Numerical analysis of an evolutionary variational–hemivariational inequality with application in contact mechanics

2017 ◽  
Vol 318 ◽  
pp. 882-897 ◽  
Author(s):  
Mikaël Barboteu ◽  
Krzysztof Bartosz ◽  
Weimin Han
Keyword(s):  
Numerical Analysis ◽  
Contact Mechanics ◽  
Hemivariational Inequality

Numerical analysis of hemivariational inequalities in contact mechanics

Acta Numerica ◽  
2019 ◽  
Vol 28 ◽  
pp. 175-286 ◽  
Author(s):  
Weimin Han ◽  
Mircea Sofonea
Keyword(s):  
Numerical Analysis ◽  
Mathematical Models ◽  
Contact Mechanics ◽  
Numerical Solutions ◽  
Deformable Body ◽  
Industrial Process ◽  
Contact Problems ◽  
Hemivariational Inequalities ◽  
Uniqueness Results ◽  
Simulation Results

Contact phenomena arise in a variety of industrial process and engineering applications. For this reason, contact mechanics has attracted substantial attention from research communities. Mathematical problems from contact mechanics have been studied extensively for over half a century. Effort was initially focused on variational inequality formulations, and in the past ten years considerable effort has been devoted to contact problems in the form of hemivariational inequalities. This article surveys recent development in studies of hemivariational inequalities arising in contact mechanics. We focus on contact problems with elastic and viscoelastic materials, in the framework of linearized strain theory, with a particular emphasis on their numerical analysis. We begin by introducing three representative mathematical models which describe the contact between a deformable body in contact with a foundation, in static, history-dependent and dynamic cases. In weak formulations, the models we consider lead to various forms of hemivariational inequalities in which the unknown is either the displacement or the velocity field. Based on these examples, we introduce and study three abstract hemivariational inequalities for which we present existence and uniqueness results, together with convergence analysis and error estimates for numerical solutions. The results on the abstract hemivariational inequalities are general and can be applied to the study of a variety of problems in contact mechanics; in particular, they are applied to the three representative mathematical models. We present numerical simulation results giving numerical evidence on the theoretically predicted optimal convergence order; we also provide mechanical interpretations of simulation results.

Comparison of Analytical Model for Contact Mechanics Parameters with Numerical Analysis and Experimental Results

2019 ◽  
Vol 48 (3) ◽  
pp. 168-187
Author(s):  
Sunish Vadakkeveetil ◽  
Arash Nouri ◽  
Saied Taheri
Keyword(s):  
Finite Element ◽  
Numerical Analysis ◽  
Finite Element Model ◽  
Penetration Depth ◽  
Contact Mechanics ◽  
Analytical Model ◽  
Element Model ◽  
Experimental Results ◽  
Nano Indentation ◽  
Interfacial Separation

ABSTRACT Being able to estimate tire/rubber friction is very important to tire engineers, materials developers, and pavement engineers. This is because of the need for estimating forces generated at the contact, optimizing tire and vehicle performance, and estimating tire wear. Efficient models for contact area and interfacial separation are key for accurate prediction of friction coefficient. Based on the contact mechanics and surface roughness, various models were developed that can predict real area of contact and penetration depth/interfacial separation. In the present work, we intend to compare the analytical contact mechanics models using experimental results and numerical analysis. Nano-indentation experiments are performed on the rubber compound to obtain penetration depth data. A finite element model of a rubber block in contact with a rough surface was developed and validated using the nano-indentation experimental data. Results for different operating conditions obtained from the developed finite element model are compared with analytical model results, and further model improvements are discussed.

scholarly journals Numerical analysis of history-dependent quasivariational inequalities with applications in contact mechanics

2014 ◽  
Vol 48 (3) ◽  
pp. 919-942 ◽  
Author(s):  
Kamran Kazmi ◽  
Mikael Barboteu ◽  
Weimin Han ◽  
Mircea Sofonea
Keyword(s):  
Numerical Analysis ◽  
Contact Mechanics ◽  
Quasivariational Inequalities

Numerical Analysis of a Hyperbolic Hemivariational Inequality Arising in Dynamic Contact

2015 ◽  
Vol 53 (1) ◽  
pp. 527-550 ◽  
Author(s):  
Mikaël Barboteu ◽  
Krzysztof Bartosz ◽  
Weimin Han ◽  
Tomasz Janiczko
Keyword(s):  
Numerical Analysis ◽  
Dynamic Contact ◽  
Hemivariational Inequality
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