Frictional Contact Conditions Research Articles

Variational inequalities of multilayer elastic contact systems with interlayer friction: Existence and uniqueness of solution and convergence of numerical solution

Inspired by the layered structure models in pavement mechanics research, in this study, a class of multilayer elastic contact systems with interlayer frictional contact conditions and deformable supporting frictional contact conditions on the foundation has been constructed. Based on the nonlinear elastic constitutive equations, the corresponding system of partial differential equations and variational inequalities are respectively introduced. Under the framework of variational inequalities, the existence and uniqueness of solutions for such models, along with the approximation properties of finite element numerical solutions, are proven and analyzed. The aforementioned conclusions provide fundamental and broadly applicable theoretical support for addressing mechanical problems in multilayer elastic contact systems within the framework of variational inequalities. Finally, the numerical experimental results based on the mixed finite element method also substantiate our theoretical conclusions.

Complex function stress solution of cold region tunnels under frictional contact condition of lining and surrounding rock with support delay

Complex function stress solution of cold region tunnels under frictional contact condition of lining and surrounding rock with support delay

Development and Investigation of a Grasping Analysis System with Two-Axis Force Sensors at Each of the 16 Points on the Object Surface for a Hardware-Based FinRay-Type Soft Gripper.

The FinRay soft gripper achieves passive enveloping grasping through its functional flexible structure, adapting to the contact configuration of the object to be grasped. However, variations in beam position and thickness lead to different behaviors, making it important to research the relationship between structure and force. Conventional research using FEM simulations has tested various virtual FinRay models but replicating phenomena such as buckling and slipping has been challenging. While hardware-based methods that involve installing sensors on the gripper and the object to analyze their states have been attempted, no studies have focused on the tangential contact force related to slipping. Therefore, we developed a 16-way object contact force measurement device incorporating two-axis force sensors into each of the 16 segmented objects and compared the normal and tangential components of the enveloping grasping force of the FinRay soft gripper under two types of contact friction conditions. In the first experiment, the proposed device was compared with a device containing a six-axis force sensor in one segmented object, confirming that the proposed device has no issues with measurement performance. In the second experiment, comparisons of the proposed device were made under various conditions: two contact friction states, three object contact positions, and two object motion states. The results demonstrated that the proposed device could decompose and analyze the grasping force into its normal and tangential components for each segmented object. Moreover, low friction conditions result in a wide contact area with lower tangential frictional force and a uniform normal pushing force, achieving effective enveloping grasping.

A smoothed assumed enhanced strain method for frictional contact with constant strain elements

This paper presents a finite element framework for imposing frictional contact conditions on embedded fracture faces, implemented by the constant-strain assumed enhanced strain (AES) method, where penalty method is used to impose both non-penetration constraint and Coulomb's law of friction. The proposed constant-strain AES method for modeling embedded frictional contact can be cast into an integration algorithm similar to those used in the classical plasticity theory, where displacement jump is calculated from the local traction equilibrium at Gauss point, so the method does not introduce any additional global degrees of freedom. Moreover, constant-strain elements are often desirable in practice because they can be easily created automatically for large-scale engineering applications with complicated geometries. As encountered in other enriched finite element methods for frictional contact, the problem of normal contact pressure oscillations is also observed in the constant-strain AES method. Therefore, we developed a strain-smoothing procedure to effectively mitigate the oscillations. We investigated and verified the proposed AES framework through several numerical examples, and illustrated the capability of this method in solving challenging nonlinear frictional contact problems.

Effect of ureteral stent length and implantation position on migration after implantation.

Ureteral obstruction is a urinary system disease that causes urinary retention, renal injury, renal colic, and infection. Ureteral stents are often used for conservative treatment in clinics, and their migration usually results in ureteral stent failure. The migrations include proximal migration to the kidney side and distal migration to the bladder side, but the biomechanism of stent migration is still unknown. Finite element models of stents with lengths from 6-30cm were developed. The stents were implanted into the middle of the ureter to analyze the effect of stent length on its migration, and the effect of stent implantation position on 6-cm-long stent migration was also observed. The stents' maximum axial displacement was used to assess the ease of stent migration. A time-varying pressure was applied to the ureter outer wall to simulate peristalsis. The stent and ureter adopted friction contact conditions. The two ends of the ureter were fixed. The radial displacement of the ureter was used to evaluate the effect of the stent on peristalsis. The maximum migration occurs in the positive direction for a 6-cm-long stent implanted at the proximal ureter (CD and DE), but in the negative direction at the distal ureter (FG and GH). The 6-cm-long stent demonstrated almost no effect on ureteral peristalsis. The 12-cm-long stent diminished the radial displacement of the ureter from 3-5s. The 18-cm stent diminished the radial displacement of the ureter from 0-8s, and the radial displacement within 2-6s was weaker than other time. The 24-cm stent diminished the radial displacement of the ureter from 0-8s, and the radial displacement within 1-7s was weaker than other time. The biomechanism of stent migration and ureteral peristalsis weakening after stent implantation was explored. Shorter stents were more likely to migrate. The implantation position had less influence on ureteral peristalsis compared with the stent length, which provided a reference for stent design aimed at reducing stent migration. Stent length was the main factor affecting ureteral peristalsis. This study provides a reference for the study of ureteral peristalsis.

Analysis of Traction Coefficient Subject to Rail Cleaning Effect Based on Tribomachine Measurements

The proper representation of friction contact conditions between each wheel and the rail is necessary to accurately model the behaviour of a heavy haul locomotive since friction conditions at the wheel-rail interface affect the locomotive’s dynamic performance under traction and braking conditions. In normal operations, a phenomenon commonly known as rail cleaning effect occurs. The rail cleaning effect causes increased friction coefficients between the following wheel treads and the rail head. The wheel-rail interaction causes the third body layer to be partly or wholly eliminated from the surfaces in contact and generates new layer. An experimental analysis of the changes in friction coefficients under simulated locomotive wheel-rail contact conditions, in terms of contact pressure and slip, is presented in this paper. For this study, data processing equations are presented to obtain the experimental traction coefficient and slip. Furthermore, the rail cleaning effect is examined under different slip conditions. The experiment shows the traction coefficient increases for a given number of cycles until reaching a steady value, demonstrating that the rail cleaning effect is measurable in various slip conditions on a twin disc machine.

Subsurface Stresses in Flat-Punch Contact Problems Including Friction

This work analyzes the influence of friction on the surface and subsurface contact stresses generated—in an elastic half-space—by a cylindrical flat-ended punch. For this purpose, the computational framework presented by [J. M. Juliá and L. Rodríguez-Tembleque, Subsurface stress evolution under orthotropic wear and frictional contact conditions, Int. J. Mech. Sci. 234 (2022) 107695] is extended to solve this problem. After the validation of this computational scheme, several numerical studies have allowed us to obtain the following conclusions. (i) The location of the maximum values of the subsurface Von Mises stresses in the [Formula: see text]–[Formula: see text] plane does not depend on the friction coefficient and is located at the contact zone limits — similarly to the normal pressure — (ii) However, the [Formula: see text]-location and the magnitude of the maximum value of the subsurface Von Mises stress is clearly affected by the values of the friction coefficient. (iii) The magnitude of the maximum value of the subsurface Von Mises stress increases and its location can be shifted from the subsurface region to the solid surface, when the friction coefficient increases its value.

Frictionless vs. Frictional Contact in Numerical Wear Predictions of Conformal and Non-conformal Sliding Couplings

The role of friction on wear evolution is manifold since it interplays with lubrication regime, nominal contact point, and contact pressure distribution. Nevertheless, in the literature many wear models simulate wear assuming frictionless contact conditions to simplify the analyses. That assumption, physically not realistic, often appears as a contradiction, permitted in numerical simulations where friction and wear can be considered independent phenomena.This study aims to validate the frictionless assumption in wear models with steady nominal contact point, such as in many common configurations, e.g. pin on plate/pin on disc. Wear was simulated according to the Archard wear law for both non-conformal and conformal pin-on-plate contact pairs in reciprocating motion, assuming frictionless and frictional contact conditions, varying the coefficient of friction f in the range 0–0.4. Finite Element wear models were developed in Ansys® both with implicit and explicit kinematics. Results demonstrate that the effect of friction on contact pressure distribution and worn profiles and on their evolution is negligible (differences lower than 0.05%). Thus, wear can be predicted using models in frictionless conditions which allow to extremely reduce the computational costs that represent a limit of FE wear simulations. Additionally, a procedure with implicit kinematics was compared to the explicit one resulting valid and computationally convenient, especially in case of non-conformal contact.

Subsurface stress evolution under orthotropic wear and frictional contact conditions

This work presents a computational framework to study the evolution of the subsurface stresses in 3D solids under orthotropic frictional contact and wear conditions. The formulation is based on the influence coefficients methodology to relate the discrete elastic response (i.e., displacements and stresses) to the sampled excitation (i.e., surface contact tractions). The proposed methodology is validated by solving several benchmark problems and is applied to analyze how the subsurface stress distribution (i.e. maximum value and its location) – and its evolution – caused by orthotropic wear conditions are clearly affected not only by the considered wear problems (i.e., sliding wear or fretting wear) but also by the friction coefficient values and the sliding direction angle — relative to the tribological axes. Several numerical examples are presented to show the importance of these last two aspects when orthotropic wear conditions are considered. In other case, we could over- or underestimate the maximum values of the subsurface stresses during the wear process.

Applications of generalized fractional hemivariational inequalities in solid viscoelastic contact mechanics

This paper studies a generalized fractional hemivariational inequality in infinite-dimensional spaces. Under the suitable assumptions, the existence result is delivered by using the temporally semi-discrete scheme and the surjectivity result for multivalued pseudomonotone operator. As an illustrative application, we propose a frictional contact model that describes the quasi-static contact between a viscoelastic body and a solid foundation. The viscoelastic constitutive equation is modeled by fractional Kelvin-Voigt law with ψ-Caputo derivative, and the frictional contact conditions are expressed as the Clarke subdifferentials of the nonconvex and nonsmooth functionals. Finally, the weak solvability of the mechanical system is obtained by using our abstract mathematical result.

A Scaled Boundary Finite-Element Method with B-Differentiable Equations for 3D Frictional Contact Problems

Contact problems are among the most difficult issues in mathematics and are of crucial practical importance in engineering applications. This paper presents a scaled boundary finite-element method with B-differentiable equations for 3D frictional contact problems with small deformation in elastostatics. Only the boundaries of the contact system are discretized into surface elements by the scaled boundary finite-element method. The dimension of the contact system is reduced by one. The frictional contact conditions are formulated as B-differentiable equations. The B-differentiable Newton method is used to solve the governing equation of 3D frictional contact problems. The convergence of the B-differentiable Newton method is proven by the theory of mathematical programming. The two-block contact problem and the multiblock contact problem verify the effectiveness of the proposed method for 3D frictional contact problems. The arch-dam transverse joint contact problem shows that the proposed method can solve practical engineering problems. Numerical examples show that the proposed method is a feasible and effective solution for frictional contact problems.

A unilateral constraint contact problem for viscoelastic materials with wear

The aim of this work is to investigate a mathematical model that describes the frictional contact between viscoelastic materials with a long memory and a moving foundation. The contact condition is modeled with a version of normal compliance condition with unilateral constraint in which wear of foundation is considered. Friction contact condition follows a sliding version of Coulomb's law of dry friction. We derive a variational formulation of the problem, which couples a variational inequality and an integral equation. Then, we obtain the unique weak solvability of the contact problem by virtue of a fixed point theorem. By using the penalization method, we discuss the convergence of the contact problem. Further, we obtain the unique solution of the penalized problem and this solution converges to the solution of the original contact model as the penalization parameter converges to zero.

Energy-stable discretization of two-phase flows in deformable porous media with frictional contact at matrix–fracture interfaces

We address the discretization of two-phase Darcy flows in a fractured and deformable porous medium, including frictional contact between the matrix–fracture interfaces. Fractures are described as a network of planar surfaces leading to the so-called mixed- or hybrid-dimensional models. Small displacements and a linear elastic behavior are considered for the matrix. Phase pressures are supposed to be discontinuous at matrix–fracture interfaces, as they provide a better accuracy than continuous pressure models even for high fracture permeabilities.The general gradient discretization framework [31] is employed for the numerical analysis, allowing for a generic stability analysis and including several conforming and nonconforming discretizations. We establish energy estimates for the discretization, and prove existence of a solution. To simulate the coupled model, we employ a Two-Point Flux Approximation (TPFA) finite volume scheme for the flow and second-order (P2) finite elements for the mechanical displacement coupled with face-wise constant (P0) Lagrange multipliers on fractures, representing normal and tangential stresses, to discretize the frictional contact conditions. This choice allows to circumvent possible singularities at tips, corners, and intersections between fractures, and provides a local expression of the contact conditions. We present numerical simulations of two benchmark examples and one realistic test case based on a drying model in a radioactive waste geological storage structure.

An Uzawa-type augmented Lagrangian numerical manifold method for frictional discontinuities in rock masses

The problem of frictional discontinuities in rock masses is addressed computationally in the context of the NMM (numerical manifold method). The use of the NMM allows the use of nonmatching meshes to discretize the problem domain. To impose frictional contact conditions, the Uzawa-type ALM (augmented Lagrange method), which inherits the merits of the LMM (Lagrange multiplier method) and the PM (penalty method), is incorporated into the NMM, and a numerical model termed as Uzawa-type augmented Lagrangian numerical manifold method (UALNMM) is proposed. In the UALNMM, two layers of iterations are adopted, which are Newton-Raphson iterations for the inner layer and augmentation iterations for the outer layer. The implementation of the UALNMM is discussed in details. Four benchmark examples of frictional/frictionless contact problems and an example of rock slope with multiple frictional fractures are used to validate the accuracy and robustness of the UALNMM. The proposed UALNMM deserves further investigation for three dimensional rock mechanics problems with frictional contact.

Numerical manifold computational homogenization for hydro-dynamic analysis of discontinuous heterogeneous porous media

In this paper, a mixed two-scale numerical manifold computational homogenization model is presented for dynamic analysis and wave propagation of the discontinuous heterogeneous porous media based on the first-order homogenization theory. Instead of the conventional version which neglects microscopic dynamics, the extended Hill–Mandel lemma is employed to incorporate the microscale dynamic effects. Microscale and macroscale Initial Boundary Value Problems (IBVPs) are solved simultaneously using the Numerical Manifold Method (NMM) with the information conveyed between different scales. The microscale IBVP is solved under Linear Boundary Conditions (LBCs) and Periodic Boundary Conditions (PBCs) that are defined with macroscale solid displacement, fluid pressure and their first-order gradients. The discontinuous macroscale IBVP is solved iteratively using the Newton method with the macroscale internal forces and Jacobian determined by solving the microscale IBVPs. A stick–slip contact model is implemented using an augmented Lagrange multiplier method to impose frictional contact conditions along the macroscale discontinuities. Through various numerical simulations, the presented two-scale NMM is shown to be able to effectively and accurately capture the fully dynamic and wave propagation responses of the discontinuous heterogeneous porous media under the fluid injection and impact loading condition.

A semi-smooth Newton and Primal–Dual Active Set method for Non-Smooth Contact Dynamics

Multi-rigid-body dynamic contact systems, in other words Non Smooth Contact Dynamics (NSCD) problems, generate some inherent difficulties to multivocal laws, which results in non-linearities and non-smoothness associated to frictional contact models. Recently, Primal–Dual Active Set strategies (PDAS) have emerged as a promising method for solving contact problems. These methods are based on the following principle: the frictional contact conditions are restated as non-linear complementary functions for which the solution is provided by the iterative semi-smooth Newton method. Based on these prerequisites, this contribution aims to provide a generalization of the NSCD-PDAS for dynamic frictional contact problems. Several numerical experiments are reported for algorithm validation purposes and also to assess the efficiency and performances of PDAS methods with respect to the Newton/Augmented Lagrangian and the Bi-Potential methods.

Numerical Modelling of Convection-Driven Cooling, Deformation and Fracturing of Thermo-Poroelastic Media

Convection-driven cooling in porous media influences thermo-poro-mechanical stresses, thereby causing deformation. These processes are strongly influenced by the presence of fractures, which dominate flow and heat transfer. At the same time, the fractures deform and propagate in response to changes in the stress state. Mathematically, the model governing the physics is tightly coupled and must account for the strong discontinuities introduced by the fractures. Over the last decade, and motivated by a number of porous media applications, research into such coupled models has advanced modelling of processes in porous media substantially. Building on this effort, this work presents a novel model that couples fracture flow and heat transfer and deformation and propagation of fractures with flow, heat transfer and thermo-poroelasticity in the matrix. The model is based on explicit representation of fractures in the porous medium and discretised using multi-point finite volume methods. Frictional contact and non-penetration conditions for the fractures are handled through active set methods, while a propagation criterion based on stress intensity factors governs fracture extension. Considering both forced and natural convection processes, numerical results show the intricate nature of thermo-poromechanical fracture deformation and propagation.

Displacement field measurements in traditional and rotational diamond anvil cells

A digital image correlation-based method has been developed to measure the displacement field during compression in a traditional diamond anvil cell (DAC) and torsion in rotational DAC (RDAC) employing ruby fluorescence microscopy imaging. The optical arrangements for these measurements are adaptable at any commercial or customized micro-confocal system used for in situ high-pressure Raman or ruby fluorescence spectroscopy. In this paper, we describe details of the setup developed at Iowa State University along with a few demonstrative measurements for a zirconium sample. In particular, under compression in DAC, no adhesion zone is found, and relative sliding increases almost linearly along the radius. During torsion in RDAC, actual angular displacement of the material is found to be 5 times smaller than the rotation angle of an anvil, which is routinely used in the definition of the plastic shear for the determination of stress–strain curves and plastic strain-induced kinetics of phase transformations and grain refinement in materials. Obtained displacements can be used as the boundary conditions for finite element method (FEM) simulations of processes in DAC and RDAC instead of hypothetical friction conditions. After iterative fitting of FEM simulations and all measured fields from x-ray diffraction and absorption experiments, this will allow us to more precisely determine contact friction conditions and material parameters in the constitutive equations for elastoplastic flow and strain-induced phase transformations.

Diagnostics of operational wear in hybrid load-carrying cables

Along with the development of lifting devices, the new hybrid load-carrying cables were introduced to the market. The solutions of this type covered both, steel ropes of circular section and belts being a hybrid combination of many steel ropes potted with plastic coating into a single flat friction belt. Such design of ropes as compared to the traditional round steel ropes enabled to reduce the drive wheel diameter while maintaining frictional contact conditions and required ratio of the drive wheel and load-carrying cable diameters that is at least 40. Despite the above-mentioned advantages, a research issue that is of interest but so far has not been fully investigated is the process of wear of the hybrid load-carrying cables and evaluation of the technical condition of ropes being the load-carrying elements in the applied solutions, especially during the long-term operation. This article presents the possibilities of applying the magnetic method for evaluation of the technical condition of steel ropes being the load-carrying element of hybrid belts. The authors have presented their solution of the measuring head for magnetic testing of the load-carrying hybrid cables, elaborated by the team of employees of the Department of Machine Engineering and Transport at University of Science and Technology in Cracow, that enables the quantitative assessment of the hybrid load-carrying cable wear.

Inexact primal–dual active set method for solving elastodynamic frictional contact problems

In this paper, several active set methods based on classical problems arising in Contact Mechanics are analyzed, namely unilateral/bilateral contact associated with Tresca’s/Coulomb’s law of friction in small and large deformation. The purpose of this work is to extend an Inexact Primal–Dual Active Set (IPDAS) method already used in Hueber et al. (2008) to the formalism of dynamics and hyper-elasticity. This method permits to solve the unilateral problem with Coulomb’s law of friction by taking into account an alternative for the latter based on the approximation of the Coulomb’s law by a succession of states of Tresca friction in which the friction threshold is fixed at each fixed point iteration. The mechanical formulation in the hyper-elasticity framework is first presented, next, we establish weak formulations of the different cases of frictional contact problems and we give the finite element approximation of the problems. Then, we detail the numerical treatment within the framework of the primal–dual active set strategy for different frictional contact conditions. We finally provide some numerical experiments to bring into light the efficiency of the IPDAS method and to carry out a comparison with the augmented Lagrangian method by considering representative contact problems in both small and large deformation cases.