On the Contact Problem of a Rigid Punch Pressed on a Viscoelastic Beam

1972 ◽  
Vol 39 (2) ◽  
pp. 461-468 ◽  
Author(s):  
C. H. Wu ◽  
T. C. T. Ting
Keyword(s):  
Contact Problem ◽  
Smooth Surface ◽  
Contact Region ◽  
Contact Problems ◽  
Contact Boundary ◽  
Viscoelastic Beam ◽  
Rigid Punch ◽  
Loading History ◽  
Simply Supported ◽  
Rigid Smooth

The contact problem of a symmetric rigid punch pressed at the midspan of a simply supported viscoelastic beam is studied. This is equivalent to a cantilever beam loaded at the free end against a rigid smooth surface. Explicit solutions are obtained for the length of the contact region, the contact pressure, the contact force at the contact boundary, and the curvature of the beam outside of the contact regions. As in other contact problems, the solution does not depend on the entire loading history.

Contact Between Viscoelastic Bodies

1976 ◽  
Vol 43 (4) ◽  
pp. 630-632 ◽  
Author(s):  
Maria Comninou
Keyword(s):  
Linear Viscoelasticity ◽  
Contact Region ◽  
Contact Problems ◽  
Loading History ◽  
Plane Contact ◽  
General Properties ◽  
Viscoelastic Bodies

Similarly to elasticity, it is useful to classify contacts between viscoelastic bodies by comparing the regions of contact in the loaded and load-free states. General properties are obtained for the class of contacts in which the contact region does not exceed the natural (load-free) contact. The displacements, strains, and stresses in such problems are proportional to the level of the loading history, but the scaling of load histories leaves the contact region unaltered. The results are valid within linear viscoelasticity, either quasi-static or dynamic. Additional properties are derived for plane contact problems in quasi-static viscoelasticity when the contact is monotonically receding.

A Rigid Punch on an Elastic Half-Space Under the Effect of Friction: A Finite Difference Solution

2008 ◽  
Author(s):  
Avraham Dorogoy ◽  
Leslie Banks-Sills
Keyword(s):  
Finite Difference ◽  
Contact Problem ◽  
Half Space ◽  
Contact Zone ◽  
Contact Problems ◽  
Elastic Half Space ◽  
Rigid Punch ◽  
Normal Loading ◽  
Receding Contact ◽  
Stationary Contact

The accuracy of the finite difference technique in solving frictionless and frictional advancing contact problems is investigated by solving the problem of a rigid punch on an elastic halfspace subjected to normal loading. Stick and slip conditions between the elastic and the rigid materials are added to an existing numerical algorithm which was previously used for solving frictionless and frictional stationary and receding contact problems. The numerical additions are first tested by applying them in the solution of receding and stationary contact problems and comparing them to known solutions. The receding contact problem is that of an elastic slab on a rigid half-plane; the stationary contact problem is that of a flat rigid punch on an elastic half-space. In both cases the influence of friction is examined. The results are compared to those of other investigations with very good agreement observed. Once more it is verified that for both receding and stationary contact, load steps are not required for obtaining a solution if the loads are applied monotonically, whether or not there is friction. Next, an advancing contact problem of a round rigid punch on an elastic half-space subjected to normal loading, with and without the influence of friction is investigated. The results for frictionless advancing contact, which are obtained without load steps, are compared to analytical results, namely the Hertz problem; excellent agreement is observed. When friction is present, load steps and iterations for determining the contact area within each load step, are required. Hence, the existing code, in which only iterations to determine the contact zone were employed, was modified to include load steps, together with the above mentioned iterations for each load step. The effect of friction on the stress distribution and contact length is studied. It is found that when stick conditions appear in the contact zone, an increase in the friction coefficient results in an increase in the stick zone size within the contact zone. These results agree well with semianalytical results of another investigation, illustrating the accuracy and capabilities of the finite difference technique for advancing contact.

A Fast Solution of the Dry Contact Problem and the Associated Sub-Surface Stress Field, Using Multilevel Techniques

1991 ◽  
Vol 113 (1) ◽  
pp. 128-133 ◽  
Author(s):  
A. A. Lubrecht ◽  
E. Ioannides
Keyword(s):  
Stress Distribution ◽  
Contact Problem ◽  
Surface Stress ◽  
Smooth Surface ◽  
Computing Time ◽  
Contact Problems ◽  
3 Dimensional ◽  
Dry Contact ◽  
Solution Methods ◽  
Fast Solution

The most time-consuming routine in the present EHL and dry contact computations is the calculation of the elastic deformation integrals. Using Multilevel Multi-Integration (MLMI) these integrals can be computed in O(n log n) instead of O(n2) operations. This fast integration is applied to the dry contact problem. To make optimal use of this integration, it is also necessary to construct an efficient solver for the integral equation. This is again accomplished using multilevel techniques. The total complexity of the new dry contact solver is O (n log n) which gives a big reduction in computing time over “classical” solution methods, enabling the solution of contact problems on grids with so many points that a realistic modelling of the surface roughness lies within reach. The fast integration is then applied to compute the stress distribution below the surface. As an example, the stress distribution under a smooth surface with a bump in contact is calculated for both a 2-dimensional and for a 3-dimensional contact case, and for a 2-dimensional rough surface in contact

scholarly journals The Indentation Rolling Resistance in Belt Conveyors: A Model for the Viscoelastic Friction

Lubricants ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 58 ◽  
Author(s):  
Nicola Menga ◽  
Francesco Bottiglione ◽  
Giuseppe Carbone
Keyword(s):  
Contact Problem ◽  
Finite Thickness ◽  
Numerical Procedure ◽  
Contact Problems ◽  
Accurate Solution ◽  
Rolling Contact ◽  
Viscoelastic Layer ◽  
Force Coefficient ◽  
Belt Conveyors ◽  
Energy Dissipated

In this paper, we study the steady-state rolling contact of a linear viscoelastic layer of finite thickness and a rigid indenter made of a periodic array of equally spaced rigid cylinders. The viscoelastic contact model is derived by means of Green’s function approach, which allows solving the contact problem with the sliding velocity as a control parameter. The contact problem is solved by means of an accurate numerical procedure developed for general two-dimensional contact geometries. The effect of geometrical quantities (layer thickness, cylinders radii, and cylinders spacing), material properties (viscoelastic moduli, relaxation time) and operative conditions (load, velocity) are all investigated. Physical quantities typical of contact problems (contact areas, deformed profiles, etc.) are calculated and discussed. Special emphasis is dedicated to the viscoelastic friction force coefficient and to the energy dissipated per unit time. The discussion is focused on the role played by the deformation localized at the contact spots and the one in the bulk of the thin layer, due to layer bending. The model is proposed as an accurate solution for engineering applications such as belt conveyors, in which the energy dissipated on the rolling contact of idle rollers can, in some cases, be by far the most important contribution to their energy consumption.

scholarly journals Air mediates the impact of a compliant hemisphere on a rigid smooth surface

Soft Matter ◽  
2021 ◽  
Author(s):  
Siqi Zheng ◽  
Sam Dillavou ◽  
John M. Kolinski
Keyword(s):  
Elastic Body ◽  
Elastic Properties ◽  
Impact Velocity ◽  
Solid Surface ◽  
High Speed ◽  
Smooth Surface ◽  
High Speed Imaging ◽  
The Impact ◽  
Rigid Smooth

When a soft elastic body impacts upon a smooth solid surface, the intervening air fails to drain, deforming the impactor. High-speed imaging with the VFT reveal rich dynamics and sensitivity to the impactor's elastic properties and the impact velocity.

3-D Elasto-Plastic Contact Finite Element Analysis for Bearings Design

1990 ◽  
Author(s):  
Wang Shigang ◽  
Yu Jun ◽  
Zhou Ji ◽  
Li Mingzhang
Keyword(s):  
Finite Element ◽  
Contact Problem ◽  
Geometrical Nonlinearity ◽  
Contact Problems ◽  
Plastic State ◽  
Element Analysis ◽  
Surface Pressure Distribution ◽  
Tangential Stiffness ◽  
Stiffness Method ◽  
Error Method

Abstract In this paper, A 3-D elasto-plastic contact problem in bearings is studied by Finite Element Method (FEM). A computer program has been developed for this purpose. A trial-error method is employed to cope with the geometrical nonlinearity and a tangential stiffness method is employed to tackle the material nonlinearity appeared in elasto-plastic contact problems. A frictionless contact problem of roller bearings is analysed, the result reveals that in 3-D elasto-plastic state the trend of the contact surface pressure distribution is similar to Hertz problem’s but flater.

scholarly journals SOLUTION OF ADHESIVE CONTACT PROBLEM ON THE BASIS OF THE KNOWN SOLUTION FOR NON-ADHESIVE ONE

2018 ◽  
Vol 16 (1) ◽  
pp. 93 ◽  
Author(s):  
Valentin L. Popov
Keyword(s):  
Contact Problem ◽  
Material Properties ◽  
Present Method ◽  
Additional Assumption ◽  
Short Communication ◽  
Contact Problems ◽  
Adhesive Contact ◽  
Contact Shape

The well-known procedure of reducing an adhesive contact problem to the corresponding non-adhesive one is generalized in this short communication to contacts with an arbitrary contact shape and arbitrary material properties (e.g. non homogeneous or gradient media). The only additional assumption is that the sequence of contact configurations in an adhesive contact should be exactly the same as that of contact configurations in a non-adhesive one. This assumption restricts the applicability of the present method. Nonetheless, the method can be applied to many classes of contact problems exactly and also be used for approximate analyses.

Analysis of a dynamic frictional contact problem for hyperviscoelastic material with non-convex energy density

2017 ◽  
Vol 23 (3) ◽  
pp. 359-391 ◽  
Author(s):  
Mikaël Barboteu ◽  
Leszek Gasiński ◽  
Piotr Kalita
Keyword(s):  
Contact Problem ◽  
Coulomb Friction ◽  
Frictional Contact ◽  
Tangential Velocity ◽  
Dynamic Contact ◽  
Contact Boundary ◽  
Dynamic Contact Problem ◽  
Monotone Dependence ◽  
Coulomb Friction Law ◽  
Stored Elastic Energy

Using the time approximation method we obtain the existence of a weak solution for the dynamic contact problem with damping and a non-convex stored elastic energy function. On the contact boundary we assume the normal compliance law and the generalization of the Coulomb friction law which allows for non-monotone dependence of the friction force on the tangential velocity. The existence result is accompanied by two numerical examples, one of them showing lack of uniqueness for the numerical solution.

Computing the Stresses Induced Within Multi-Layered Elastic Media That Result From Sliding Contact With a Rigid Punch

2013 ◽  
Author(s):  
Stewart Chidlow ◽  
Mircea Teodorescu
Keyword(s):  
Contact Problem ◽  
Elastic Solid ◽  
Maximum Principal Stress ◽  
Functionally Graded ◽  
Material Failure ◽  
Rigid Punch ◽  
Vertical Displacements ◽  
The Fourier Transform ◽  
Graded Interlayer ◽  
Selection Of

This paper is concerned with the solution of the contact problem that results when a rigid punch is pressed into the surface of an inhomogeneously elastic solid comprising three distinct layers. The upper and lower layers of the solid are assumed to be homogeneous and are joined together by a functionally graded interlayer whose material properties progressively change from those of the coating to those of the substrate. By applying the Fourier transform to the governing boundary value problem (BVP), we may write the stresses and displacements within the solid in terms of indefinite integrals. In particular, the expressions for the horizontal and vertical displacements of the solid surface are used to formulate a coupled pair of integral equations which may be solved numerically to approximate the solution of the stamp problem. A selection of numerical results are then presented which illustrate the effects of friction on the contact problem and it is found that the presence of friction within the contact increases the magnitude of the maximum principal stress and changes its location. These observations indicate that material failure is much more likely to occur when friction is present within the contact as expected.

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