A review of the theory of static and quasi-static frictional contact problems in elasticity

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Andersson Lars-Erik and Klarbring Anders 2001A review of the theory of static and quasi-static frictional contact problems in elasticityPhil. Trans. R. Soc. A.3592519–2539http://doi.org/10.1098/rsta.2001.0908SectionRestricted accessA review of the theory of static and quasi-static frictional contact problems in elasticity Lars-Erik Andersson Lars-Erik Andersson Department of Mathematics, SE-581 83 Linköping, Sweden Google Scholar Find this author on PubMed Search for more papers by this author and Anders Klarbring Anders Klarbring Department of Mechanical Engineering, Linköping University, SE-581 83 Linköping,Sweden (; ) Google Scholar Find this author on PubMed Search for more papers by this author Lars-Erik Andersson Lars-Erik Andersson Department of Mathematics, SE-581 83 Linköping, Sweden Google Scholar Find this author on PubMed Search for more papers by this author and Anders Klarbring Anders Klarbring Department of Mechanical Engineering, Linköping University, SE-581 83 Linköping,Sweden (; ) Google Scholar Find this author on PubMed Search for more papers by this author Published:15 December 2001https://doi.org/10.1098/rsta.2001.0908AbstractThis paper gives a review of mathematical results of existence and uniqueness of solutions to problems of linear elasticity involving friction. Static, steady sliding and quasi-static problems are discussed. Both the case of a continuum body and that of a space-discrete one are treated. The intention is to describe the state of the art for these problems. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Vodička R, Mantič V and Roubíček T (2017) Quasistatic normal-compliance contact problem of visco-elastic bodies with Coulomb friction implemented by QP and SGBEM, Journal of Computational and Applied Mathematics, 10.1016/j.cam.2016.10.010, 315, (249-272), Online publication date: 1-May-2017. Bartosz K and Sofonea M (2016) Modeling and analysis of a contact problem for a viscoelastic rod, Zeitschrift für angewandte Mathematik und Physik, 10.1007/s00033-016-0718-z, 67:5, Online publication date: 1-Oct-2016. Mielke A and Roubíček T (2015) Applications in continuum mechanics and physics of solids Rate-Independent Systems, 10.1007/978-1-4939-2706-7_4, (235-458), . Hu Z, Wang Z, Zhang S, Zhang Y and Zhou H (2014)(2014) A combined reordering procedure for preconditioned GMRES applied to solving equations using Lagrange multiplier method, Engineering Computations, 10.1108/EC-07-2013-0184, 31:7, (1283-1304), Online publication date: 30-Sep-2014., Online publication date: 30-Sep-2014. Hu Z, Zhang S, Zhang Y, Zhou H and Li D (2014)(2014) An efficient preconditioned Krylov subspace method for large-scale finite element equations with MPC using Lagrange multiplier method, Engineering Computations, 10.1108/EC-03-2013-0077, 31:7, (1169-1197), Online publication date: 30-Sep-2014., Online publication date: 30-Sep-2014. Chen Q, Gunzburger M and Perego M (2013) Well-Posedness Results for a Nonlinear Stokes Problem Arising in Glaciology, SIAM Journal on Mathematical Analysis, 10.1137/110848694, 45:5, (2710-2733), Online publication date: 1-Jan-2013. Zozulya V (2011) Variational formulation and nonsmooth optimization algorithms in elastodynamic contact problems for cracked body, Computer Methods in Applied Mechanics and Engineering, 10.1016/j.cma.2010.07.005, 200:5-8, (525-539), Online publication date: 1-Jan-2011. (2011) Numerical Analysis of Cable Networks Nonsmooth Mechanics and Convex Optimization, 10.1201/b10839-13, (205-228) Hintermüller M, Kovtunenko V and Kunisch K (2011) Obstacle Problems with Cohesion: A Hemivariational Inequality Approach and Its Efficient Numerical Solution, SIAM Journal on Optimization, 10.1137/10078299, 21:2, (491-516), Online publication date: 1-Apr-2011. Angelov T (2009) Modelling and Solvability of a Rigid-Plastic Rolling Problem, Mathematics and Mechanics of Solids, 10.1177/1081286509105148, 15:6, (639-654), Online publication date: 1-Aug-2010. Angelov T (2009) Variational and numerical approach to a steady-state rolling problem, Journal of Engineering Mathematics, 10.1007/s10665-009-9284-0, 66:4, (311-323), Online publication date: 1-Apr-2010. Ahn Y (2010) Discontinuity of quasi-static solution in the two-node Coulomb frictional system, International Journal of Solids and Structures, 10.1016/j.ijsolstr.2010.06.007, 47:21, (2866-2871), Online publication date: 1-Oct-2010. Argatov I (2009) Averaging of a finely laminated elastic medium with roughness or adhesion on the contact surfaces of the layers, Journal of Applied Mathematics and Mechanics, 10.1016/j.jappmathmech.2010.01.014, 73:6, (734-746), Online publication date: 1-Jan-2009. Hild P (2009) Two results on solution uniqueness and multiplicity for the linear elastic friction problem with normal compliance, Nonlinear Analysis: Theory, Methods & Applications, 10.1016/j.na.2009.04.061, 71:11, (5560-5571), Online publication date: 1-Dec-2009. Mielke A A Mathematical Framework for Generalized Standard Materials in the Rate-Independent Case Multifield Problems in Solid and Fluid Mechanics, 10.1007/978-3-540-34961-7_12, (399-428) Mielke A (2005) Evolution of Rate-Independent Systems Handbook of Differential Equations Evolutionary Equations, 10.1016/S1874-5717(06)80009-5, (461-559), . Huang S and Schimmels J (2005) The Motion of a Compliantly Suspended Rigid Body Constrained by Multipoint Frictional Contact, Journal of Dynamic Systems, Measurement, and Control, 10.1115/1.2098878, 127:4, (623-632), Online publication date: 1-Dec-2005. Huang S and Schimmels J (2016) Spatial Compliant Motion of a Rigid Body Constrained by a Frictional Contact, The International Journal of Robotics Research, 10.1177/02783649030229004, 22:9, (733-756), Online publication date: 1-Sep-2003. This Issue15 December 2001Volume 359Issue 1789Theme Issue ‘Non-smooth mechanics’ compiled by F. G. Pfeiffer Article InformationDOI:https://doi.org/10.1098/rsta.2001.0908Published by:Royal SocietyPrint ISSN:1364-503XOnline ISSN:1471-2962History: Published online15/12/2001Published in print15/12/2001 License: Citations and impact Keywordsquasi-static problemexistenceunilateral contactlinear elasticityuniquenessCoulomb friction