized for the evaluation of the double surface integrals appearing in the discretized equations are detailed. By using quadratic isoparametric quadrilateral and triangular elements, some example crack problems are solved to assess the efficiency and robustness of the method. Received 6 November 2000     

Local analysis and global nonlinear behaviour of periodic assemblies of bodies in elastic contact

This work attempts to capture the effects of microstructural changes on the overall response of a composite made of bodies in elastic contact, and to define numerically a homogenised constitutive relationship for the global behaviour. The analysis is restricted to small strains, plane problems and monotonic proportional loads. An important feature of this work is the quasi-static frictional contact analysis of the microstructure composed of deformable elastic bodies by means of parametric quadratic programming principle and its corresponding algorithmic implementation. The generality of the homogenisation algorithm, which, in principle, can be applied to a large variety of non-linear behaviour affecting the representative volume element, is clearly described. Numerical examples are given to demonstrate the efficiency and validity of the algorithm presented in the paper. Received 15 August 1998     

基于参数二次规划与精细积分方法的动力弹塑性问题分析

给出了将参数二次规划方法与精细积分方法相结合进行结构弹塑性动力响应分析的一条新途径。基于参变量变分原理与有限元参数二次规划方法建立了动力弹塑性问题的求解方程，方法对于关联与非关联问题的求解在算法上是完全一致的。对于动力非线性方程求解则进一步采用了被线性问题分析所广泛采用的精细积分方法，推导了方法在动力弹塑性问题求解上的算法列式。所给出的数值算例在验证本文理论与算法的同时，进一步证实了精细积分方法在动力学分析中所具有的各种良好性态。     

Numerical analysis of the influence of crack surface roughness on the crack path

The influence of the 3D frictional crack surface interaction on the fracture mechanical parameters as well as on the crack path is numerically investigated. For the solution of the boundary value problem the 3D dual boundary element method in terms of the discontinuous formulation is utilized. This method is especially suited for contact problems because it directly deals with the discontinuities at the crack surfaces. The contact problem is solved by the application of the penalty method. Coulomb’s frictional law is utilized for the consideration of the dissipative nature of friction. For discrete steps within one load cycle the stress intensity factors are determined by an extrapolation procedure from the stress field. Based on the analysis of a load cycle, the cyclic stress intensity factors are obtained. For the simulation of crack propagation an implicit time integration scheme of a crack propagation law implemented in terms of a predictor-corrector scheme is applied. The influence of the crack surface roughness on the crack path is shown by numerical examples.     

压气机过盈配合的弹塑性有摩擦接触的研究

增压器压气机叶轮、轴套和轴采用过盈配合技术联成一体,这是三维多体弹塑性有摩擦接触问题,是两种非线性相互耦合的边值待定问题。采用有限元参数二次规划法,并结合多重子结构技术,充分利用两种方法各自的长处分析求解柴油机涡轮增压器叶轮与轴套、轴套与轴的三维弹塑性有摩擦接触问题,针对不同的过盈量、摩擦因数、转速和轴套壁厚进行了大量计算,获得了叶轮、轴套与轴之间接触应力的相应分布规律。轴套与轴的装配过盈量是影响轮轴接触应力的重要因素。在选择叶轮、轴套和轴三者装配尺寸时,尤其采用压力组装法时应严格控制轴套与轴的过盈量。研究结果表明,此方法对压气机弹塑性接触特性是有效的,能够反映接触区域的接触法向应力、变形以及摩擦力的大小和分布情况。