Frictional Contact Conditions Research Articles

탄소성 최소 제곱 수식화와 이를 이용한 무요소법

A new meshfree method for the analysis of elasto-plastic deformations is presented. The method is based on the proposed first-order least-squares formulation, to which the moving least-squares approximation is applied. The least-squares formulation for the classical elasto-plasticity and its extension to an incrementally objective formulation for finite deformations are proposed. In the formulation, the equilibrium equation and flow rule are enforced in least-squares sense, while the hardening law and loading/unloading condition are enforced exactly at each integration point. The closest point projection method for the integration of rate-form constitutive equation is inherently involved in the formulation, and thus the radial-return mapping algorithm is not performed explicitly. Also the penalty schemes for the enforcement of the boundary and frictional contact conditions are devised. The mam benefit of the proposed method is that any structure of cells is not used during the whole process of analysis Through some numerical examples of metal forming processes, the validity and effectiveness of the method are presented.

Numerical formulation for solving soil/tool interaction problem involving large deformation

Purpose – The aim of this work is to provide a global 3D finite element (FE) model devoted to the modelling of superficial soil ploughing in the large deformation range and for a vast class of soil treatment tools. Design/methodology/approach – We introduced soil constitutive equation in a FE software initially designed for the metal forming. We performed the numerical integration of the non‐linear ploughing problem. Non‐linearities encountered by the problem can be summed up: as soil constitutive equation (idealized with non‐associated compressible plastic law), unilateral frictional contact conditions (with a rigid body), geometrical non‐linearities (the ploughing tool) and large deformation range. To handle such difficulties we performed several numerical methods as implicit temporal scheme, Newton‐Raphson, non‐symmetric iterative solver, as well as proper approximation on stress and strain measures. Findings – Main results deal with the validation of the integration of the non‐linear constitutive equation in the code and a parametric study of the ploughing process. The influence of tool geometric parameters on the soil deformation modes and on the force experienced on the tools had been point out. As well, the influence of soil characteristics as compressibility had been analyzed. Research limitations/implications – This research is devoted to perform a numerical model applicable for a large range of soil treatment tools and for a large class of soil. However, taking into account all kind of soil is utopist. So limitations met are essentially related to the limit of the accuracy of the elasto‐plastic idealization for the soil. Practical implications – In practice the numerical model exposed in the paper can clearly help to improve and optimize any process involving superficial soil submitted to the mechanical action of a rigid body. Originality/value – The original value of the paper is to provide a global and an applicable numerical model able to take into account the main topics related to the ploughing of superficial soils. Industrials in geotechnics, in agriculture or in military purposes can benefit in using such numerical model.

강소성 변형 해석을 위한 최소 제곱 무요소법

The least-squares formulation for rigid-plasticity based on J₂-flow rule and infinitesimal theory and its meshfree implementation using moving least-squares approximation are proposed. In the least-squares formulation the squared residuals of the constitutive and equilibrium equations are minimized. Those residuals are represented in a form of rust-order differential system using the velocity and stress components as independent variables. For the enforcement of the boundary and frictional contact conditions, penalty scheme is employed. Also the reshaping of nodal supports is introduced to avoid the difficulties due to the severe local deformation near the contact interface. The proposed least-squares meshfree method does not require any structure of extrinsic cells during the whole process of analysis. Through some numerical examples of metal forming processes, the validity and effectiveness of the method are investigated.br/

Covariant description for frictional contact problems

A fully covariant description, based on the consideration of contact from the surface geometry point of view, is used for a consistent formulation of frictional contact conditions. All necessary operations for the description of the contact problems: kinematics, all differential operations etc. are defined in the covariant form in the local coordinate system which corresponds to the closest point procedure. The main advantage is a geometrical structure of the full tangent matrix, which is is subdivided into main, rotational and curvature parts. The consistent linearization of the penalty regularized contact integral leads to a symmetrical tangent matrix in the case of sticking. Representative examples show the effectiveness of the approach for problems where the definition of sticking-sliding zones is necessary as well as for the case of fully developed sliding zones.

A numerical modelling of non linear 2D-frictional multicontact problems: application to post-buckling in cellular media

In this paper a numerical modelling of non linear problems involving large deformations and frictional contact conditions is proposed. The motivation of this work comes from the study of the cellular materials (such as wood or foams) undergoing strong deformations. We restrict our study to a regular cellular network of hexagonal cells with thin walls. Strong loadings can generate at first buckling phenomena, then self-contact in the cell. Renouncing homogenization procedures, not always pertinent in this case, we have developed direct simulations. After giving the mechanical and mathematical formulations of the problem, we present two advanced numerical tools to solve large non linear frictional multicontact problems. This numerical modelling is based on an arc-length continuation method which permits to snap through singular points due to buckling phenomena and on an optimal domain decomposition method adapted to frictional contact problems. Finally, mechanical investigations of the contactless buckling and the post-buckling provide some pertinent parameters controlling the deformation process.

Asymptotic Numerical Method for strong nonlinearities

Plastic constitutive laws and frictional contact conditions induce strong nonlinearities that one has to take into account in the numerical simulation of material forming processes. In this work, we present a review of the different techniques which permit the asymptotic numerical method (ANM) to be adapted to these nonlinearities. ANM needs regular relations and quadratic equations if possible. Several examples show the effectiveness of the proposed method.

ON ANGULAR SPEED LOSS ANALYSIS OF FLAT BELT TRANSMISSION SYSTEM BY FINITE ELEMENT METHOD

International Journal of Computational Engineering ScienceVol. 04, No. 01, pp. 1-18 (2003) No AccessON ANGULAR SPEED LOSS ANALYSIS OF FLAT BELT TRANSMISSION SYSTEM BY FINITE ELEMENT METHODWEN-HWA CHEN and CHYUAN-JAU SHIEHWEN-HWA CHENDepartment of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, Taiwan 30043, R.O.CCorresponding author. Search for more papers by this author and CHYUAN-JAU SHIEHDepartment of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, Taiwan 30043, R.O.C Search for more papers by this author https://doi.org/10.1142/S1465876303000752Cited by:3 Next AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractThe effect of angular speed loss between the driver and driven pulleys for a flat belt transmission system is derived and analyzed by a rigorous three-dimensional finite element frictional contact analysis procedure established in this work. For modeling the flexible property of the flat belt, three-dimensional bar and eight-node brick elements are employed together to simulate the tension member and rubber layer, respectively. To accurately describe the bending effect of the rubber layer at the end zones of the contact area, the displacement approximation of the eight-node brick element is modified with the incremental Wilson displacement modes. In addition, to estimate the angular speed loss, appropriate frictional contact and loading conditions are provided to account for the physical contact phenomena between the belt and pulleys. The sliding region of the contact surfaces can thus be identified. The comparisons between the computed angular speed loss and referenced analytical/experimental results are made. Finally, the effects of dynamic friction coefficient, traction coefficient and material properties of the flat belt on the angular speed loss are studied as well.Keywords:Angular speed lossflat belttransmission systemfrictional contact analysis References T. H. C. Childs and I. K. Parker , Tribological Design of Machine Elements , Tribology Series 14 ( Elsevier , Amsterdam , 1989 ) . Google ScholarT. H. C. Childs and D. Cowburn, Proceedings of the Institution of Mechanical Engineers 201, 41 (1987), DOI: 10.1243/PIME_PROC_1987_201_156_02. Crossref, Google ScholarT. C. Firbank, Int. J. Mechanism Society 12, 1053 (1970), DOI: 10.1016/0020-7403(70)90032-9. Crossref, Google Scholar T. C. Firbank , Mechanics of the flat belt drive , ASME Mechanisms Conference and International Symposium on Gearing and Transmission ( 1972 ) . Google ScholarB. G. Gerbert, ASME J. Mech. Design 118, 432 (1996), DOI: 10.1115/1.2826904. Crossref, Google ScholarV. I. Chukanov, Russian Eng. J. 46, 26 (1966). Google Scholar T. C. Firbank , On the forces between the belt and driving pulley of a flat belt drive , ASME Design Engineering Technical Conference, III ( 1977 ) . Google ScholarT. H. C. Childs, Int. J. Mechanism Society 22, 117 (1980), DOI: 10.1016/0020-7403(80)90048-X. Crossref, Google ScholarH. Kim, K. M. Marshek and M. Naji, Mechanism and Machine Theory 22(1), 97 (1987), DOI: 10.1016/0094-114X(87)90082-6. Crossref, Google ScholarH. Kim and K. M. Marshek, J. Mechanisms, Transmissions and Automation in Design 110, 93 (1989), DOI: 10.1115/1.3258912. Crossref, Google ScholarC. J. Shieh and W. H. Chen, The Chinese J. Mech. 17, 189 (2001). Google ScholarW. H. Chen and J. T. Yeh, Comput. Struct. 35(5), 541 (1990), DOI: 10.1016/0045-7949(90)90382-C. Crossref, Google ScholarE. L. Wilsonet al., Numerical and Computer Methods in Structural Mechanics, eds. S. F. Fenveset al. (Academic Press, Inc, New York, 1973) p. 43. Google Scholar N. Kikuchi and J. T. Oden , Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods ( Addison-Wesley Publishing Company , Philadelphia , 1988 ) . Crossref, Google ScholarC. J. Shieh and W. H. Chen, Int. J. Mech. Sci. 44(9), 1879 (2002), DOI: 10.1016/S0020-7403(02)00136-4. Crossref, Google ScholarB. G. Gerbert, ASME J. Eng. Industry 96, 877 (1974). Crossref, Google ScholarB. G. Gerbert, ASME J. Mech. Design 100, 208 (1978). Crossref, Google ScholarT. Koyama, ASME J. Eng. Industry 103, 28 (1984). Google ScholarT. H. C. Childs and D. Cowburn, Wear 100, 59 (1984), DOI: 10.1016/0043-1648(84)90006-1. Crossref, Google Scholar FiguresReferencesRelatedDetailsCited By 3Estimación empírica del pretensado de una banda trapezoidal mediante el deslizamiento de las poleasEduardo Hernández-Dávila, Julio Cajamarca-Villa, Luis Cacuango-Eugenio and Verónica López-Pérez29 December 2018 | Ingenius, No. 21Effect of Flat Belt Thickness on Steady-State Belt Stresses and SlipTamer M. Wasfy, Cagkan Yildiz, Hatem M. Wasfy and Jeanne M. Peters3 February 2016 | Journal of Computational and Nonlinear Dynamics, Vol. 11, No. 5Speed losses in V-ribbed belt drivesBerna Balta, Fazil O. Sonmez and Abdulkadir Cengiz1 Apr 2015 | Mechanism and Machine Theory, Vol. 86 Recommended Vol. 04, No. 01 Metrics History Received 24 July 2002 Accepted 18 September 2002 KeywordsAngular speed lossflat belttransmission systemfrictional contact analysisPDF download

Three-dimensional stress analyses in composite laminates with an elastically pinned hole

We present a three-dimensional (3-D) stress analysis for composite laminates with an elastically pinned circular hole. The effects of friction, bearing force and bypass loading on the stress redistribution are studied in detail. The numerical approach is based on a multilayer boundary element method (MLBEM), a non-traditional BEM particularly designed for anisotropic composite laminates, coupled with the traditional BEM for the pin filling the hole. The unique characteristic of the MLBEM is that the fundamental solution employs Green’s functions that satisfy the interfacial continuity conditions and top- and bottom-surface traction-free and symmetry conditions. This fundamental solution allows us to design a BE scheme without involving discretization on the interfaces and surfaces unless the laminates are imposed by different boundary conditions. Consequently, in this case of pinned joint, only the hole surface among the composite boundary and interfaces needs to be discretized. A Coulomb-type friction law is used to simulate the frictional contact interaction between the composite and pin. To solve the frictional contact problem, an iterative scheme of successive over-relaxation has been proposed where the contact location and frictional contact condition are determined at the same time in the iteration solution. By applying the MLBEM, stress analyses are performed for a laminate plate with the stacking sequence (0/∓45/ 90) s . The issues of engineering interests, such as the loading-sequence and cycling dependencies of stress state due to the presence of friction, are addressed. The solutions, shown by complicated contact maps and stress states around the hole, suggested that a 3-D approach to pinned composite joints is necessary for the interpretation of the underlying physics.

An iterative complementarity approach for elastoplastic analysis involving frictional contact

We consider the nonholonomic (path-dependent) elastoplastic analysis of suitably discretized structures involving classical frictional contact conditions. A mixed generalized variable finite element approach within a mathematical programming framework is developed. Various models of generalized variables plasticity laws and contact conditions can be accommodated. The numerical solution is carried out in typical stepwise holonomic (path-independent) fashion. In particular, the iterative algorithm proposed involves solving a series of complementarity problems, with appropriate updating being carried out to account for changes in contact and possibly also plasticity conditions. Application is illustrated through several examples.

Finite element simulation of metal forming and in-plane crack propagation using ductile continuum damage model

The continuum damage model for ductile damage and ductile fracture is applied to metal forming and crack propagation by finite element method. The highly nonlinear equilibrium equation is formulated in order to include geometric, material nonlinearities and frictional contact condition. The effect of friction on the damage concentration is shown in the upsetting process. Then it is verified that the ductile fracture using this damage model is reasonable by the comparison with the experimental result in CCT specimen. The influence of the hole at the crack tip is shown through the numerical simulations of edge-cracked plates with different hole size. Finally, the strain energy release rate in this damage model is compared with J-integral using ABAQUS to relate the result of damage analysis to the concept of fracture mechanics.

Large displacement dynamic analysis with frictional contact by linear complementarity formulation

The linear complementarity formulation used for 2-D frictional contact conditions is combined with the method of a large displacement nonlinear dynamic analysis. The solution procedure is based on the total Lagrangian formulation and a single step time integration with a predictor and corrector scheme. For contact searching, a hierarchical scheme with a circular territory is used. Impact time and positions are detected using a second-order approximation of displacements and the velocity discontinuities during impact are considered using an impact condition. The formulation is illustrated by means of three numerical examples.

Factors influencing friction in steel sheet forming

The strip drawing test of sheet metal was used in the simulation of the steel sheet/steel tool friction contact conditions during a drawing operation. As the factors produce a dispersion effect on friction, the following variables were chosen: sample orientation, lubricant, velocity of sample displacement, plastic strain and contact pressure. The average friction coefficient was calculated from experimental data and a linear regression model was build to predict the dispersion effect.

Large-sliding contact elements accurately predict levels of bone–implant micromotion relevant to osseointegration

Primary stability is recognised as an important determinant in the aseptic loosening failure process of cementless implants. An accurate evaluation of the bone–implant relative micromotion is becoming important both in pre-clinical and clinical studies. If the biological threshold for micro-movements is in the range 100–200 μm then, in order to be discriminative, any method used to evaluate the primary stability should have an accuracy of 10–20 μm or better. Additionally, such method should also be able to report the relative micromotion at each point of the interface. None of the available experimental methods satisfies both requirements. Aim of the present study is to verify if any of the current finite element modelling techniques is sufficiently accurate in predicting the primary stability of a cementless prosthesis to be used to decide whether the micromotion may or may not jeopardise the implant osseointegration. The primary stability of an anatomic cementless stem, as measured in vitro, was used as a benchmark problem to comparatively evaluate different contact modelling techniques. Frictionless contact, frictional contact and press-fitted frictional contact conditions were modelled using alternatively node-to-node, node-to-face and face-to-face contact elements. The model based on face-to-face contact elements accounting for frictional contact and initial press-fit was able to predict the micromotion measured experimentally with an average (RMS) error of 10 μm and a peak error of 14 μm. All the other models presented errors higher than 20 μm assumed in the present study as an accuracy threshold.

Shape Design Sensitivity Analysis and Optimization of Elasto-Plasticity with Frictional Contact

A shape design sensitivity analysis and optimization are proposed for the ine nitesimal elasto ‐plasticity with a frictional contact condition. Rate-independent plasticity is considered with a return mapping algorithm and a von Mises yield criterion. The contact condition is formulated using the penalty method and the modie ed coulomb friction law. A continuum-based shape design sensitivity formulation is developed for structural and frictional contact variational equations. The direct differentiation method is used to compute the displacement sensitivity, and the sensitivities of various performance measures are computed from the displacement sensitivity. Path dependency of the sensitivity equation due to the constitutive relation and friction is discussed. It is shown that no iteration is required to solve the sensitivity equation. Response analysis and the proposed sensitivity formulation are implemented using the mesh-free method where the mesh distortion problem can be resolved. Numerical examples show accurate results of the proposed method compared to the e nite difference method. Dife culties in the sensitivity formulation for the e nite deformation problem are discussed. I. Introduction B ECAUSEoftherecentdevelopmentofcomputationalmechanics, it is now possible to analyze practical examples of complicated structural problems. Many design engineers, who are not satise ed with response analysis alone, have keen interests in the methodology of the design. For more than two decades, signie cant research efforthasbeen focused on the rate of response with respect to the changes in structural shape under shape design sensitivity analysis (DSA). Analysis of the design sensitivity information is the most important and costly procedure in the automated optimum design process. It supplies useful quantitative information to the design engineer about the direction of the desired design change. In a classical linear problem, DSA research has proved the differentiability of the solution of the response analysis using the linear operator theory and has derived specie c sensitivity expressions for variousproblems. 1 Aresultworthy of attention in linear DSAis that theoriginalresponseandthesensitivityoftheresponsebelongtothe samekinematicallyadmissiblespaceandhavethesameregularities. Owing to the development of the response analysis capability, engineers have directed their interest to the nonlinear problems that are dealt with efe ciently. Because many design application problems are accompanied by plastic deformation, the design sensitivity of nonlinear problems has been actively developed, and many research results are reported. In the procedure of nonlinear response analysis, the projection, called a return mapping, of the elastic trial stress is carried out to satisfy the variational inequality (VI)through an iteration in the stress space. 2 The DSA, on the other hand, computes the rate of change of the projected response in the tangential direction of the constraint set without iteration. Note that the sensitivity analysis is linear and can be computed without iteration even thoughtheresponseanalysisisnonlinear. 3 Unlikethenonlinearelastic problem, the sensitivity equation of the plastic problem requires sensitivity of the stress and internal evolution variables at the previous time. The sensitivity equation is solved at each time without iteration, and the sensitivity of the stress and evolution variables are

Development of a representative test specimen for frictional contact in spline joint couplings

The frictional contact conditions in a helical spline joint coupling under torsional and axial loads are studied using finite element analyses. Comparisons of spline root torsional stresses are made with photoelastic measurements. Surface contact tractions, relative slip distributions and subsurface localized stress component and equivalent stress distributions are presented for both the external and the internal spline contact surfaces. The work is important as a basis for understanding and predicting the fatigue, contact fatigue, fretting fatigue, wear and fretting wear characteristics of the coupling. A representative test specimen concept is presented which seeks to capture the local contact variable distributions in the spline coupling, with a view to predicting the wear and the contact and fretting fatigue performance of the coupling.

A Structural Nonlinear Analysis Workspace (SNAW) based on meshless methods

In this paper, a Structural Nonlinear Analysis Workspace (SNAW) based on meshless methods is presented. Using the meshless methods in SNAW, the modeling of structures for nonlinear analysis is accomplished by a set of particles, and the use of an explicit structured mesh as in the conventional finite element methods is unnecessary. Due to the use of smooth shape functions in the meshless methods, SNAW effectively deals with large structural deformations that usually lead to mesh distortion and solution divergence in finite elements. The meshless formulation in SNAW is applicable to hyperelastic and elasto-plastic materials, explicit and implicit time integrations, and rigid-to-flexible-body frictional contact conditions. This SNAW development interfaces meshless analysis code with MSC/PATRAN for pre- and post-processing using graphical menu-driven functionalities. A number of example problems, including engine mount, rubber seal, metal bar impact and metal-forming simulations, are presented to demonstrate the effectiveness of SNAW.

Numerical analysis of a hot‐strip rolling problem with Coulomb‐Siebel friction

An isothermal, steady‐state, hot‐strip rolling problem for rigid‐plastic, strain rate sensitive and incompressible materials with coulomb‐siebel friction contact conditions is considered. The corresponding penalty variational statement is given and a convergent finite element ‐ secant‐modulus method is presented. Two‐dimensional example problems are solved and comparisons with the available experimental and numerical results are made. The influence of the friction coefficient on the contact velocities, stresses and equivalent strain rates is illustrated.

Application of Reproducing Kernel Particle Method to Large Deformation Contact Analysis of Elastomers

Abstract A meshless formulation based on the Reproducing Kernel Particle Method (RKPM) is applied to the large deformation and contact analysis of elastomeric components. In this approach, a kernel estimate that ensures the completeness requirement of a linear field is introduced to construct the global Reproducing Kernel shape functions of the displacements. The Galerkin approximation of the variational equation is formulated using the Reproducing Kernel shape functions, and the discretization can be performed without the need of a structured mesh. In this paper, a RKPM formulation for rubber materials including frictional contact conditions is presented. The contact constraint equations and essential boundary conditions are formulated in the nodal coordinate using a direct transformation method. The global Reproducing Kernel shape functions expressed in a material description are used in the total Lagrangian formulation of hyperelasticity. By the use of the smooth Reproducing Kernel shape functions, the method is effective in dealing with large deformation and contact conditions in elastomeric applications.

Correlation Between Acoustic Emission and Wear of Multi-Layer Ceramic Coated Carbide Tools

Acoustic emission (AE) was used to monitor the machining process and tool condition during turning of AISI 4340 steel with uncoated, two-layer (TiC/Al2O3) coated, and three-layer (TiC/Al2O3/TiN) coated cemented WC-Co tools. The experiments were performed at four different feedrates and constant cutting speed and depth of cut. The variation of the AE signal with cutting time is interpreted in light of the dominant mechanisms, rates, and patterns of wear and the contact friction conditions at the tool/workpiece and tool/chip interfaces. Correlations between intrinsic frequencies and AE sources are identified by examining the root-mean-square, dominant amplitude, type, and count rate of the AE signals. It is shown that AE frequencies in the range of 50–100 kHz are primarily due to plastic deformation in the near-surface tool regions and the primary, secondary, and tertiary shear zones of the workpiece, whereas cracking leading to coating delamination and WC grain pull-out generates frequencies in the range of 170–200 kHz. The tool life estimated from the root-meansquare of the AE signal is shown to be in good agreement with that determined from measurements of the maximum wearland width on the tool nose. The obtained results demonstrate that AE is an effective technique for in-process wear monitoring and wear mechanism identification of multi-layer ceramic coated tools.

A finite element-mathematical programming method for elastoplastic contact problems with friction

Both the elastoplastic constitutive equations and the frictional contact conditions are described as a kind of linear complementarity condition. Then based on the principle of virtual work and the finite element discretization, a mathematical programming method is obtained for the solution of elastoplastic contact problems with friction. This work is an extension of our previous work on the elastic contact problem (Zhu and Jin, Comput. Struct. 52, pp. 149–155 (1994)) and elastoplasticity problem (Zhu and Jin, Appl. Math. Mech. 14, pp. 635–642 (1993)). Two examples are chosen to illustrate the applicability of the method.