Frictional Contact Model Research Articles

Сompression and Shear of an Ideal-plastic Wedge with a Rough Stamp (Frictional Contact Model)

The transfer of shear force through frictional contact on rough surfaces of precompressed plastic bodies is studied. As a contact model, we consider the problem of plastic compression of a wedge by a rough flat stamp with the condition of Prandtl friction on the contact surface. A technique is proposed for determining the maximum shear load perceived by frictional contact.

Peridynamics modelling of projectile penetration into concrete targets

A non-ordinary state-based peridynamics (NOSB-PD) model is proposed to simulate the projectile penetration into concrete targets. In this model, the Kong-Fang concrete material model recently proposed is firstly implemented into the NOSB-PD framework to describe the complex dynamic behavior and failures in concrete material subjected to penetration loading, and then an improved point-to-volume discrete frictional contact model is proposed to simulate the physical interaction between projectile and target. After the mesh-free discretization and explicit time integration, the proposed NOSB-PD model is used to numerically predict two sets of projectile penetration experiments into low-strength and high-strength concrete targets. And numerical predictions are found to be in good agreements with corresponding test data including penetration depth, projectile deceleration, deformation of projectile and failures in concrete targets.

A conforming frictional beam contact model

We develop a model for predicting the mechanical behavior of a system of slender one-dimensional bodies (fibers or beams) interacting via frictional contact. Relying on an integral penalty-based formulation, it can robustly capture the behavior in the case of conforming contact occurring over regions of finite size. Two formulations of the model are presented and validated against fully resolved continuum finite element simulations. Overall, the proposed framework is an effective tool in exploring the mechanical behavior of fabrics, textiles as well as three-dimensional frictional architected solids, as demonstrated by the simulation of the effective response of a periodic intertwined metamaterial.

Modeling of Fiber Optic Acoustic Coupler for Ultrasonic Sensing

Abstract Fiber Bragg grating (FBG) sensors have been applied in the remote bonding configuration for structural health monitoring, in which ultrasonic modes are propagated along the optical fiber to the sensor. Recently coupling of the ultrasonic mode from optical fiber to optical fiber through an adhesive coupler has also been demonstrated. This paper develops a finite element (FE) model to describe the coupler behavior as a function of the fiber and coupler properties, for future optimization of couplers. The FE model is validated with previous experimental data. We also compare the FE model to three theoretical models (spring and damper frictional contact models and coupled mode theory). The results show that the FE model and spring well replicate the experimental results. Future work will use the resulting FE and spring models to derive solutions for the coupling coefficient as a function of the geometrical and material parameters of the coupler.

Multiscale modeling of friction hysteresis at bolted joint interfaces

Friction at connection interfaces plays an important role in understanding the nonlinear vibration response of jointed structures. A reliable friction contact model capable of reproducing nonlinear behaviors at the friction interface is critical in the design and optimization of jointed structures. In this paper, a multiscale friction model is proposed. This approach provides a novel perspective for improving prediction accuracy by combining the predictability offered by a physics-based model and the convenience of a phenomenological model. Specifically, this method considers the actual topography of joint interfaces by measuring the three-dimensional (3D) topography data with high-resolution instruments. The surface topography data is then processed to obtain the geometry data at different scales, and the finite element method is used to determine the physics-based multiscale contact pressure distribution of surfaces. The twofold Weibull mixture model is used to represent the contact pressure distribution and further determine the Iwan density function. The effectiveness of the proposed approach is validated by comparing the model predictions with the experiment results of a new as-built structure. Moreover, the effects of the surface roughness and waviness on the friction behavior are discussed.

Computational Modeling of Tool-Rock Frictional Contact With Anisotropic Damage

The mechanism of frictional contact is investigated between a blunt tool and quasi-brittle rocks with anisotropic damage. A recently developed anisotropic elasto-plastic-damage model is further validated using experimental results under monotonic and cyclic loadings for rocks and concrete. A finite element model of tool-rock frictional contact is validated by analytical results in the two asymptotic regimes of an elastoplastic rock. The mesh sensitivity is reduced using a fracture energy-based method for anisotropic damage. The tool-rock frictional contact is predominantly controlled by three dimensionless parameters: η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta$$\\end{document}, ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi$$\\end{document}, and ζ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\zeta$$\\end{document}, which characterize elastoplasticity, brittleness, and anisotropic damage, respectively. The newly introduced damage coefficient ζ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\zeta$$\\end{document} controls the ratio of damage in different directions. As the elastoplastic parameter η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta$$\\end{document} increases with more plastic deformation, the dimensionless average contact stress Π~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\widetilde{\\Pi }}$$\\end{document} increases and then slightly varies before stabilizing. As the brittleness number ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi$$\\end{document} increases in a more brittle mode, the contact stress Π~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\widetilde{\\Pi }}$$\\end{document} generally decreases. When the damage coefficient ζ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\zeta$$\\end{document} decreases from isotropic to anisotropic damage, the contact stress Π~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\widetilde{\\Pi }}$$\\end{document} generally increases. The magnitudes of the average contact stress in numerical modeling are closer to experimental results when considering anisotropic damage.

Error estimates and numerical simulations of a thermoviscoelastic contact problem with damage and long memory

This paper aims to investigate a thermal frictional contact model with damage and long memory effects. We consider a deformable body made of viscoelastic material and assume the process to be dynamic. The material is expected to adhere to the Kelvin–Voigt constitutive law, with damage and thermal effects incorporated. The variational formulation of the model results in a coupled system comprising a history-dependent hemivariational inequality governing the displacement field, a parabolic variational inequality describing the damage field and an evolution equation for the temperature field. In the analysis of this system, we initially introduce a fully discrete scheme, and then concentrate on deriving error estimates of numerical solutions. An optimal order error estimate is attained under some appropriate solution regularity assumptions. At the tail of this manuscript, numerical simulations are provided for the contact problem to validate the theoretical results.

A computational framework for drop time assessment of a control element assembly under fuel assembly deformations with fluid-structure interaction and frictional contact

This paper presents a computational framework for drop time assessment of a control element assembly (CEA) under fuel assembly (FA) deformations. The proposed framework consists of three key components: 1) finite element modeling of CEA, 2) fluid-structure interaction to compute drag force, and 3) modeling of frictional contact between CEA and FA. Specially, to accommodate the large motion of CEA, beam elements based on absolute nodal coordinate formulation (ANCF) are adopted. The continuity equation is utilized to calculate the drag force, considering flow changes in the cross-sectional area during the CEA drop. Lastly, beam-inside-beam frictional contact model is employed to capture practical contact conditions between CEA and FA. The proposed framework is validated through experiments under two scenarios: free falls of CEA within FA, encompassing undeformed and deformed scenarios. The experimental validation of the framework demonstrated that the drop time of CEA can be accurately predicted under the complex coupling effects of fluid and frictional contact. The drop times of the S-shaped deformation case is longer than those of the C-shaped deformation case, affirming the time delay due to frictional force. The validation confirms the potential applicability to access the safety and reliability of nuclear power plants under extreme conditions.

A thermo-mechanical numerical method for modelling heating due to frictional sliding

Heating due to frictional sliding is an important phenomenon in tribological applications. The present study develops a numerical method based on the finite elements (FE) for modelling frictional sliding induced heating. More specifically, the method is designed for applications where the behavior of the tool part of the frictional contact couple is not critical so that it can be idealized as a rigid body. The contact between the tool and the target, assuming linear elastic material, is modelled with the penalty method. The FE-discretized balance of linear momentum is time discretized with the Newmark scheme, and the FE-discretized heat equation is time discretized with the backward Euler scheme. The global coupled thermo-mechanical problem is solved with a globally iterative staggered approach. The frictional contact model is verified against analytical solution of a rotating blade pressed against a plane. Finally, a validation simulation of a pin-on-disc tribology test is carried out.

Well-posedness of evolutionary differential variational–hemivariational inequalities and applications to frictional contact mechanics

In this paper, we study the well-posedness of a class of evolutionary variational–hemivariational inequalities coupled with a nonlinear ordinary differential equation in Banach spaces. The proof is based on an iterative approximation scheme showing that the problem has a unique mild solution. In addition, we established the continuity of the flow map with respect to the initial data. Under the general framework, we consider two new applications for modeling of frictional contact for viscoelastic materials. In the first application, we consider Coulomb’s friction with normal compliance, and in the second, normal damped response. The structure of the friction coefficient μ is new with motivation from geophysical applications in earth sciences with dependence on an external state variable α and the slip rate | u · τ | .

Study on the Friction Contact Model between a Rigid Ball and Rubber Surface with Various Rubber Materials: A Numerical Investigation

Study on the Friction Contact Model between a Rigid Ball and Rubber Surface with Various Rubber Materials: A Numerical Investigation

Research on Vibration Response of Shrouded Blades Based on Contact State

The shrouded is widely used in vibration reduction of turbine blades. In this study, the damping characteristics of the shrouded blade in gas turbine were studied. Firstly, a finite element model of the shrouded blade was established, and the full set of blades was reduced to a single sector based on the principle of cyclic symmetry. The contact state of the contact surface of the blade at different interference and speeds was calculated based on the displacement extraction method. Secondly, a microslip friction contact model was established based on the contact state of the contact surface. The nonlinear vibration response of shrouded blades was calculated based on the harmonic balance method. The results indicate that the shrouded has excellent vibration reduction performance. The interference and rotational speed of the blade will affect the damping efficiency.

An effective model for bolted flange joints and its application in vibrations of bolted flange joint multiple-plate structures: Theory with experiment verification

Bolted flange joints are widely used in various engineering structures to combine two or more substructures together. However, the understanding of mechanical mechanism of bolted flange joints is still insufficient due to the lack of efficient mathematical models. This paper proposes an effective mathematical model for bolted flange joints, which is then employed to conduct vibration analysis on bolted flange joint multiple-plate structures. During the modeling process, the flange is modeled by the Kirchhoff plate theory, and the bolted joints are modeled by the two-dimensional face constraint in bolted joint affected region (BJAR). The artificial spring technique is adopted to simulate the face constraint. The friction contact model and equivalent linearization technique are adopted to analyze the stick and slip states of bolted joints. By adopting the Chebyshev orthogonal polynomials as admissible functions, governing equations are derived. Then, the Rayleigh-Ritz method is applied to study the free vibration characteristics, and the Newmark-beta method is employed to study the vibration response under base excitation. The experimental studies are performed on the bolted flange joint two-plate structure (BFJTPS) to illustrate the effectiveness of the proposed theoretical model. The results indicate that the proposed mathematical model can well predict the vibration characteristics of multiple-plate structures under both bolt looseness and no-looseness conditions. The soft nonlinearity phenomenon under bolt looseness condition can be successfully revealed by the model.

Research on wing crack propagation of closed crack under uniaxial compression based on peridynamics

To investigate the influence of the interaction between closed crack surfaces on crack propagation, a nonlocal friction contact model is proposed for numerical simulation of wing crack propagation under uniaxial compression. The closed cracks with different inclination angles are defined by mathematical models, and cracks are generated by breaking off bonds at specific positions. In terms of numerical model validation, the comparison with FEM results indicates the correctness of the friction contact numerical model. Subsequently, the maximum principal stress criterion was applied to determine the breakage of the bond. The simulation results showed that under uniaxial compression, the closed crack tips undergo tensile failure, and the wing cracks will gradually expand towards the direction of the maximum principal stress. Both the crack inclination angle α and friction coefficient fc have an impact on crack initiation and propagation, increasing α or fc will reduce the initiation angle θ of crack propagation. At the same inclination angle α, the larger the friction coefficient fc, the shorter the crack propagation length, while the smaller the inclination angle α, the more significant the influence of friction coefficient fc on the initiation angle θ and crack path.

Resultant Normal Contact Force-Based Contact Friction Model for the Combined Finite-Discrete Element Method and Its Validation

In the conventional FDEM (Combined Finite and Discrete Element Method), each contact pair might have multiple contact points where friction forces are applied, leading to non-unique friction force assignments and potentially introducing computational errors. This study introduces a new contact friction algorithm for FDEM based on the resultant normal contact force. This method necessitates determining the friction force at a unique equivalent contact point, thereby significantly simplifying the computational flow and reducing memory usage. A series of numerical tests are performed to validate the effectiveness of the proposed contact model. Using collision and block sliding tests, the proposed contact friction model is verified to be able to accurately capture the frictional effect between discrete bodies and circumvent the problematic kinetic energy dissipation issue associated with the original contact friction algorithm. For the Brazilian splitting and uniaxial compression tests, the simulated results closely align with those generated using the original contact friction algorithm and match the experimental measurements well, demonstrating the applicability of the proposed algorithm in fracturing analysis. Furthermore, by using the proposed contact friction algorithm, a computational efficiency enhancement of 8% in contact force evaluation can be achieved.

Predicting transformation patterns in pseudoelastic NiTi tubes under proportional axial–torsion loading

We present a comprehensive modeling study on the patterns of propagating instabilities in NiTi tubes under proportional axial–torsion loading. Our study directly refers to the experimental work of Reedlunn et al. (2020), with a particular focus on the unique longitudinal transformation bands that occur in torsion-dominated loading paths. A previously-developed gradient-enhanced model of pseudoelasticity is employed and is adapted to incorporate the residual stresses. In addition, our finite-element setup accounts for the impact of collet grips on the NiTi tubes via a simplified frictional contact model. The results demonstrate the capability of the model in capturing subtle features of the transformation patterns observed in the experiment, including the multi-finger fronts in tension-dominated loading and longitudinal bands in torsion-dominated loading. Our study suggests that the combination of the residual stresses and the collet grips facilitates the formation of longitudinal bands.

Thermomechanical modeling of pellet-cladding interaction using state-based peridynamics

Pellet-Cladding Interaction (PCI) is a significant concern for the safe and reliable design of nuclear fuel rods. This study presents a modeling approach for investigating PCI employing the Ordinary State-Based PeriDynamics (OSB-PD) while considering irregular discretization to improve the modeling of curved boundaries of fuel rods with geometric precision. Unlike the existing PD models for fuel pellet, the present study considers contact and heat transfer between fuel pellet and cladding. Also, it presents a new frictional contact model with stick and slide friction. The heat conduction is modeled through gas, contact and radiation between pellet and cladding. In order to capture complex fragmentation and failure in pellet, material variability is considered by applying randomized critical stretch values with normal distribution. Specifically, it presents the effects of friction coefficient, gap size, and power level on crack patterns in fuel pellets while considering PCI. The PD predictions show that the number of major radial cracks remains constant as the friction coefficient increases; however, the number of circumferential cracks increases significantly. As the gap size increases, both the temperature in fuel pellet and the temperature difference across the gap increase. Also, the number of cracks in fuel pellet increases with the increasing value of gap size. The power level has a strong influence on the temperature gradient of the fuel rod, and the number of cracks in fuel pellet directly correlates with the power level.

Step-by-step simulation of wear of working surfaces in roller bearings

The purpose of this work was to develop effective methods for calculating the wear rate of raceways and roller bearings under dynamic loads. The wear of the working surfaces of rolling bearings in many practical cases is an important critical factor affecting their performance and durability. However, only a limited number of publications are devoted to this issue. In most of them, Archard's law, which has been experimentally confirmed during hydrodynamic friction of bearing steels, is used to calculate the wear rate of the contacting surfaces. Based on this law, the article presents a method of direct step-by-step calculation of the wear rate at variable contact loads and sliding speeds. In accordance with it, the change in the normal force, sliding speed and thickness of the oil film in contact is determined in the dynamic calculation of the bearing, and the finite element method is used to calculate the contact pressure field. The multi-mass model of bearing dynamics includes a contact friction model that allows adequately reproducing the conditions of hydrodynamic contact of solids. The direct calculation method involves a large number of calculations that make the impact of individual factors on the wear rate opaque. Therefore, along with it, a method for calculating the wear rate by averaged parameters is proposed. Using these two methods, the wear calculations of the raceway of the inner ring and the rollers of a double-row tapered roller bearing were performed. The comparison of the results confirms the acceptable accuracy of the calculation according to the averaged parameters.

A numerical framework for modelling tire mechanics accounting for composite materials, large strains and frictional contact

We present a general framework for the analysis and modelling of frictional contact involving composite materials. The study has focused on composite materials formed by a matrix of rubber and synthetic or metallic fibres, which is the case of standard tires. We detail the numerical treatment of incompressibility at large deformations that rubber can experience, as well as the stiffening effect that properly oriented fibres will induce within the rubber. To solve the frictional contact between solids, a Dual Augmented Lagrangian Multiplier Method is used together with the Mortar method. This ensures a variationally consistent estimation of the contact forces. A modified Serial-Parallel Rule of Mixtures is employed to model the behaviour of composite materials. This is a simple and novel methodology that allows the blending of constitutive behaviours as diverse as rubber (very low stiffness and incompressible behaviour) and steel (high stiffness and compressible behaviour) taking into account the orientation of the fibres within the material. The locking due to the incompressibility constraint in the rubber material has been overcome by using Total Lagrangian mixed displacement-pressure elements. A collection of numerical examples is provided to show the accuracy and consistency of the methodology presented when solving frictional contact, incompressibility and composite materials under finite strains.

Multibody Dynamics of Cross Groove Constant Velocity Ball Joints for High Performance Racing Applications

Accurate prediction of constant velocity joint transient contact loading and complex kinematics is necessary to improve joint design and prevent incurring failure from rolling contact fatigue. A detailed multibody dynamic model is presented for cross groove constant velocity joints used in high performance automotive racing applications, hitherto not reported in the open literature. The developed model includes detailed contact mechanics and friction models for all contacts made between the components. A novel semi-Hertzian contact model is adopted for the cage-race conjunction. Local contact kinematics is evaluated based on a methodology used in tribological analysis. The proposed model is validated against available computational models provided in literature for cross groove designs. Using the model, contact pressures occurring in the ball-race and ball-cage contacts are shown to reach levels as high as 4 and 5 GPa, respectively. The assumed value of friction coefficient is shown to have a strong influence on the predicted contact forces. Local contact motions are presented for the ball-race and ball-cage contacts, demonstrating complex motion which varies between pure rolling and pure sliding within a single cycle.