Three-dimensional Frictional Contact Research Articles

Three-dimensional frictional contact within the framework of couple stress elasticity

This work investigates a three-dimensional size-dependent frictional contact problem of a rigid spherical punch sliding on an elastic half-space. The size-dependent material behaviors are governed by the couple stress theory, and the corresponding frequency response functions, which include two additional length-related elastic parameters, are obtained. Based on the conjugate gradient method and the discrete convolution-fast Fourier transform algorithm, a semi-analytical model is established to predict the frictional size-dependent contact behaviors and then the detailed parameter analysis is performed. The transverse effects of the couple stress, which are induced due to the considerations of the two additional elastic parameters in couple stress theory, are investigated in the contact problems for the first time. And the dependences of the size-dependent contact behavior on the coupling effects of the friction and the two additional elastic parameters are presented.

Effects of electromagnetic fields on the contact of magneto-electro-elastic materials

The three-dimensional (3D) frictional contact between a magneto-electro-elastic (MEE) material and a perfectly conducting rigid spherical punch under electromagnetic fields is investigated. This multiphysical contact problem is solved by the semi-analytical method (SAM), in which the frequency response functions (FRFs) with respect to unit mechanical, electric and magnetic loads are derived and converted into influence coefficients (ICs). The proposed model is validated with both analytical solutions and the finite element method (FEM). The effects of electromagnetic fields on contact performance and electromagnetic output are studied, and two types of electric and magnetic loads are considered by applying the surface density (closed circuit) or total amount (open circuit) of electric and magnetic charges. Parametric studies are conducted, and dimensionless curve-fitting equations are proposed to predict the average electric and magnetic potentials as functions of electric and magnetic loads, which are validated for arbitrary mechanical loads and radii of spherical punches.

Collision in the expansion joint effects on the seismic behavior of large-scale aqueduct

ABSTRACT Under earthquake, two beams of the aqueduct’s expansion joint may collide; thus, this will endanger the safety of the structure and even lead to girder falling accident. Quite a few studies of this issue use the simple one-dimensional model, but little takes the collision phenomenon under the action of multi-dimensional earthquake into account. According to the Contact-Impact Problems of large-scale aqueduct under earthquake action between the adjacent beam segments, a three-dimensional contact analysis model has been used to simulate the collision phenomenon. And the response of aqueduct structure collision one-dimensional seismic and multidimensional earthquake is compared; the results reveal that the three-dimensional frictional contact impact finite element model can simulate the real aqueduct structure under seismic pounding effect.

Semi-analytic modelling of transversely isotropic magneto-electro-elastic materials under frictional sliding contact

Functionally graded magneto-electro-elastic (FGMEE) materials has been increasingly used in engineering applications, particularly in smart material or intelligent structure systems. This paper proposes a semi-analytical approach for sliding frictional contact problem between a rigid insulating sphere and a transversely isotropic FGMEE film and half-space based on frequency response functions (FRFs). Multilayered approximation is used to model the functionally graded material (FGM), and the FRFs for each MEE layer are derived explicitly. The unknown coefficients in FRFs are formulated by two matrix equations, and their efficient solution process is proposed. Based on the obtained FRFs, a highly efficient semi-analytical model (SAM) is developed which is able to solve the three-dimensional frictional contact of FGMEE materials with arbitrary layer designs. The model is validated with finite element method and the literature. Furthermore, the pressure/stress distribution and electric/magnetic potential are studied in different FGM designs to investigate the influence of material layout.

A node-to-node scheme for three-dimensional contact problems using the scaled boundary finite element method

A node-to-node (NTN) scheme for modeling three-dimensional contact problems within a scaled boundary finite element method (SBFEM) framework is proposed. Polyhedral elements with an arbitrary number of faces and nodes are constructed using the SBFEM. Only the boundary of the polyhedral element is discretized to accommodate a higher degree of flexibility in mesh transitioning. Nonmatching meshes can be simply converted into matching ones by appropriate node insertions, thereby allowing the use of a favorable NTN contact scheme. The general three-dimensional frictional contact is explicitly formulated as a mixed complementarity problem (MCP). The inherent nonlinearity in the three-dimensional friction condition is treated accurately without requiring piecewise linearization. Contact constraints for non-penetration and stick-slide are enforced directly in a complementarity format. Numerical examples with 1st and 2nd order elements demonstrate the accuracy and robustness of the proposed scheme.

High-order mortar-based contact element using NURBS for the mapping of contact curved surfaces

In this paper, we present a high-order mortar-based contact element for the solution of two and three-dimensional frictional contact problems, considering small and large deformations. The Neo-Hookean isotropic compressible hyperelastic material model is considered. The mapping of curved surfaces of elements is performed with Non-Uniform Rational B-Splines. The behavior of the element in small and large deformations is verified by comparing it with solutions available in the literature, presenting studies of accuracy and processing time exhibited by the contact elements considering the h- and p-refinements. The comparative results show that the high-order interpolation is a strategy which has a better performance for the contact problems analysed, while improving solution accuracy of the contact stresses and forces with a lower processing time.

3D coupled multifield magneto-electro-elastic contact modelling

The present work deals with the general contact problem for coupled magneto-electro-elastic materials. Despite of the relevant technological applications, this topic of research has been treated only in some analytical works. But analytical solutions lack the generality of numerical methodologies, being restricted typically to simple geometries, loading conditions, idealized contact conditions and mostly taking into account transversely isotropic material symmetry with the symmetry axis normal to the contact surface. In this work, a numerical procedure for the three-dimensional frictional contact modelling of anisotropic coupled magneto-electro-elastic materials in presence of both electric and magnetic fields is presented for the first time. An orthotropic frictional law is considered, so anisotropy is present both in the bulk and in the surface. The methodology uses the boundary element method with explicit evaluation of the fundamental solutions in order to compute the magneto-electro-elastic influence coefficients. The contact model is based on an augmented Lagrangian formulation and it uses an iterative Uzawa scheme of resolution. Conducting, semi-conducting and insulated electric and/or magnetic indentation conditions, as well as orthotropic frictional contact conditions are considered. The methodology is validated by comparison with benchmark analytical solutions. Then, additional exploration examples are presented and discussed in detail, revealing that magneto-electric material coupling, conductivity contact conditions lead to a significant effect on the indentation force and contact pressure distributions. The influence of friction in electric and magnetic potential responses has been also proved to be very significant. Moreover, tangential loads exhibit an important influence both on the maximum values of the electric and magnetic potentials as well as on their distributions.

Three-dimensional contact analysis of coupled surfaces by a novel contact transformation method based on localized Lagrange multipliers

Instead of obsessively emphasizing to reduce the number of time increments and reshape the models, a novel surface contact transformation to increase efficiency is presented in this study. Wear on the bearing surfaces was investigated following the coupled regions from the pressure distribution, computed by means of three-dimensional finite element method models; an approximate analytical model and formulation in three-dimensional frictional contact problems based on modified localized Lagrange multiplier method have also been developed and discussed. Understanding wear behavior patterns in mechanical components is a significant task in engineering design. The proposed approach provides a complete and effective solution to the wear problem in a quasi-dynamic manner. However, expensive computing time is needed in the incremental procedures. In this article, an alternative and efficient finite element approach is introduced to reduce the computation costs of wear prediction. Through the successful verification of wear depth and volume loss of the pin-on-plate, block-on-ring, and metal-on-plastic artificial hip joint wear behaviors, the numerical calculations are shown to be both valid and feasible. Furthermore, the results also show that the central processing unit time required by the proposed method is nearly half that of the previous methods without loss of accuracy.

3D BEM for orthotropic frictional contact of piezoelectric bodies

A numerical methodology to model the three-dimensional frictional contact interaction of piezoelectric materials in presence of electric fields is presented in this work. The boundary element method (BEM) is used in order to compute the electro-elastic influence coefficients. The proposed BEM formulation employs an explicit approach for the evaluation of the corresponding fundamental solutions, which are valid for general anisotropic behaviour meanwhile mathematical degeneracies in the context of the Stroh formalism are allowed. The contact methodology is based on an augmented Lagrangian formulation and uses an iterative Uzawa scheme of resolution. An orthotropic frictional law is implemented in this work so anisotropy is present both in the bulk and in the surface. The methodology is validated by comparison with benchmark analytical solutions. Some additional examples are presented and discussed in detail, revealing the importance of considering orthotropic frictional contact conditions in the electro-elastic analysis of this kind of problems.

Research about Slider Three-Dimensional Frictional Contact Problem of the Polygonal and Similar-Oval Jib

The existence of boundary condition and friction are difficult to predict which makes the sliders contact situation extremely complex. The actual response of the contact region becomes a tough research by using traditional method. Taking the cylinder supporting function into account, the polygonal and similar-oval Jib models are established. Research of the stress distribution and the stress concentration phenomenon is analyzed. The results indicate that stress distribution of the sliders of the similar-oval Jib is more uniform in comparison with the polygonal Jib that it can ameliorate the stress state of the contact region and enhance the partial stability of the Jib.

3D contact modelling of large plastic deformation in powder forming processes

In this paper, the three-dimensional large frictional contact deformation of powder forming process is modeled using a node-to-surface contact algorithm based on the penalty and augmented-Lagrange approaches. The technique is applied by imposing the normal and tangential contact constraints and modifying the contact properties of frictional slip. The Coulomb friction law is employed to simulate the friction between the rigid punch and the work piece. It is shown that the augmented-Lagrange technique significantly improves imposing of the constraints on contact surfaces. In order to predict the non-uniform relative density and stress distributions during the large deformation of powder die-pressing, the nonlinear contact friction algorithm is employed within the framework of large finite element deformation, in which a double-surface cap plasticity model is used for highly nonlinear behavior of powder. Finally, the numerical schemes are examined for accuracy and efficiency in modeling of a set of powder components.

Squat growth—Some observations and the validation of numerical predictions

Abstract This paper presents evidences obtained by field monitoring, measurement and survey to show the validity of some numerical predictions about squat growth. The predictions concerns a postulated squat growth process, the relationship between the dynamic contact force and the corrugation-like wave pattern that often follows squats, the high frequency wheel–rail interaction related to squats, and the influence of tangential force on squat growth. The observations reveal signature tunes of squats which may be used for early detection of squats, show the necessity to include high frequency dynamic wheel–rail interaction in squat-related analyses, and provide evidence of relationship between rolling stock performance and squat initiation and growth. In validating the numerical results the model is also verified for its applicability to analyses of squat-related problem and other problems similar in nature. The model can be employed for the solution of three-dimensional frictional rolling contact problems. It can also be used for analyses of loading conditions of wheel–rail contact at short wave defects, and the associated damages such as wear, plastic deformation, fatigue and corrugation.

New second-order cone linear complementarity formulation and semi-smooth Newton algorithm for finite element analysis of 3D frictional contact problem

We propose a new second-order cone linear complementarity problem (SOCLCP) formulation for the numerical finite element analysis of three-dimensional (3D) frictional contact problems by the parametric variational principle. Specifically, we develop a regularization technique to resolve the multi-valued difficulty involved in the frictional contact law, and use a second-order cone complementarity condition to handle the regularized Coulomb friction law in contact analysis. The governing equations of the 3D frictional contact problem is represented by an SOCLCP via the parametric variational principle and the finite element method, which avoids the polyhedral approximation to the Coulomb friction cone so that the problem to be solved has much smaller size and the solution has better accuracy. In this paper, we reformulate the SOCLCP as a semi-smooth system of equations via a one-parametric class of second-order cone complementarity functions, and then apply the non-smooth Newton method for solving this system. Numerical results confirm the effectiveness and robustness of the SOCLCP approach developed.

Sensitivity analysis for frictional contact problems in the augmented Lagrangian formulation

Direct differentiation method of sensitivity analysis is developed for frictional contact problems. As a result of the augmented Lagrangian treatment of contact constraints, the direct problem is solved simultaneously for the displacements and Lagrange multipliers using the Newton method. The main purpose of the paper is to show that this formulation of the augmented Lagrangian method is particularly suitable for sensitivity analysis because the direct differentiation method leads to a non-iterative exact sensitivity problem to be solved at each time increment. The approach is applied to a general class of three-dimensional frictional contact problems, and numerical examples are provided involving large deformations, multibody contact interactions, and contact smoothing techniques.

Finite element method-based three-dimensional frictional contact analysis of turbocharger compressor

In the long-distance transport of material, turbocharger compressors are playing an important role. The impeller mounted onto the compressor shaft assembly via interference fit is one of the key components of a centrifugal compressor stage. The assembly creates a complicated frictional contact problem on the interface of the contacting parts when the rotating speed is high. A locomotive-type turbocharger compressor with 24 blades under combined centrifugal and interference-fit loading is used for the analysis. The finite element parametric quadratic programming method that was developed based on the parametric variational principle is used for the analysis of the stress distribution of three-dimensional frictional contact problem between the impeller and the shaft assembly. The advantages of the parametric programming method when compared with the conventional ones are that the penalty factors can be cancelled and the solutions can be obtained directly without tedious iterative procedures such as general incremental iterative method. The effects of fit tolerance, coefficient of friction, the wall thickness of the shaft sleeve, rotational speed, and the contact stress distribution on the contacting surfaces are discussed in section 2. It is found that non-uniform initial amount of interference in the structural design would avoid relative displacement generated and ensure uniformity of the contact stress. To assure the quality of press-fitting, the amount of interference between the shaft sleeve and the shaft should be controlled strictly to avoid the rapid increase of the contact stress. The results obtained play a key role in deciding the proper fit tolerance and improving design and manufacturing technology of the compressor impellers. The current study also provides an effective approach which achieves more reliable interference-fitted connections and more precise assembly accuracy with lower manufacturing cost in the structural design.

Construction of an Intraplate Fault System Model of South Australia, and Simulation Tool for the iSERVO Institute Seed Project

To foster ongoing international cooperation beyond ACES (APEC Cooperation for Earthquake Simulation) on the simulation of solid earth phenomena, agreement was reached to work towards establishment of a frontier international research institute for simulating the solid earth: iSERVO = International Solid Earth Research Virtual Observatory institute (http://www.iservo.edu.au). This paper outlines a key Australian contribution towards the iSERVO institute seed project, this is the construction of: (1) a typical intraplate fault system model using practical fault system data of South Australia (i.e., SA interacting fault model), which includes data management and editing, geometrical modeling and mesh generation; and (2) a finite-element based software tool, which is built on our long-term and ongoing effort to develop the R-minimum strategy based finite-element computational algorithm and software tool for modelling three-dimensional nonlinear frictional contact behavior between multiple deformable bodies with the arbitrarily-shaped contact element strategy. A numerical simulation of the SA fault system is carried out using this software tool to demonstrate its capability and our efforts towards seeding the iSERVO Institute.

Earthquake safety assessment of concrete arch and gravity dams

Based on research studies currently being carried out at Dalian University of Technology, some important aspects for the earthquake safety assessment of concrete dams are reviewed and discussed. First, the rate-dependent behavior of concrete subjected to earthquake loading is examined, emphasizing the properties of concrete under cyclic and biaxial loading conditions. Second, a modified four-parameter Hsieh-Ting-Chen viscoplastic consistency model is developed to simulate the rate-dependent behavior of concrete. The earthquake response of a 278m high arch dam is analyzed, and the results show that the strain-rate effects become noticeable in the inelastic range. Third, a more accurate non-smooth Newton algorithm for the solution of three-dimensional frictional contact problems is developed to study the joint opening effects of arch dams during strong earthquakes. Such effects on two nearly 300m high arch dams have been studied. It was found that the canyon shape has great influence on the magnitude and distribution of the joint opening along the dam axis. Fourth, the scaled boundary finite element method presented by Song and Wolf is employed to study the dam-reservoir-foundation interaction effects of concrete dams. Particular emphases were placed on the variation of foundation stiffness and the anisotropic behavior of the foundation material on the dynamic response of concrete dams. Finally, nonlinear modeling of concrete to study the damage evolution of concrete dams during strong earthquakes is discussed. An elastic-damage mechanics approach for damage prediction of concrete gravity dams is described as an example. These findings are helpful in understanding the dynamic behavior of concrete dams and promoting the improvement of seismic safety assessment methods.

Non-interior smoothing algorithm for frictional contact problems

A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.

An effective BE algorithm for 3D elastoplastic frictional contact problems

This paper is concerned with an effective boundary element algorithm for the elasto-plastic analysis of three-dimensional frictional contact problems using a quadratic boundary element formulation in the framework of small strains and small displacements. The contact conditions are used to unite the different system of equations for each body in contact. Several types of contact interface conditions are covered including infinite friction, frictionless and Coulomb friction. In order to include plastic deformation, the initial stain formulation and von Mises yield criterion are employed. The proposed algorithm is applied to the elasto-plastic analysis of the frictionless rigid punch, a large plate with a rigid, circular, cylindrical inclusion under the increasing load and the frictional punch contact problem.

Effect of angular speed on behavior of a V-belt drive system

For a V-belt drive system, the effect of angular speed on the three-dimensional frictional contact behaviors on the contact surfaces between the V-belt and pulley flange is studied in this work. To deal with the frictional contact phenomena for the V-belt drive system, an effective three-dimensional finite element procedure is developed herein. By this procedure, the deformation of the V-belt and the normal/tangential contact forces occurring on the contact surfaces can be estimated accurately. The friction angles of contact points along the edge of the V-belt cross section are also presented for various dynamic friction coefficients. From the computed results, it is found that smaller friction angles are obtained as dynamic friction coefficients get larger. The results achieved are very helpful for the estimation of operation efficiency of the V-belt drive system.