Contact Boundary Conditions Research Articles

Automated RVE computations for evaluation of microdamage initiation in structural stitched non-crimp fabric composites

This contribution presents an approach to generate unit-cell models of structural stitched non-crimp fabric composites. Resin-rich regions and out-of-plane undulations caused by the stitching yarn are represented by initially straight discretised lines, while the stitching yarn is represented initially by a single discretised line which can be transformed into a multi-line configuration to model stitch cross-section variations. The discretised lines are shaped by geometrical operations with a contact treatment and boundary conditions being used to account, respectively, for line interactions and to control the shape of the bottom and top surfaces of each lamina respectively. A fiber-reinforced distorted zone with local variations in fiber volume fraction and fiber direction is modelled in cross-sections of the lamina in a post-processing step. Models for different stacking sequences and stitching parameters are then automatically generated and subsequently being in the stiffness calculation and damage initiation assessment using finite element based mechanical simulations.

Collapse mechanism investigation of the direct tension indicator washers under axial compression

ABSTRACT Direct tension indicators (DTIs) are one alternative method that is commonly used to verify that high-strength bolts have been properly tensioned during installation. This paper investigates collapse mechanisms and crushing load during the axial compression of the DTI washer. An experimental technique is used to evaluate the function of the DTI washer under compressive quasi-static strain rate. A numerical model is presented based on finite element analysis to simulate crushing of DTI washer considering nonlinear responses due to material behaviour, contact boundary conditions and large deformations. The predicted numerical crushing load and collapse pattern were found to be in good agreement with the experimental results. Finally, the effect of the geometry parameters of the DTI washer on crushing loads is investigated. This study provides practical information about using the DTI washers to confirm proper pre-tensioning of bolts in structural steel fasteners industry.

Drift\u2013diffusion simulation of S-shaped current\u2013voltage relations for organic semiconductor devices

We present an electrothermal drift–diffusion model for organic semiconductor devices with Gauss–Fermi statistics and positive temperature feedback for the charge carrier mobilities. We apply temperature-dependent Ohmic contact boundary conditions for the electrostatic potential and discretize the system by a finite volume based generalized Scharfetter–Gummel scheme. Using path-following techniques, we demonstrate that the model exhibits S-shaped current–voltage curves with regions of negative differential resistance, which were only recently observed experimentally.

A dynamic thermo-mechanical actuator system with contact and Barber's heat exchange boundary conditions

AbstractThis work, motivated by the rapid developments in Micro-Electro-Mechanical Systems (MEMS) structures, especially actuators and grippers, analyses the dynamics of a thermo-mechanical system consisting of a horizontal beam joined at one end to a vertical rod. As a result of thermal expansion or vibration of the rod, the other end may come into contact with another part of the MEMS device and that closes an electrical circuit, which is the actuating or switching function of such a beam–rod system. The interaction between the rod's contacting end and the supporting device is described by a normal compliance contact law for the displacements and by an inclusion-type Barber's heat exchange condition for the temperature. The heat-exchange coefficient is a multi-function taking into account the air resistance in the gap when there is no contact and the contact pressure when contact occurs. The model consists of a nonlinear variational inclusion for the temperature coupled with a nonlinear variational equation for the displacements. The existence of a weak solution to the problem is proved by using the Galerkin method, a regularization of Barber's condition with the Yosida approximation of a maximal monotone operator, and a priori estimates.

Experimental verification of the boundary conditions in the success of the Brazilian test with loading arcs. An uncertainty approach using concrete disks

The present work analyses the reliability of the Brazilian test with loading arcs. A new testing set up has allowed to determine in an effective way the real load of the failure initiation as this moment was not always or correctly detected by the universal testing machine. The instrumentation used is a simple and low-cost method that allows to know the possible pressure distribution in the contact zone as well as the final contact angle. It has been observed that the success of the test depends mainly on the surface finish of the parts involved, their geometric tolerances and the symmetry of the applied load. These boundary conditions have a direct effect in the contact pressure distribution. The possible failure modes observed experimentally have been simulated with the finite element methods. For this, the contact boundary condition has been changed and the possible stress distribution in term of Griffith equivalent stress has been obtained. The numerical analysis allows to study the influence of the initial contact condition on the success of the test and agrees with the experimental results. Furthermore, an uncertainty analysis in the expression of the tensile strength confirms that, when the test is valid, a crack appears suddenly in the central area of the disk, as observed experimentally, so there is no need to determine if the starting point is in the centre. Additionally, it has been observed that the initial crack length depends on the type of pressure distribution in the contact zone. Finally, a series of recommendations are given in order to minimize both the variability of the final contact angle and the risk of premature failure of the Brazilian disk.

A new class of hyperbolic variational–hemivariational inequalities driven by non-linear evolution equations

The aim of the paper is to introduce and investigate a dynamical system which consists of a variational–hemivariational inequality of hyperbolic type combined with a non-linear evolution equation. Such a dynamical system arises in studies of complicated contact problems in mechanics. Existence, uniqueness and regularity of a global solution to the system are established. The approach is based on a new semi-discrete approximation with an application of a surjectivity result for a pseudomonotone perturbation of a maximal monotone operator. A new dynamic viscoelastic frictional contact model with adhesion is studied as an application, in which the contact boundary condition is described by a generalised normal damped response condition with unilateral constraint and a multivalued frictional contact law.

The velocity-stress finite-difference method with a rotated staggered grid applied to seismic wave propagation in a fractured medium

To enable a mathematical description, geologic fractures are considered as infinitely thin planes embedded in a homogeneous medium. These fracture structures satisfy linear slip boundary conditions, namely, a discontinuous displacement and continuous stress. The general finite-difference (FD) method described by the elastic wave equations has challenges when attempting to simulate the propagation of waves at the fracture interface. The FD method expressed by velocity-stress variables with the explicit application of boundary conditions at the fracture interface facilitates the simulation of wave propagation in fractured discontinuous media that are described by elastic wave equations and linear slip interface conditions. We have developed a new FD scheme for horizontal and vertical fracture media. In this scheme, a fictitious grid is introduced to describe the discontinuous velocity at the fracture interface and a rotated staggered grid is used to accurately indicate the location of the fracture. The new FD scheme satisfies nonwelded contact boundary conditions, unlike traditional approaches. Numerical simulations in different fracture media indicate that our scheme is accurate. The results demonstrate that the reflection coefficient of the fractured interface varies with the incident angle, wavelet frequency, and normal and tangential fracture compliances. Our scheme and conclusions from this study will be useful in assessing the properties of fractures, enabling the proper delineation of fractured reservoirs.

Discrete element model (DEM) simulations of cone penetration test (CPT) measurements and soil classification

This paper presents a study on the simulation of cone penetration tests (CPTs) using the discrete element model (DEM) method. This study’s main objective is to investigate the effect of different modeling parameters and simulation configurations on the ability of three-dimensional DEM simulations to replicate realistic CPT tip resistance (qc) and friction sleeve shear stress (fs) measurements. The CPT tests were simulated in virtual calibration chambers (VCCs) containing particles calibrated to model the behavior of sand. The parameters investigated included the granular assembly properties, interparticle contact parameters, particle–probe interface characteristics, and simulation configuration. Results indicate that the interparticle contact parameters, boundary conditions, and void ratio have an important role in the tip resistance and friction sleeve measurements obtained from the simulations. Particle-level interactions such as particle displacements and rotations and interparticle contact forces were analyzed throughout to provide insight into the differences in measured CPT response. Interpretation of the qcand fsmeasurements using soil behavior type (SBT) charts for soil classification indicates that the simulated CPT response is representative of the response of coarse-grained soils measured during field soundings. Analysis of results within the SBT framework can provide insight into the influence of soil particle properties on CPT-based soil classification.

Equilibrium and Forced Vibration of an Axially Moving Belt with Belt-Pulley Contact Boundaries

Axially moving materials have usually dealt with classic boundary conditions, i.e. zero boundaries, such as the simply supported and the fixed ends. In this paper, the dynamics responses of the axially moving belt with beltpulley contact boundary conditions are studied for the first time. Therefore, due to the fact that non-homogeneous terms are included in the boundary conditions, the traditional generalized eigenvalue method is no longer applicable. In this work, the belt is numerically discretized by using the differential quadrature method (DQM). Iterative schemes are proposed for determining the equilibrium configuration. Harmonic inertia excitation is considered to be the vertical motion of the whole system. The steady-state responses of the forced vibration are also numerically solved by applying the DQM. The parametric effects on the equilibrium configuration and the steady-state response are investigated. The numerical investigations reveal that the radius of the support pulley has significant effects on both the equilibrium configuration and the transition phase of the transverse vibration of the axially moving belt under inertia excitation.

PREDICTION OF COMPRESSION AND EXTENSION ZONES IN GEOLOGICAL STRUCTURES BASED ONLY ON THE VELOCITIES OF LONGITUDINAL WAVES IN THE GEOLOGICAL MEDIUM

The article presents accurate solutions for the problem for two elastic half‐spaces with an arbitrary curvilinear interface. Our study shows that dilatation solutions (Poisson integrals) are dependent on neither an overall compression modulus nor the Poisson ratio, and depend only on the velocity of longitudinal waves. These specific solutions can be supplemented by general solutions for an incompressible elastic medium, and the boundary conditions of the rigid contact for the sum of the solutions can thus be satisfied. Relatively simple calculations make it possible to determine the divergence of the displacement field and reduce the entire problem solving process to a study of Poisson equations with a known divergence. Furthermore, predictions of volumetric compression or extension are important for geological investigations, since the zones characterized by reduced pressure rates may act as fluid attractors.

Stability analysis of stationary variational and hemivariational inequalities with applications

In this paper, we provide a comprehensive stability analysis for stationary variational inequalities, hemivariational inequalities, and variational-hemivariational inequalities. With contact mechanics as application background, stability is analyzed for solutions with respect to combined or separate perturbations in constitutive relations, external forces, constraints, and non-smooth contact boundary conditions of the inequality problems. The stability result is first proved for a general variational-hemivariational inequality. Then, stability results are obtained for various variational inequalities and hemivariational inequalities as special cases. Finally, we illustrate applications of the theoretical results for the stability analysis of model problems in contact mechanics.

Fractional heat conduction in solids connected by thin intermediate layer: nonperfect thermal contact

We examine the transition region between two solids which state differs from the state of contacting media. Small thickness of the intermediate region allows us to reduce a three-dimensional problem to a two-dimensional one for a median surface endowed with equivalent physical properties. In the present paper, we consider the generalized boundary conditions of nonperfect thermal contact for the time-fractional heat conduction equation with the Caputo derivative and solve the problem for a composite medium consisting of two semi-infinite regions. Numerical results are illustrated graphically.

Well-posedness of a class of generalized mixed hemivariational–variational inequalities

The purpose of this paper is to investigate a class of generalized mixed hemivariational–variational inequalities of elliptic type in a Banach space. A well-posedness result for the inequality is obtained, including existence, uniqueness, and stability of solution. The approach is based on a set-valued fixed point theorem combined with the theory of nonsmooth analysis. An elastic contact problem with the constitutive law involving a convex subdifferential inclusion is considered as an illustrative application, in which the contact boundary conditions are described by a unilateral frictionless contact condition, and a bilateral multivalued frictional contact law.

Розрахунок методом скінченних тіл плоского напруженого стану прямокутної пластини із прямокутним отвором

The paper is devoted to the determination of the stress-deformed state of structurally heterogeneous bearing rectangular plates with a rectangular hole. The new analytical-numerical method (finite bodies) was used, to find the stress state of the plate with a hole. The method of finite bodies uses the conditional partition of the doubly-connected surface of the plate into simpler connected rectangular parts. On the lines of conditional contact, the conditions of ideal contact are taken into account, which ensure the equality of stresses, deformations and displacements. The perturbed stressed state, which is presented in the form of a series of functions, which is rapidly intercepted at a distance from the outline of the hole, is considered. A finite sum of solutions of a plane problem is used and the stress state of a perturbed state is given as a sum of a series for nonorthogonal functions. The components of vector of displacements and stresses are written. The determination of the coefficients of the sum of a series is based on the proposed method of satisfying all boundary conditions and the conditions of ideal contact to find the minimum of a generalized quadratic form. The numerical criterion for the convergence of the method is theoretically established. It is shown that the accuracy of satisfaction of boundary conditions and conditions of ideal contact is estimated by one number – the minimum of a generalized quadratic form.

Numeric simulation model for long-term orthodontic tooth movement with contact boundary conditions using the finite element method

Introduction Although many attempts have been made to simulate orthodontic tooth movement using the finite element method, most were limited to analyses of the initial displacement in the periodontal ligament and were insufficient to evaluate the effect of orthodontic appliances on long-term tooth movement. Numeric simulation of long-term tooth movement was performed in some studies; however, neither the play between the brackets and archwire nor the interproximal contact forces were considered. The objectives of this study were to simulate long-term orthodontic tooth movement with the edgewise appliance by incorporating those contact conditions into the finite element model and to determine the force system when the space is closed with sliding mechanics. Methods We constructed a 3-dimensional model of maxillary dentition with 0.022-in brackets and 0.019 × 0.025-in archwire. Forces of 100 cN simulating sliding mechanics were applied. The simulation was accomplished on the assumption that bone remodeling correlates with the initial tooth displacement. Results This method could successfully represent the changes in the moment-to-force ratio: the tooth movement pattern during space closure. Conclusions We developed a novel method that could simulate the long-term orthodontic tooth movement and accurately determine the force system in the course of time by incorporating contact boundary conditions into finite element analysis. It was also suggested that friction is progressively increased during space closure in sliding mechanics.

Active Sensing for Measuring Contact of Thin Film Gecko-Inspired Adhesives

Active sensing provides a way to assess whether a thin film of gecko-inspired adhesive has made good contact with a surface. This knowledge is useful for applications like gripping objects in space where a failed grasp could lead to loss of the object. Our active sensing approach uses Lamb waves in thin bilayers, excited, and detected by piezoelectric strips. From the theory, we describe how attenuation increases with contact boundary condition changes. We validated the theory using frustrated total internal reflection imaging, showing that attenuation increases as the contact area grows. Pull tests on different textures of acrylic plate show that the slope change of the signal can predict the maximum adhesion limit with a 10 N window and predict impending failure with a detection rate >80%. Lifting a cylindrical object shows that the sensor can signal different types of failures with a detection rate >85%, associated with unstable grasping.

Numerical modeling of dynamic frictional rolling contact with an explicit finite element method

The modeling of dynamic frictional rolling contact is crucial for accurately predicting behavior and deterioration of structures under dynamic interactions such as wheel/rail, tire/road, bearings and gears. However, reliable modeling of dynamic frictional rolling contact is challenging, because it requires a careful treatment of friction and a proper consideration of the dynamic effects of the structures on the contact. This study takes the wheel-rail dynamic interaction as an example to systematically explore the core algorithms for the modeling of dynamic frictional rolling contact by way of explicit finite element analyses. The study also theoretically demonstrates that the explicit finite element method handles nonlinearities in friction, material properties, arbitrary contact geometries and boundary conditions, and fully couples the calculation of frictional rolling contact with the calculation of high-frequency structural dynamics. An indirect validation method for dynamic contact solutions is proposed. To promote the broad use of the method, this paper proposes a detailed procedure for establishing robust wheel-rail dynamic interact tion models and obtaining dynamic contact responses. The proposed procedure can also be applied to the modeling of dynamic interactions occurring to tire-road, bearings and gears.

Effect of patterns of stainless steel ligation on orthodontic bracket with contact boundary conditions using finite element analysis

The objective of this work was to analyse the stress and deformation in the orthodontic bracket and archwire with different patterns of ligature tying namely full round pattern I (P-I), the figure of eight pattern II (P-II) and figure of eight pattern III (P-III) using finite element analysis (FEA). A standard edgewise stainless steel (SS) maxillary right central incisor orthodontic bracket was measured using profile projector. Solid models of the bracket, archwire and three patterns of ligature tie were done. The archwire was modelled and assembled into the bracket slot. The FE model of the assembly was done. Effect of three patterns of ligation on the archwire and bracket was analysed by applying archwire torque as a couple. The stress in the bracket and archwire for the patterns of ligation P-I, P-II and P-III were noted. The maximum deformation of the bracket and archwire for the patterns of ligation P-I, P-II and P-III were obtained. From the analysis, it was concluded that the magnitude of stress in the archwire and the deformation value in the bracket was high in P-I pattern. Ligature pattern P-II developed the least amount of stress and deflection in the bracket and archwire.

Optimal error estimates of the unilateral contact problem in a curved and smooth boundary domain by the penalty method

Abstract We consider linear finite elements to approximate the elasticity equations with unilateral contact boundary conditions, in a bounded two- or three-dimensional domain with curved and smooth boundary. We use the penalty method to weakly impose these boundary conditions. We establish an error estimate in the energy norm with respect to the mesh size $h$ and the penalty parameter $\varepsilon $. Assuming $\boldsymbol{H}^{\frac{3}{2}+\nu }\left (\varOmega \right )$ regularity of the solution, $0 < \nu \leq \frac{1}{2}$, we obtain an $\mathcal{O}\,(h^{\frac{1}{2}+\nu } + \varepsilon ^{\frac{1}{2}+\nu })$ convergence rate. Therefore, if the penalty parameter is chosen as $\varepsilon (h) := ch^{\theta }$ with $0 < \theta \leq 1$, we obtain an $\mathcal{O}\,(h^{\theta (\frac{1}{2}+\nu )})$ convergence rate. Thus, the optimal linear convergence rate is obtained when $\varepsilon $ behaves like $h$ (that is, $\theta = 1$) and $\nu = \frac{1}{2}$. We present a numerical example to illustrate the theoretical analysis.

A quasistatic frictional contact problem for viscoelastic materials with long memory

Abstract The aim of this paper is to study a quasistatic frictional contact problem for viscoelastic materials with long-term memory. The contact boundary conditions are governed by Tresca’s law, involving a slip dependent coefficient of friction. We focus our attention on the weak solvability of the problem within the framework of variational inequalities. The existence of a solution is obtained under a smallness assumption on a normal stress prescribed on the contact surface and on the coefficient of friction. The proof is based on a time discretization method, compactness and lower semicontinuity arguments.