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In this paper, we analyze a system for brittle delamination between two visco-elastic bodies, also subject to inertia, which can be interpreted as a model for dynamic fracture. The rate-independent flow rule for the delamination parameter is coupled with the momentum balance for the displacement, including inertia. This model features a nonsmooth constraint ensuring the continuity of the displacements outside the crack set, which is marked by the support of the delamination parameter. A weak solvabi- lity concept, generalizing the notion of energetic solution for rate-independent systems to the present mixed rate-dependent/rate-independent frame, is proposed. Via refined variational convergence techniques, existence of solutions is proved by passing to the limit in approximating systems which regularize the nonsmooth constraint by conditions for adhesive contact. The presence of the inertial term requires the design of suitable recovery spaces small enough to provide compactness but large enough to recover the information on the crack set in the limit.

The large deformation of an elastic axisymmetric membrane in adhesive contact with a rigid flat punch is studied. Detachment of membrane is analyzed using a critical energy release rate criterion. Two types of incompressible hyperelastic material models are considered: neo-Hookean and a class of materials whose elastic energy density functions are independent of the trace of the Cauchy–Green tensor ( I 2 -based material). We also include pre-stretch in our formulation and study the stability of detachment process. Closed form analytical solutions for the membrane stresses, deformed profiles and energy release rate are obtained in the regime of large longitudinal stretch. For the I 2 -based material, we discover an interesting “pinching” instability where the contact angle suddenly increases in a displacement controlled test. The region of validity of our analytical solutions is determined by comparing them with numerical solutions of the governing equations. We found that the accuracy of our solution improves with pre-stretch; for pre-stretch ratios greater than 1.3, our analytical solution also works well in the small deformation regime.

In this paper, adhesive contact of a rigid cylinder on an elastic power-law graded half-space is studied analytically with the theory of weakly singular integral equation and orthogonal polynomial method. Emphasis is placed on the coupling effect between tangential and normal directions which was often neglected in previous works. Our analysis shows that the coupling effect tends to reduce the contact area in the compressive regime. The effect of bending moment on the adhesion behavior is also examined. Like a pull-off force, there also exists a critical bending moment at which the cylinder can be bended apart from the substrate. However, unlike pull-off force, the critical bending moment is insensitive to the gradient exponent of the graded material.

The aim of the present paper is to investigate the adhesive behavior between a transversely isotropic piezoelectric half-space and a cylinder punch subjected to combined mechanical and electric loads under plane-strain condition. The effect of adhesion is described by using a generalized JKR-model which can account for the non-slip condition in the contact regions. Analytical function theory is employed to find the solution of the resulting singular integral equations. Our analysis shows that the adhesive contact behavior for different types of piezoelectric materials may be quite different. The results obtained in this paper may be helpful to understand the contact mechanics of piezoelectric materials at micro-scale.

The applications of inflatable membrane structures are increasing rapidly in the various fields of engineering and science. The geometric, material, force and contact non-linearities complicate this subject further, which in turn increases the demand for computationally efficient methods and interpretations of counter-intuitive behaviors noted by the scientific community. To understand the complex behavior of membranes in biological and medical engineering contexts, it is necessary to understand the mechanical behavior of a membrane from a physics point of view. The first part of the present work studies the pre-stretched circular membrane in contact with a soft linear substrate. Adhesive and frictionless contact conditions are considered during inflation, while only adhesive contact conditions are considered during deflation. The peeling of membrane during deflation is studied, and a numerical formulation of the energy release rate is proposed. It is observed that the pre-stretch is having a considerable effect on the variation of the energy release rate. In the second part, free and constrained inflation of a cylindrical membrane is investigated. Adhesive and frictionless contact conditions are considered between the membrane and substrate. It is observed that the continuity of principal stretches and stresses depend on contact conditions and the inflation/deflation phase. The adhesive traction developed during inflation and deflation arrests the axial movement of material points, while an adhesive line force created at the contact boundary is responsible for a jump in stretches and stresses at the contact boundary. The pre-stretch produces a softening effect in free and constrained inflation of cylindrical membranes. The third part of the thesis discusses the instabilities observed for fluid containing cylindrical membranes. Both limit points and bifurcation points are observed on equilibrium branches. The secondary branches emerge from bifurcation points, with their directions determined by an eigen-mode injection method. The occurrence of critical points and the stability of equilibrium branches are determined by perturbation techniques. The relationship between eigenvalue analysis and symmetry is highlighted in this part of the thesis. QC 20150227

In this paper we introduce and investigate a model for adhesive contact with friction between a thermoviscoelastic body and a rigid support. A PDE system, consisting of the evolution equations for the temperatures in the bulk domain and on the contact surface, of the momentum balance, and of the equation for the internal variable describing the state of the adhesion, is derived on the basis of a surface damage theory by M. Fremond . The existence of global-in-time solutions to the associated initial–boundary value problem is proved by passing to the limit in a carefully tailored time-discretization scheme.

A quasistatic rate-independent adhesive delamination problem of laminated plates with a finite thickness is considered. By letting the thickness of the plates go to zero, a rate-independent delamination model for a laminated Kirchhoff-Love plate is obtained as limit of these quasistatic processes. The same dimension reduction procedure is eventually applied to processes which are sensitive to delamination modes, namely opening vs. shearing is distinguished.

The method of reduction of dimensionality in contact mechanics is based on a mapping of some classes of three-dimensional contact problems onto one-dimensional contacts with elastic foundations. Recently, a rigorous mathematical proof of the method has been provided for contacts of arbitrary bodies of revolution with and without adhesion. The method of reduction of dimensionality has been further verified for randomly rough surfaces. The present paper gives an overview of the physical foundations of the method and of its applications to elastic and viscoelastic contacts with adhesion and friction. Both normal and tangential contact problems are discussed.

Starting from the classical theory of contact mechanics it is shown that the relationship between load, penetration and contact radius of any axisymmetric contact can be mapped exactly on a one-dimensional system, thus the reduction method of dimensionality is valid for conforming and non-conforming contacts. Furthermore the reduction method has been successfully extended to adhesive contact problems. The mapping of the classical theory of Johnson, Kendall and Roberts derived for spherical contacts as well as its application to axisymmetric contacts of arbitrary shape is possible; all results are reproduced precisely.

A quasistatic rate-independent brittle delamination problem and also an adhesive unilateral contact problem is considered on a prescribed normally-positioned surface in a plate with a finite thickness. By letting the thickness of the plate go to zero, two quasistatic rate-independent crack models with prescribed path for Kirchhoff-Love plates are obtained as limit of these quasistatic processes.

International audience; A general framework for models describing adhesive contact between rigid bodies is proposed. The intensity of adhesion is supposed to decrease under the action of prescribed tangential and normal relative displacements. The reduction is attributed to progressive damage, and comes with energy dissipation. Additional dissipation due to viscosity and friction is also taken into account. The response of the interface is described by a single state variable. It is determined by general laws expressing a mechanical version of the first two laws of thermodynamics, combined with a set of phenomenological assumptions.

This paper deals with the large-time analysis of a PDE system modelling contact with adhesion, in the case when thermal effects are taken into account. The phenomenon of adhesive contact is described in terms of phase transitions for a surface damage model proposed by M. Fremond. Thermal effects are governed by entropy balance laws. The resulting system is highly nonlinear, mainly due to the presence of internal constraints on the physical variables and the coupling of equations written in a domain and on a contact surface. We prove existence of solutions on the whole positive time half-line by a double approximation procedure. Hence, we are able to show that solution trajectories admit cluster points which fulfil the stationary problem associated with the evolutionary system, and that in the large-time limit dissipation vanishes.

The main purpose of this project is to investigate different tool steels in terms of their ability to withstand material transfer buildup, so-called galling, occurring in SMF (sheet metal forming) operations. The ability to withstand galling is vital to optimize cost-effectiveness and increase the work tool’s effective operational time. This investigation studies four different tool steels, including a TiN-coating, with the intention of evaluating the microstructures, chemical composition and hardness effect on galling resistance in dry conditions using a slider-on-flatsurface (SOFS) tribo-tester which measures the coefficient of friction during sliding. An OP (optical profilometer) was used to measure the size and geometry of lump growth on the tool and damage on the work sheet. A scanning electron microscope (SEM) was used to identify the interacting tribological mechanisms exhibited at different stages during the slide. The SEM figures confirmed three different types of characteristic patterns exhibited in the tracks after tribo- testing which were categorized as mild adhesive, abrasive and severe adhesive damage. A SEM figure that illustrates a ragged contact surface and an obvious change in the sheet materials plastic behavior is in this report regarded as a sign of severe adhesive contact, the characteristics could possibly be explained by local high temperature and high pressure followed by a sudden pressure drop and creation of hardened welds or solders between the two surfaces which increase the frictional input needed for further advancement. Friction coefficients observed in the initial 100% mild adhesive stage were, μ=0,22-0,26 succeeded by abrasive SEM characteristics often in association with mild adhesive contact and friction values between μ=0,25-0,4 which where sometimes followed by severe adhesive SEM characteristics in 100% of the contact zone with friction values between μ=0,34- 0,9 respectively. The tool material that performed best according to the friction detection criteria was Sv21 closely followed by Sleipner (TiN coated) and Va40 (HRC 63.3). Unfortunately was the friction criteria, a significant raise in friction for defining a sliding length to galling, not adequate for dry conditions due to immediate material transfer succeeded by cyclic changes between partial or 100% abrasive+mild adhesive and severe adhesive contact. The mechanism that change abrasive wear in association with mild adhesive contact, (moderate friction input), to sever adhesive wear, (higher friction input), is dependent on lump shape (lump geometry) and can appear at comparably low speeds 0,04-0,08 [m/s] and low friction energy input (μ=0,34), the magnitude of the change in friction is therefore not always significant and hardly detectable on the friction graph. This was quite unexpected but could be explained by concentration of friction energy rater than the absolute amount. The problem with using friction graphs for galling evaluation was increased even further when a very small lump size and low corresponding rate of material transfer to the tool surface caused a sustainable high raise in friction (μ≈0,3→0,6) on a TiN-coated tool steel called Sleipner. A hardly detectable or similar friction raise for Sv21 and Va40 showed much larger corresponding lump size and rate of material transfer. This means that friction graphs demonstrate a clear problem with quantifying lump size [m3] and rate of material transfer [m3/s]. Another phenomenon called stick slip behavior, material transfer and lump growth followed by a sudden decrease in lump size and transfer of material back to the work sheet, is also not possible to detect on a friction graph. Because a drop in friction can easily be a change in contact temperature and lump attack angle due to a growing lump and not a decreasing lump. The conclusion, a friction graph is not suited for galling evaluation and ranking in dry SOFS conditions. A ranking should primarily be based on dimensional OP measurements of the cross section of formed tracks and scratches or preferably by repeated OP measurements of the tool surface during a single test, the last revel the exact lump growth history and true lump growth even in the sliding direction. civilingenjörsexamen

We study variational models for flexural beams and plates interacting with a rigid substrate through an adhesive layer. The general structure of the minimizers is investigated and some properties characterizing the behavior of the systems in dependence of the load and the material stiffnesses are discussed.

International audience; This paper presents a 3D non-locking contact approach, within the eXtended Finite Element Method (X-FEM) framework. X-FEM allows one to introduce interface independently of the mesh. The contact problem on the interface leads to an Augmented Lagrangian formulation derived from the discretization of its continuous formulation. It is shown that a simple choice of the Lagrange multiplier space is not suitable and leads to contact pressure oscillations. An algorithm for the restriction of the Lagrange multiplier approximation space is proposed to stabilize the formulation. The stability of the mixed displacement-contact pressure formulation is discussed in terms of convergence of the energy error. Numerical examples performed with the Finite Element software Code_Aster illustrate this approach while solving three-dimensional problems with contact.; Cet article présente une formulation stabilisée pour les problèmes de contact en 3D, dans le cadre de la méthode des éléments finis étendue (X-FEM), méthode qui autorise des interfaces indépendantes du maillage. Pour la formulation du problème de contact sur l’interface, nous utilisons un Lagrangien Augmenté, qui dérive de la discrétisation du problème de contact écrit sous sa forme continue. Nous montrons qu’un choix simple del’espace des multiplicateurs de Lagrange n’est pas satisfaisant car cela conduit à des oscillations des pressions de contact. Un algorithme de restriction de l’espace d’approximation des multiplicateurs de Lagrange est proposé afin de stabiliser la formulation. La stabilité de la formulation mixte (déplacement-pression de contact) est démontrée à l’aide des taux de convergence des erreurs. Des exemples numériques réalisés avec le logiciel éléments finis Code_Aster illustrent cette approche pour la résolution de problèmes tridimensionnels avec contact

The paper aimed to study the effect of large deformation and material nonlinearity on the adhesive contact between a smooth rigid spherical indenter and a Neo-Hookean layer of finite thickness, for the cases of the layer thickness/indenter radius ratio between 1 and 2. Our analysis was based on the large-deformation JKR (LDJKR) theory, which models the adhesive contact of two elastic solids in large-deformation regime by knowing the solution of the corresponding non-adhesive contact problem. In this paper, the non-adhesive contact between a spherical indenter and a Neo-Hookean layer was solved by finite element analysis. Combined these numerical results and the LDJKR theory, approximate analytic expressions of the applied load and displacement of adhesive contact of Neo-Hookean layers were obtained. The effects of layer thickness were also discussed.

We consider the forced detachment of a thin-walled vesicle bonded to a substrate for two particular cases. In both cases, the configuration is three-dimensional and the bonding is assumed to occur under conditions of axial symmetry for which the adhered area is always circular. Detachment is driven by a force applied to the top of the vesicle in a direction normal to the substrate surface. The first case is the static or time-independent situation of a vesicle for which bonding is the result of nonspecific interactions between the vesicle and substrate surfaces. For this case, it is shown that the radius of the adhesion patch is determined implicitly by the pulling force F. The maximum pulling force Fcr, beyond which the adhered configuration is unstable and the detachment proceeds spontaneously, can also be calculated implicitly. For the particular case of weak adhesion, all significant parameters of the detachment process can be determined explicitly. The second case studied is the time-dependent debonding of a vesicle for which adhesion with the substrate is the result of specific interactions between binders on the two surfaces, typical of biological materials for which the binders are ligand–receptor protein pairs. By treating the detachment process as a result of the debonding of the protein pairs at the edge of the circular adhesion patch, the governing equation for the radius of the adhesion patch is obtained. If a constant force is suddenly applied, it is found that the elapsed time to full detachment is proportional to the magnitude of this force to the power −1.1; alternatively, if the force applied to the vesicle increases linearly in time, it is found that the value of the force at complete detachment is proportional to the applied loading rate F˙ to the power 0.39, in agreement with recent experimental observations.

A generalized plane strain JKR model is established for non-slipping adhesive contact between an elastic transversely isotropic cylinder and a dissimilar elastic transversely isotropic half plane, in which a pulling force acts on the cylinder with the pulling direction at an angle inclined to the contact interface. Full-coupled solutions are obtained through the Griffith energy balance between elastic and surface energies. The analysis shows that, for a special case, i.e., the direction of pulling normal to the contact interface, the full-coupled solution can be approximated by a non-oscillatory one, in which the critical pull-off force, pull-off contact half-width and adhesion strength can be expressed explicitly. For the other cases, i.e., the direction of pulling inclined to the contact interface, tangential tractions have significant effects on the pull-off process, it should be described by an exact full-coupled solution. The elastic anisotropy leads to an orientation-dependent pull-off force and adhesion strength. This study could not only supply an exact solution to the generalized JKR model of transversely isotropic materials, but also suggest a reversible adhesion sensor designed by transversely isotropic materials, such as PZT or fiber-reinforced materials with parallel fibers. (c) 2007 Elsevier Ltd. All rights reserved.

Geological faults movements generating earthquakes, a vehicles' tyres rolling on the pavement, and a chalk writing on a blackboard are all different examples of frictional systems. In these systems, which are everywhere around us, two separate bodies are in contact and in relative motion, interacting with one another. Under these conditions, several phenomena arise at the interface: friction, wear, and lubrication being the main ones. Wear, in particular, is the loss of material from the surface of one (or both) the moving bodies. This phenomenon is of interest as it leads to loss of usefulness of manufactured objects and health concerns for patients with implants, to name just a few of important consequences due to material degradation. Yet, our knowledge on the topic of wear is still scattered, with many observations and models that are system dependent. How the surface morphology changes during wear processes is one of those aspects that are not well understood, and that at the same time affect significantly wear itself. Therefore, the aim of this dissertation is to investigate the role of surface roughness in wear processes upon dry sliding. The work focuses on wear of the adhesive type, as it is the most common one (together with the abrasive type). The first part of the thesis addresses the topic with numerical investigations. Two-dimensional systems are modelled with a discrete approach, where two surfaces are rubbed against one another. In this setup, a wear debris particle is eventually formed and it is constrained to roll between the sliding surfaces. It is shown that the method reproduces the evolution of the surface roughness into the self-affine morphology that is observed for different frictional surfaces. Furthermore, the interplay between surface roughness, adhesion, and wear debris particle size is investigated, and a minimum size for the debris particle is determined, based on a critical length scale recently derived for adhesive wear processes. These sets of simulations bring further observations on the wear process, like the evolution of the work due to the tangential forces and of the wear volume. The latter in particular displays an overall increase: debris particle accretion is favoured over its break down. This leads to the second part of the dissertation, where an analytical framework is presented that allows to explain the tendency of the debris particle to grow in volume, instead of depositing material onto the mating surfaces. The general approach of the work aims at uncovering underlying mechanisms of wear processes, and it is not restrained to some specific application. While on one hand this means that the work cannot cover the specificity of some frictional systems, on the other hand it leads to fundamental insights that are relevant from the nano- to the geological-scale.