A Numerical Solution for Quasistatic Viscoelastic Frictional Contact Problems

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Fatin F. Mahmoud ◽  
Ahmed G. El-Shafei ◽  
Amal E. Al-Shorbagy ◽  
Alaa A. Abdel Rahman
Keyword(s):  
Contact Problem ◽  
Frictional Contact ◽  
Programming Model ◽  
Contact Problems ◽  
Computational Procedure ◽  
Friction Model ◽  
Relaxation Phenomena ◽  
Contact Interface ◽  
Linear Behavior ◽  
Deformable Bodies

The tribological aspects of contact are greatly affected by the friction throughout the contact interface. Generally, contact of deformable bodies is a nonlinear problem. Introduction of the friction with its irreversible character makes the contact problem more difficult. Furthermore, when one or more of the contacting bodies is made of a viscoelastic material, the problem becomes more complicated. A nonlinear time-dependent contact problem is addressed. The objective of the present work is to develop a computational procedure capable of handling quasistatic viscoelastic frictional contact problems. The contact problem as a convex programming model is solved by using an adaptive incremental procedure. The contact constraints are incorporated into the model by using the Lagrange multiplier method. In addition, a local-nonlinear nonclassical friction model is adopted to model the friction at the contact interface. This eliminates the difficulties that arise with the application of the classical Coulomb’s law. On the other hand, the Wiechert model, as an effective model capable of describing both creep and relaxation phenomena, is adopted to simulate the linear behavior of viscoelastic materials. The resulting constitutive integral equations are linearized; therefore, complications that arise during the integration of these equations, especially with contact problems, are avoided. Two examples are presented to demonstrate the applicability of the proposed method.

An Incremental Adaptive Procedure for Viscoelastic Contact Problems

2006 ◽  
Vol 129 (2) ◽  
pp. 305-313 ◽  
Author(s):  
Fatin F. Mahmoud ◽  
Ahmed G. El-Shafei ◽  
Mohamed A. Attia
Keyword(s):  
Contact Problem ◽  
Contact Problems ◽  
Vital Role ◽  
Time Dependent ◽  
Viscoelastic Materials ◽  
Adaptive Procedure ◽  
Linear Behavior ◽  
Material Contact ◽  
Proposed Model ◽  
Deformable Bodies

Contact pressure distribution throughout the contact interface has a vital role on the tribological aspects of the contact systems. Generally, contact of deformable bodies is a nonlinear problem. Viscoelastic materials have a time-dependent response, since both viscous and elastic characteristics depend on time. Such types of materials have the capability of storing and dissipating energy. When at least one of the contacting bodies is made of a viscoelastic material, contact problems become more difficult, and a nonlinear time-dependent contact problem is obtained. The objective of this paper is to develop an incremental adaptive computational model capable of handling quasistatic viscoelastic frictionless contact problems. The Wiechert model, as an effective model capable of describing both creep and relaxation phenomena, is adopted to simulate the linear behavior of viscoelastic materials. The resulting constitutive integral equations are linearized and, therefore, complications that arise during the direct integration of these equations, specially with contact problems, are avoided. In addition, the incremental convex programming method is adopted and modified to accommodate the contact problem of viscoelastic bodies. The Lagrange multiplier method is adopted to enforce the contact constraints. Two different contact problems are presented to demonstrate the efficient applicability of the proposed model.

The Influence of the Elastoplastic Behavior and the Load Pattern on the Tribological Properties of Two-Dimensional Frictional Contact Problems

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Waleed S. Abdalla ◽  
Soliman S. Ali-Eldin ◽  
Mohamed R. Ghazy
Keyword(s):  
Frictional Contact ◽  
Programming Model ◽  
Tribological Behavior ◽  
Contact Problems ◽  
Flow Rule ◽  
The Finite Element Method ◽  
Elastoplastic Behavior ◽  
Coulomb’S Friction ◽  
Elastic And Plastic Deformations ◽  
Load Pattern

The macromechanical tribological mechanism describes the friction phenomenon by considering the stress and the strain distributions, and the total elastic and plastic deformations. Based on the finite element method (FEM), the elastoplastic frictional contact problem is formulated as an incremental convex programming model (CPM). The Lagrange multiplier approach is adopted for imposing the inequality contact constraints. The Coulomb's friction law and the Prandtl–Reuss flow rule are used for the friction conditions and the elastoplastic behavior, respectively. The frictional contact examples are analyzed using the developed adaptive incremental procedure to elucidate the tribological behavior of the contact bodies and the model applicability.

ADAPTIVE INCREMENTAL FINITE ELEMENT PROCEDURE FOR SOLVING ELASTOPLASTIC FRICTIONAL CONTACT PROBLEMS SUBJECTED TO NORMAL AND TANGENTIAL LOADS

2014 ◽  
Vol 06 (03) ◽  
pp. 1450031 ◽  
Author(s):  
W. S. ABDALLA ◽  
S. S. ALI-ELDIN ◽  
M. R. GHAZY
Keyword(s):  
Finite Element ◽  
Frictional Contact ◽  
Programming Model ◽  
Yield Criterion ◽  
Contact Problems ◽  
Flow Rule ◽  
Friction Behavior ◽  
Elastoplastic Behavior ◽  
Coulomb’S Friction ◽  
Von Mises

This paper presents a numerical model for analyzing the stresses and displacements of deformable bodies in contact with the presence of friction and material nonlinearity. Based on the finite element method (FEM), the elastoplastic frictional contact problem is formulated as an incremental convex programming model (ICPM) under inequality contact constraints and friction conditions. The classical Coulomb's friction law and the Prandtl–Reuss flow rule with the von Mises yield criterion are used to simulate the interface friction conditions and the elastoplastic behavior of the contacting bodies, respectively. The Lagrange multiplier approach is adopted for imposing the contact constraints. Furthermore, an effective adaptive incremental procedure is developed for solving the elastoplastic frictional contact problems. Examples for the frictional contact having advancing and receding nature are analyzed. The obtained results prove the ability of the developed procedure to investigate the sequence of different events during monotonic application of external loads. In addition, the results elucidate the effect of external side force on the friction behavior in the presence of plastic deformation. Good agreement has been found with published results.

Using fuzzy logic control approach and model reduction for solving frictional contact problems

2016 ◽  
Vol 33 (4) ◽  
pp. 1006-1032 ◽  
Author(s):  
H Do ◽  
F Massa ◽  
T Tison
Keyword(s):  
Finite Element ◽  
Fuzzy Logic ◽  
Contact Problem ◽  
Fuzzy Logic Control ◽  
Frictional Contact ◽  
Contact Problems ◽  
Computational Time ◽  
Contact Method ◽  
Content Type ◽  
Logic Control

Purpose – The purpose of this paper is to expand the previously published fuzzy logic controller for contact method to normal frictionless contact for solving mechanical frictional contact problems. The secondary aim is to integrate a reduction model for each component in contact to decrease the size of the global finite element contact problem. Design/methodology/approach – The proposed strategy relies on the design of two fuzzy logic controllers currently used in the automation domain. These controllers are considered to link normal and tangential gaps (for sticking conditions) with normal and tangential contact loads. A direct consequence of integrating a control-based approach into the numerical solving approach is the decomposition of the non-linear problem into a set of linear problems. Findings – With this new strategy, no tangent or coupling matrix is defined for the contact problem that allows to consider a projection matrix to reduce the size of each component in contact and subsequently to decrease the associated computational time. As in condensation techniques, this matrix is composed of both modal bases of each component in contact and static modes that capture behaviors at the contact interface. Moreover, the proposed numerical application highlights the efficiency of the proposal in terms of computation time and precision of contact data. Research limitations/implications – The developments are currently implemented in Matlab only for 2D static numerical applications. Therefore, as obtained results are very promising in terms of precision and computational time, the objective is to complete the proposed method in future research to manage frictional contact for 3D finite element models in a dynamic context. Originality/value – In conclusion, this paper highlights the interest of studying mechanical frictional contact problems by considering fuzzy logic control approaches.

On the Finite Element Solution of Fractional Contact Problems Using Variational Inequalities

1994 ◽  
Author(s):  
M. H. Refaat ◽  
S. A. Meguid
Keyword(s):  
Contact Problem ◽  
Variational Inequalities ◽  
Frictional Contact ◽  
Contact Problems ◽  
Penalty Methods ◽  
Test Cases ◽  
Current Investigation ◽  
Element Solution ◽  
Frictional Contact Problem ◽  
Lagrange’S Multipliers

Abstract This article is devoted to the development and implementation of a variational inequalities approach to treat the general frictional contact problem. Unlike earlier studies which adopt penalty methods, the current investigation uses Quadratic Programming and Lagrange’s multipliers to solve the frictional contact problem and to identify the candidate contact surface. The proposed method avoids the use of user defined penalty parameters, which ultimately govern the convergence and accuracy of the solution. To establish the validity of the method, a number of test cases are examined and compared with existing solutions where penalty methods are employed.

Effect of Material Characteristics on Viscoelastic Frictionless Contact Configuration

2008 ◽  
Author(s):  
Fatin F. Mahmoud ◽  
Ahmed G. El-Shafei ◽  
Mohamed A. Attia
Keyword(s):  
Computational Model ◽  
Viscoelastic Material ◽  
Contact Problems ◽  
Contact Interface ◽  
Viscoelastic Materials ◽  
Frictionless Contact ◽  
Material Parameters ◽  
Contact Configuration ◽  
Linear Behavior ◽  
Vital Effect

The tribological status of contact systems is affected by the contact configuration; contact stress distribution throughout the contact interface. Viscoelastic materials have the capability of storing and dissipating energy. When the contacting bodies are made of viscoelastic material, viscous and elastic properties of the material have a vital effect upon the contact pressure distribution and the extent of the contact interface. This paper illustrates the effect of viscoelastic material parameters on the contact configuration. Two material parameters are considered; the ratio of the delayed elasticity to the instantaneous elasticity and the material relaxation time. The results are obtained by using a time-dependent nonlinear computational model capable of analyzing quasistatic viscoelastic frictionless contact problems. This computational model adopts the Wiechert model to simulate the linear behavior of viscoelastic materials and the modified incremental convex programming method to accommodate the contact problem of viscoelastic bodies.

Three benchmark examples for frictional contact modelling using finite element and boundary elements methods

1993 ◽  
Vol 28 (4) ◽  
pp. 293-301 ◽  
Author(s):  
O A Olukoko ◽  
A A Becker ◽  
R T Fenner
Keyword(s):  
Finite Element ◽  
Frictional Contact ◽  
Contact Problems ◽  
Boundary Element Methods ◽  
Shear Stresses ◽  
Contact Interface ◽  
Stick Slip ◽  
Normal Contact ◽  
Slip Partitioning ◽  
Contact Modelling

Three benchmark examples for two-dimensional and axisymmetric contact problems with friction are presented using the finite element and boundary element methods. The examples have relatively simple geometries and boundary conditions, and involve frictional sticking and slipping modes at the interface according to Coulomb's law of friction. Results are presented in the form of normal contact stresses, shear stresses, relative tangential displacements, and the stick-slip partitioning of the contact interface.

Propagation of SH waves in a layered half-space with a frictional contact interface

1998 ◽  
Vol 88 (5) ◽  
pp. 1300-1310
Author(s):  
Yue-Sheng Wang ◽  
Gui-Lan Yu ◽  
Bing-Zheng Gai
Keyword(s):  
Half Space ◽  
Incident Wave ◽  
Frictional Contact ◽  
Mixed Boundary ◽  
Singular Integral Equations ◽  
Friction Model ◽  
Contact Interface ◽  
Sh Waves ◽  
Local Slip ◽  
Layered Half Space

Abstract The propagation of SH waves in a layered half-space with a frictional contact interface is considered. The incident wave is assumed to be sufficiently strong so that friction may be broken, and the local slip may take place at the interface. In the stick zones, both the displacements and stresses are continuous, while in the slip zones, the Coulomb friction model is adopted. The mixed boundary conditions lead to recurrence relations for the subcritical angle incidence or singular integral equations for the supercritical angle incidence. The extent and location of slip zones, which are unknown before the solution of the problem, are determined. The local slip velocities and the interface shearing tractions are calculated in detail for the subcritical angle incidence. The results show that the solution of the problem is dependent on the frequency of the incident wave due to the presence of the characteristic length—the thickness of the elastic layer. It is also found that, in some situations, there exist four slip zones instead of two over one representative period. All these features are quite different from those for infinite media.

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