Editing Friction (section)

===Numerical simulation of the Coulomb model===
Despite being a simplified model of friction, the Coulomb model is useful in many [[numerical simulation]] applications such as [[multibody system]]s and [[granular material]]. Even its most simple expression encapsulates the fundamental effects of sticking and sliding which are required in many applied cases, although specific algorithms have to be designed in order to efficiently [[Numerical integration|numerically integrate]] mechanical systems with Coulomb friction and bilateral or unilateral contact.<ref>{{cite journal |last1=Haslinger |first1=J. |title=Approximation of the Signorini problem with friction, obeying the Coulomb law |journal=Mathematical Methods in the Applied Sciences |volume=5 |issue=1 |pages=422–437 |year=1983 |bibcode=1983MMAS....5..422H |doi=10.1002/mma.1670050127 |last2=Nedlec |first2=J.C. |hdl=10338.dmlcz/104086 |url=http://dml.cz/bitstream/handle/10338.dmlcz/104086/AplMat_29-1984-3_6.pdf |access-date=2019-09-19 |archive-date=2024-10-07 |archive-url=https://web.archive.org/web/20241007083034/http://dml.cz/bitstream/handle/10338.dmlcz/104086/AplMat_29-1984-3_6.pdf |url-status=live }}</ref><ref>{{cite journal |last1=Alart |first1=P. |last2=Curnier |first2=A. |title=A mixed formulation for frictional contact problems prone to Newton like solution method |journal=Computer Methods in Applied Mechanics and Engineering |volume=92 |pages=353–375 |year=1991 |bibcode=1991CMAME..92..353A |doi=10.1016/0045-7825(91)90022-X |issue=3 |url=https://hal.science/hal-04264964/file/Alart1991.pdf |access-date=2024-03-29 |archive-date=2024-10-07 |archive-url=https://web.archive.org/web/20241007091441/https://hal.science/hal-04264964/file/Alart1991.pdf |url-status=live }}</ref><ref>{{cite journal |last1=Acary |first1=V. |last2=Cadoux |first2=F. |last3=Lemaréchal |first3=C. |last4=Malick |first4=J. |title=A formulation of the linear discrete Coulomb friction problem via convex optimization |journal=Journal of Applied Mathematics and Mechanics |volume=91 |issue=2 |pages=155–175 |year=2011 |doi=10.1002/zamm.201000073 |bibcode=2011ZaMM...91..155A |s2cid=17280625 |url=https://hal.inria.fr/inria-00495734/document |access-date=2018-04-20 |archive-date=2024-10-07 |archive-url=https://web.archive.org/web/20241007083036/https://hal.inria.fr/inria-00495734/document |url-status=live }}</ref><ref>{{cite journal |last1=De Saxcé |first1=G. |last2=Feng |first2=Z.-Q. |title=The bipotential method: A constructive approach to design the complete contact law with friction and improved numerical algorithms |journal=Mathematical and Computer Modelling |volume=28 |issue=4 |pages=225–245 |year=1998 |doi=10.1016/S0895-7177(98)00119-8|doi-access=free }}</ref><ref>{{cite journal |last1=Simo |first1=J.C. |last2=Laursen |first2=T.A. |title=An augmented lagrangian treatment of contact problems involving friction |journal=Computers and Structures |volume=42 |issue=2 |pages=97–116 |year=1992 |doi=10.1016/0045-7949(92)90540-G|doi-access=free }}</ref> Some quite [[Nonlinear system#Types of nonlinear dynamic behaviors|nonlinear effects]], such as the so-called [[Painlevé paradox]]es, may be encountered with Coulomb friction.<ref>{{cite book |last1=Acary |first1=V. |last2=Brogliato |first2=B. |title=Numerical Methods for Nonsmooth Dynamical Systems. Applications in Mechanics and Electronics |publisher=[[Springer Science+Business Media|Springer Verlag Heidelberg]] |volume=35 |year=2008}}</ref>