On the treatment of frictional contact in shell structures using variational inequalities

A new variational inequality‐based formulation is presented for the large deformation analysis of frictional contact in elastic shell structures. The formulations are based on a seven‐parameter continuum shell model, which account for the normal stress and strain through the shell thickness and accommodate double‐sided shell contact. The kinematic contact conditions are enforced accurately in terms of the physical contacting surfaces of the shell. Large deformations and rotations are accounted for by invoking the appropriate stress and strain measures. Lagrange multipliers are used to ensure that the kinematic contact constraints are accurately satisfied and that the solution is free from user‐defined parameters. Three numerical examples are used to verify the developed formulations and algorithms, and test the various aspects of the solution technique. Copyright © 1999 John Wiley & Sons, Ltd.     

Modeling compressive response of 3D woven textile composites accounting for microscale geometric uncertainties

The compressive response of 3D woven textile composites (3DWTC), that consist of glass fiber tows and an epoxy matrix material, is studied using a finite element (FE)-based mechanics model. A parametric Representative Unit Cell (RUC) model is developed in a fully three-dimensional setting with geometry and textile architecture for modeling the textile microstructure. The RUC model accounts for the nonlinear behavior of the fiber tows and matrix. The computational model is utilized to predict the compressive strength of 3DWTC and its dependence on various geometrical and material parameters. The finite element model is coupled with a probabilistic analysis tool to provide probabilistic estimates for 3DWTC compressive strength. The reported results are found to be in good agreement with experimental data.     

经纬向纤维体积分数对耐碱玻璃纤维织物增强混凝土拉伸力学性能的影响

为了研究经纬向纤维体积分数对耐碱玻璃纤维织物增强混凝土(ARG-TRC)拉伸力学性能的影响,通过万能试验机对不同经向纤维体积分数(0.24vol％、0.49vol％、0.73vol％和1.09vol％)和纬向纤维体积分数(0vol％、0.20vol％、0.48vol％和0.96vol％)的试件进行准静态拉伸试验,并结合...     

A new strategy for the solution of frictional contact problems

This article is devoted to the development of a new heuristic algorithm for the solution of the general variational inequality arising in frictional contact problems. The existing algorithms devised for the treatment of the variational inequality representing frictional contact rely on the decomposition of the physical problem into two sub-problems which are then solved iteratively. In addition, the penalty function method and/or the regularization techniques are typically used in the solution of these reduced sub-problems. These techniques introduce user-defined parameters which could influence the convergence and accuracy of the solution. The new method presented in this article overcomes these difficulties by providing a solution for the general variational inequality without decomposition into sub-problems. This is accomplished using a new heuristic algorithm which utilizes mathematical programming techniques, and thus avoids the use of penalty or regularization methods. The versatility and reliability of the developed algorithm were demonstrated through implementation to the case of frictional contact of an elastic hollow cylinder with a rigid foundation. © 1998 John Wiley & Sons, Ltd.     

On the elastodynamic solution of frictional contact problems using variational inequalities

This article is concerned with the development, implementation and application of variational inequalities to treat the general elastodynamic contact problem. The solution strategy is based upon the iterative use of two subproblems. Quadratic programming and Lagrange multipliers are used to solve the respective first and second subproblems and to identify the candidate contact surface and contact stresses. This approach guarantees the imposition of the active kinematic contact constraints, avoids the use of special contact elements and the interference of the user in dictating the accuracy of the solution. A modified Newmark formulation is developed to integrate the resulting time‐dependent variational inequality. This newly devised implicit time integration scheme is unconditionally stable, second‐order accurate, avoids numerical oscillations present in the traditional Newmark method, and does not cause numerical dissipation. To demonstrate the versatility and accuracy of the newly proposed algorithm, several examples are examined and compared with existing solutions where the penalty method has been employed. Copyright © 2001 John Wiley & Sons, Ltd.     

Analysis of frictional contact problem using boundary element method and domain decomposition method

In this paper, we study the bilateral or unilateral contact with Coulomb friction between two elastic solids, using a domain decomposition method coupled with the boundary element method. The decomposition method we have selected is the Schur complement method, a non‐overlapping technique. It enables to reduce the solution of the global problem to the solution of a problem defined only on the contact surface. Moreover, its principal advantage is that computing is done separately on each solid. We have chosen to associate it with the boundary element method. Indeed, it only requires the discretization of the boundaries of solids. This technique of coupling reduces the number of unknowns and the time of computing. We have applied it to the study of indentation of an elastic foundation by an elastic flat punch and a sphere. In this last case, our results are in conformity with the Hertz theory and the analytical solution of Spence. Moreover, we have shown the influence of friction on the size of the contact radius and on the normal pressure at centre. Copyright © 1999 John Wiley & Sons, Ltd.     

A semi‐implicit time‐stepping model for frictional compliant contact problems

In this paper, we formulate a semi‐implicit time‐stepping model for multibody mechanical systems with frictional, distributed compliant contacts. Employing a polyhedral pyramid model for the friction law and a distributed, linear, viscoelastic model for the contact, we obtain mixed linear complementarity formulations for the discrete‐time, compliant contact problem. We establish the existence and finite multiplicity of solutions, demonstrating that such solutions can be computed by Lemke's algorithm. In addition, we obtain limiting results of the model as the contact stiffness tends to infinity. The limit analysis elucidates the convergence of the dynamic models with compliance to the corresponding dynamic models with rigid contacts within the computational time‐stepping framework. Finally, we report numerical simulation results with an example of a planar mechanical system with a frictional contact that is modelled using a distributed, linear viscoelastic model and Coulomb's frictional law, verifying empirically that the solution trajectories converge to those obtained by the more traditional rigid‐body dynamic model. Copyright © 2004 John Wiley Sons, Ltd.     

炭布/树脂复合摩擦材料的湿式摩擦学性能

基于炭布优异的摩擦磨损性能、自润滑性能以及低密度等特点,将其应用于湿式摩擦材料中,以适应高转速、大压力或润滑不充分等极端工况.分别以1K、3K和6K碳布为增强体,制备出三种炭布/树脂复合摩擦材料,研究了其湿式摩擦学性能.结果表明:随着纤维束内单丝数量的增加,摩擦材料的瞬时制动稳定性降低,动摩擦系数减小,但是耐磨性能提高.所有摩擦材料的磨损率小于1.10×10-5 mm3/J,表现出较好的耐磨性能,并且对偶材料的磨损率很小,仅为0.40×10-5 mm3/J.磨损主要表现为纤维断裂、拔出及树脂脱粘等形式,但是在磨损表面没有形成大尺寸磨屑和明显的“第三体”磨粒,导致摩擦材料和对偶材料的磨损率较小.     

炭布/树脂复合摩擦材料的湿式摩擦学性能

基于炭布优异的摩擦磨损性能、 自润滑性能以及低密度等特点, 将其应用于湿式摩擦材料中, 以适应高转速、 大压力或润滑不充分等极端工况。分别以1 K、 3 K和6 K碳布为增强体, 制备出三种炭布/树脂复合摩擦材料, 研究了其湿式摩擦学性能。结果表明: 随着纤维束内单丝数量的增加, 摩擦材料的瞬时制动稳定性降低, 动摩擦系数减小, 但是耐磨性能提高。所有摩擦材料的磨损率小于1.10×10^-5 mm³/J, 表现出较好的耐磨性能, 并且对偶材料的磨损率很小, 仅为0.40×10^-5 mm³/J。磨损主要表现为纤维断裂、 拔出及树脂脱粘等形式, 但是在磨损表面没有形成大尺寸磨屑和明显的"第三体"磨粒, 导致摩擦材料和对偶材料的磨损率较小。     

Three‐dimensional quasi‐static frictional contact by using second‐order cone linear complementarity problem

A new formulation is presented for the three‐dimensional incremental quasi‐static problems with unilateral frictional contact. Under the assumptions of small rotations and small strains, a second‐order cone linear complementarity problem is formulated, which consists of complementarity conditions defined by bilinear functions and second‐order cone constraints. The equilibrium configurations are obtained by using a combined smoothing and regularization method for the second‐order cone complementarity problem. Copyright © 2005 John Wiley & Sons, Ltd.     

Three‐dimensional finite element computations for frictional contact problems with non‐associated sliding rule

This paper presents an algorithm for solving anisotropic frictional contact problems where the sliding rule is non‐associated.The algorithm is based on a variational formulation of the complex interface model that combine the classical unilateral contact law and an anisotropic friction model with a non‐associated slip rule. Both the friction condition and the sliding potential are elliptical and have the same principal axes but with different semi‐axes ratio. The frictional contact law and its inverse are derived from a single non‐differentiable scalar‐valued function, called a bi‐potential. The convexity properties of the bi‐potential permit to associate stationary principles with initial/boundary value problems. With the present formulation, the time‐integration of the frictional contact law takes the form of a projection onto a convex set and only one predictor–corrector step addresses all cases (sticking, sliding, no‐contact). A solution algorithm is presented and tested on a simple example that shows the strong influence of the slip rule on the frictional behaviour. Copyright 2004 John Wiley & Sons, Ltd.     

Voxel‐based meshing and unit‐cell analysis of textile composites

Unit‐cell homogenization techniques are frequently used together with the finite element method to compute effective mechanical properties for a wide range of different composites and heterogeneous materials systems. For systems with very complicated material arrangements, mesh generation can be a considerable obstacle to usage of these techniques. In this work, pixel‐based (2D) and voxel‐based (3D) meshing concepts borrowed from image processing are thus developed and employed to construct the finite element models used in computing the micro‐scale stress and strain fields in the composite. The potential advantage of these techniques is that generation of unit‐cell models can be automated, thus requiring far less human time than traditional finite element models. Essential ideas and algorithms for implementation of proposed techniques are presented. In addition, a new error estimator based on sensitivity of virtual strain energy to mesh refinement is presented and applied. The computational costs and rate of convergence for the proposed methods are presented for three different mesh‐refinement algorithms: uniform refinement; selective refinement based on material boundary resolution; and adaptive refinement based on error estimation. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

不同结构UHMWPE纤维纬编针织复合材料压缩性能

针对高性能超高分子量聚乙烯（UHMWPE）纤维的特性,成功编织出纬平针、罗纹、畦编3种针织物。采用真空辅助树脂传递模塑成型（VARTM）技术,分别制备出6层纬平针、6层罗纹以及6层畦编织物复合材料板。对3种结构复合材料进行压缩试验,并比较分析了比压缩强度-应变曲线、比压缩能量-应变曲线、比压缩能量-应变拟合曲线,分析了压缩过程中的能量吸收情况及材料的破坏形式。结果表明:纬平针结构复合材料的比压缩强度和比压缩能量均最大,其次是罗纹,畦编最小;且3种结构复合材料的压缩破坏过程均不属于脆性破坏;由于材料表现出较好的柔韧性,试样的比压缩能量与压缩应变呈线性相关;相同结构复合材料纵、横向比压缩强度-应变曲线和比压缩能量-应变曲线几乎重合。基体沿增强结构呈分层现象的破坏和树脂的塑性变形是材料的主要破坏形式。      

Improvement of a frictional contact algorithm for strongly curved contact problems

One of the challenges in contact problems is the prediction of the actual contact surface and the kind of contact that is established in each region. In numerical simulation of deep drawing problems the contact conditions change continuously during the forming process, increasing the importance of a correct evaluation of these parameters at each load step. In this work a new contact search algorithm devoted to contact between a deformable and a rigid body is presented. The rigid body is modelled by parametric Bézier surfaces, whereas the deformable body is discretized with finite elements. The numerical schemes followed rely on a frictional contact algorithm that operates directly on the parametric Bézier surfaces. The algorithm is implemented in the deep drawing implicit finite element code DD3IMP. This code uses a mechanical model that takes into account the large elastoplastic strains and rotations. The Coulomb classical law models the frictional contact problem, which is treated with an augmented Lagrangian approach. A fully implicit algorithm of Newton–Raphson type is used to solve within a single iterative loop the non‐linearities related with the frictional contact problem and the elastoplastic behaviour of the deformable body. The numerical simulations presented demonstrate the performance of the contact search algorithm in an example with complex tools geometry. Copyright © 2003 John Wiley & Sons, Ltd.     

On the modelling of complex anisotropic frictional contact laws

In this paper, the formulation of complex anisotropic frictional models with orthotropic friction condition and non-associated sliding rule is discussed. The friction law is described by a superellipse, which allow to consider a wide range of convex friction condition by simply varying the roundness factor affecting the shape of the limit surface. The sliding potential is also a superellipse but with a different semi-axis ratio, which lead to a non-associated sliding rule. For bodies in contact, the Signorini conditions can be formulated in terms of velocities and combined with the sliding rule to give the frictional contact law describing interfacial interactions. Its is shown that the frictional contact law as well as its inverse can be derived from the same scalar valued function called bi-potential. Due to the non-associated nature of the law, this relation is implicit. The advantage of the present formulation lies in the existence of stationary points of a functional, called bi-functional, that depends on both the displacements and the stresses.     

不同层数的超高分子量聚乙烯纬平针织复合材料冲击损伤

研究了不同层数超高分子量聚乙烯(UHMWPE)纤维/环氧树脂纬平针织复合材料的冲击性能,并讨论了其冲击损伤模式。复合材料板分别为4、6、8层纬平针织结构,采用真空辅助树脂传递模塑(VARTM)工艺层合而成,以不同的冲击能量(10~55J)冲击复合材料板直至层合板被穿透,得到冲击能量与吸收能量关系图以及接触力-挠度曲线。分析了不同冲击能量下,复合材料中织物的损伤形式和破坏过程。研究结果表明:在3种针织结构复合材料中,8层纬平针织结构承受载荷的能力最强,6层纬平针织结构次之,4层纬平针织结构最差;随着冲击能量的增加,3种试样的冲击挠度均增大;基体开裂、纤维断裂是试样被渗透时有效的损伤模式,基体和纤维断裂是试样被穿孔时有效的损伤模式。     

Potentiality of utilising natural textile materials for engineering composites applications

This paper gives an overview of utilising natural textile materials as reinforcements for engineering composites applications. The definition and types of textile materials are addressed to provide readers a thoughtful view on the role of these materials in a structural composite system. Available material properties of natural textile and their composites are critically reviewed here. In general, these materials are categorised into fibre, yarn and fabric forms. The load bearing capacity of natural textile fibre reinforced polymer composites is governed by the quantity, alignment and dispersion properties of fibres. It has been found that the natural fibre reinforced composites are limited to use in low to medium load bearing applications. However, a limited research work has been performed to date and there is a significant gap between the high performance textile fabric and their use as reinforcement in fibre reinforced composite materials.     

Predicting failure in textile composites using the Binary Model with gauge-averaging

First introduced over a decade ago, the Binary Model has evolved into a computationally efficient tool for predicting the properties of textile composites. Key to the formulation is the question of what details of the textile composite and the distributions of stress, strain, temperature, etc., are necessary and sufficient to represent the physics of the problem adequately and to ensure useful engineering predictions. This paper is concerned specifically with the prediction of the ultimate strength in cases where failure follows a single substantial local damage event, such as the rupture or kinking of a tow or the creation of a shear band mediated by matrix damage, without further increase in the external load. The accuracy of predictions is assessed for some triaxially braided carbon/epoxy composites. A gauge length is introduced that is suggested by the micromechanics of the failure mechanisms. Predictions are made by reference to strains that are averaged over a volume whose sides are commensurate with this gauge, but nevertheless retain spatial variations associated with the textile architecture. Failure criteria for tow rupture and matrix shear failure are taken from a single un-notched tensile test; the calibrated model then successfully predicts the failure mechanism (matrix shear or fiber rupture) and ultimate strength in un-notched and open-hole tension tests for any orientation of the textile fabric relative to the load axis, as well as bending and simple shear tests. The successful predictions are made using strains calculated for an entirely elastic representation of the material, which is possible because of the brittle character of the stress-strain curves. Predictions are also attempted using strains computed under the assumption that the textile material is homogeneous. These predictions are significantly inferior.     

管道修复用管状纺织复合材料的管径设计

系统地介绍了管状纺织复合材料管径设计原理,提出了管状纺织复合材料的弹性与热缩性能是影响管径设计的关键因素。采用有限元方法分析了管状纺织复合材料翻衬时的环向应变。结果表明,应根据管状纺织复合材料弹性的大小, 调节管径设计值。采用SPSS 软件对管状纺织复合材料的热缩性能进行分析,建立了反映热缩时间、热缩温度与缩率之间关系的数学模型。