메뉴 건너뛰기




Volumn 1, Issue 1, 2013, Pages 41-62

Method of reduction of dimensionality in contact and friction mechanics: A linkage between micro and macro scales

Author keywords

adhesion; contact mechanics; dynamic tangential contacts; elastomers; reduction of dimensionality; rolling; rough surfaces; scale linkage; sliding friction; static friction

Indexed keywords

ADHESION; COMPUTATION THEORY; DEFORMATION; DEGREES OF FREEDOM (MECHANICS); DIMENSIONALITY REDUCTION; ELASTICITY; ELASTOMERS; ONE DIMENSIONAL; ROLLING; SMART CARDS; STICTION; SURFACE MEASUREMENT; TRIBOLOGY;

EID: 84976271925     PISSN: 22237690     EISSN: 22237704     Source Type: Journal    
DOI: 10.1007/s40544-013-0005-3     Document Type: Article
Times cited : (59)

References (60)
  • 2
    • 0000549183 scopus 로고
    • Elastic deformation and the laws of friction
    • 10.1098/rspa.1957.0214
    • Archard J F. Elastic deformation and the laws of friction. Proc R Soc A 243: 190–205 (1957)
    • (1957) Proc R Soc A , vol.243 , pp. 190-205
    • Archard, J.F.1
  • 3
    • 13344270633 scopus 로고
    • Contact and rubbing of flat surfaces
    • 10.1063/1.1721448
    • Archard J F. Contact and rubbing of flat surfaces. J of Appl Phys 24: 981–988 (1953)
    • (1953) J of Appl Phys , vol.24 , pp. 981-988
    • Archard, J.F.1
  • 4
    • 33745902250 scopus 로고    scopus 로고
    • Contact mechanics for randomly rough surfaces
    • 2248423, 10.1016/j.surfrep.2006.04.001
    • Persson B N J. Contact mechanics for randomly rough surfaces. Surf Sci Rep 61: 201–227 (2006)
    • (2006) Surf Sci Rep , vol.61 , pp. 201-227
    • Persson, B.N.J.1
  • 6
    • 84976308878 scopus 로고    scopus 로고
    • on “Numerical simulation method in tribology: possibilities and limitations”, TU Berlin, March 14–17, 2005. Contributions published in the special issue of “Tribology International”, (Trib Int, Guest editors Popov V and Ostermeyer G-P)
    • German-Russian Workshop on “Numerical simulation method in tribology: possibilities and limitations”, TU Berlin, March 14–17, 2005. Contributions published in the special issue of “Tribology International”, (Trib Int, 40, No. 6, Guest editors Popov V and Ostermeyer G-P).
  • 7
    • 33845207153 scopus 로고    scopus 로고
    • Numerical simulation methods in tribology
    • 10.1016/j.triboint.2006.02.020
    • Popov V L, Psakhie S G. Numerical simulation methods in tribology. Tribology International 40: 916–923 (2007)
    • (2007) Tribology International , vol.40 , pp. 916-923
    • Popov, V.L.1    Psakhie, S.G.2
  • 8
    • 1542344955 scopus 로고    scopus 로고
    • Bounds on the electrical resistance between contacting elastic rough bodies
    • 1993344
    • Barber J R. Bounds on the electrical resistance between contacting elastic rough bodies. Proc R Soc Lond A 495: 53–66 (2003)
    • (2003) Proc R Soc Lond A , vol.495 , pp. 53-66
    • Barber, J.R.1
  • 9
    • 34848919518 scopus 로고    scopus 로고
    • Mapping of three-dimensional contact problems into one dimension
    • 10.1103/PhysRevE.76.036710
    • Geike T, Popov V L. Mapping of three-dimensional contact problems into one dimension. Phys Rev E 76: 036710 (2007)
    • (2007) Phys Rev E , vol.76 , pp. 036710
    • Geike, T.1    Popov, V.L.2
  • 10
    • 33845192094 scopus 로고    scopus 로고
    • Reduction of three-dimensional contact problems to one-dimensional ones
    • 10.1016/j.triboint.2006.02.035
    • Geike T, Popov V L. Reduction of three-dimensional contact problems to one-dimensional ones. Tribology International 40: 924–929 (2007)
    • (2007) Tribology International , vol.40 , pp. 924-929
    • Geike, T.1    Popov, V.L.2
  • 11
    • 84876530371 scopus 로고    scopus 로고
    • Normal contact between a rigid surface and a viscous body: Verification of the method of reduction of dimensionality for viscous media
    • Kürschner S, Filippov A E. Normal contact between a rigid surface and a viscous body: Verification of the method of reduction of dimensionality for viscous media. Phys Mesomech 15: 270–274 (2012)
    • (2012) Phys Mesomech , vol.15 , pp. 270-274
    • Kürschner, S.1    Filippov, A.E.2
  • 12
    • 77954236562 scopus 로고    scopus 로고
    • Force of friction between fractal rough surface and elastomer
    • 10.1134/S1063785010060118
    • Popov V L, Filippov A E. Force of friction between fractal rough surface and elastomer. Tech Phys Lett 36: 525–527 (2010)
    • (2010) Tech Phys Lett , vol.36 , pp. 525-527
    • Popov, V.L.1    Filippov, A.E.2
  • 13
    • 79951849111 scopus 로고    scopus 로고
    • Using hierarchical memory to calculate friction force between fractal rough solid surface and elastomer with arbitrary linear rheological properties
    • 10.1134/S106378501101010X
    • Popov V L, Dimaki A. Using hierarchical memory to calculate friction force between fractal rough solid surface and elastomer with arbitrary linear rheological properties. Tech Phys Lett 37: 8–11 (2011)
    • (2011) Tech Phys Lett , vol.37 , pp. 8-11
    • Popov, V.L.1    Dimaki, A.2
  • 14
    • 84876578430 scopus 로고    scopus 로고
    • On the dependence of the static friction force between a rigid, randomly rough fractal surface and a viscoelastic body on the normal force
    • Benad J. On the dependence of the static friction force between a rigid, randomly rough fractal surface and a viscoelastic body on the normal force. Phys Mesomech 15: 300–302 (2012)
    • (2012) Phys Mesomech , vol.15 , pp. 300-302
    • Benad, J.1
  • 15
    • 84876587313 scopus 로고    scopus 로고
    • Dependence of the kinetic force of friction between a randomly rough surface and simple elastomer on the normal force
    • Li Q. Dependence of the kinetic force of friction between a randomly rough surface and simple elastomer on the normal force. Phys Mesomech 15: 303–305 (2012)
    • (2012) Phys Mesomech , vol.15 , pp. 303-305
    • Li, Q.1
  • 16
    • 84876569884 scopus 로고    scopus 로고
    • Multiscale simulation of friction with normal oscillations in the method of reduction of dimensionality
    • Heise R. Multiscale simulation of friction with normal oscillations in the method of reduction of dimensionality. Phys Mesomech 15: 316–318 (2012)
    • (2012) Phys Mesomech , vol.15 , pp. 316-318
    • Heise, R.1
  • 17
    • 84876533754 scopus 로고    scopus 로고
    • Modeling of the dynamic contact in stick-slip microdrives using the method of reduction of dimensionality
    • Teidelt E, Willert E, Filippov A E, Popov V L. Modeling of the dynamic contact in stick-slip microdrives using the method of reduction of dimensionality. Phys Mesomech 15: 287–292 (2012)
    • (2012) Phys Mesomech , vol.15 , pp. 287-292
    • Teidelt, E.1    Willert, E.2    Filippov, A.E.3    Popov, V.L.4
  • 18
    • 84876535848 scopus 로고    scopus 로고
    • Simulation of the influence of ultrasonic in-plane oscillations on dry friction accounting for stick and creep
    • Stracevic J, Filippov A E. Simulation of the influence of ultrasonic in-plane oscillations on dry friction accounting for stick and creep. Phys Mesomech 15: 330–332 (2012)
    • (2012) Phys Mesomech , vol.15 , pp. 330-332
    • Stracevic, J.1    Filippov, A.E.2
  • 19
    • 84876562915 scopus 로고    scopus 로고
    • Shakedown and induced microslip of an oscillating frictional contact
    • Wetter R. Shakedown and induced microslip of an oscillating frictional contact. Phys Mesomech 15: 293–299 (2012)
    • (2012) Phys Mesomech , vol.15 , pp. 293-299
    • Wetter, R.1
  • 20
    • 84876531147 scopus 로고    scopus 로고
    • Contact force resulting from rolling on a self- affine fractal rough surface
    • Popov M. Contact force resulting from rolling on a self- affine fractal rough surface. Phys Mesomech 15: 342–344 (2012)
    • (2012) Phys Mesomech , vol.15 , pp. 342-344
    • Popov, M.1
  • 22
    • 84876567915 scopus 로고    scopus 로고
    • On the reduction method of dimensionality: The exact mapping of axisymmetric contact problems with and without adhesion
    • Heß M. On the reduction method of dimensionality: The exact mapping of axisymmetric contact problems with and without adhesion. Phys Mesomech 15: 264–269 (2012)
    • (2012) Phys Mesomech , vol.15 , pp. 264-269
    • Heß, M.1
  • 23
    • 85040875608 scopus 로고
    • Cambridge University Press, Cambridge
    • Johnson K L. Contact Mechanics. Cambridge: Cambridge University Press, 1987.
    • (1987) Contact Mechanics
    • Johnson, K.L.1
  • 24
    • 0011713787 scopus 로고
    • The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitraryprofile
    • 183169, 0128.42002, 10.1016/0020-7225(65)90019-4
    • Sneddon I N. The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitraryprofile. Int J Eng Sci 3: 47–57 (1965)
    • (1965) Int J Eng Sci , vol.3 , pp. 47-57
    • Sneddon, I.N.1
  • 25
    • 0019624225 scopus 로고
    • The stress on an elastic half-space due to sectionally smooth-ended punch
    • 0467.73147, 10.1007/BF00058081
    • Ejike U B C O. The stress on an elastic half-space due to sectionally smooth-ended punch. Journal of Elasticity 11: 395–402 (1981)
    • (1981) Journal of Elasticity , vol.11 , pp. 395-402
    • Ejike, U.B.C.O.1
  • 26
    • 0000357002 scopus 로고
    • The phenomena of rupture and flow in solids
    • 10.1098/rsta.1921.0006
    • Griffith A A. The phenomena of rupture and flow in solids. Phil Trans R Soc Lond A 221: 163–198 (1921)
    • (1921) Phil Trans R Soc Lond A , vol.221 , pp. 163-198
    • Griffith, A.A.1
  • 27
    • 0000469962 scopus 로고
    • Surface energy and the contact of elastic solids
    • 10.1098/rspa.1971.0141
    • Johnson K L, Kendall K, Roberts A D. Surface energy and the contact of elastic solids. Proc R Soc A 324: 301–313 (1971)
    • (1971) Proc R Soc A , vol.324 , pp. 301-313
    • Johnson, K.L.1    Kendall, K.2    Roberts, A.D.3
  • 29
    • 84979308647 scopus 로고
    • Ein Gedankenmodell für den Zerreißvorgang spröder Körper
    • JFM 59.0750.03, 10.1002/zamm.19330130218
    • Prandtl L. Ein Gedankenmodell für den Zerreißvorgang spröder Körper. ZAMM 13: 129–133 (1933)
    • (1933) ZAMM , vol.13 , pp. 129-133
    • Prandtl, L.1
  • 31
    • 84876531339 scopus 로고    scopus 로고
    • Basic ideas and applications of the method of reduction of dimensionality in contact mechanics
    • Popov V L. Basic ideas and applications of the method of reduction of dimensionality in contact mechanics. Physical Mesomechanics 15: 254–263 (2012)
    • (2012) Physical Mesomechanics , vol.15 , pp. 254-263
    • Popov, V.L.1
  • 32
    • 84876545213 scopus 로고    scopus 로고
    • Adhesive properties of contacts between elastic bodies with randomly rough self-affine surfaces: A simulation with the method of reduction of dimensionality
    • Popov V L, Filippov A E. Adhesive properties of contacts between elastic bodies with randomly rough self-affine surfaces: A simulation with the method of reduction of dimensionality. Phys Mesomech 15: 324–329 (2012)
    • (2012) Phys Mesomech , vol.15 , pp. 324-329
    • Popov, V.L.1    Filippov, A.E.2
  • 33
    • 0001678918 scopus 로고
    • Sul contatto di due corpi elastici: distribuzione locale degli sforzi
    • Cattaneo C. Sul contatto di due corpi elastici: distribuzione locale degli sforzi. Rendiconti dell’Accademia nazionale dei Lincei 27: 342–348, 434–436, 474–478 (1938)
    • (1938) Rendiconti dell’Accademia nazionale dei Lincei , vol.27 , pp. 342-348
    • Cattaneo, C.1
  • 34
    • 84882729036 scopus 로고
    • Compliance of elastic bodies in contact
    • 34193, 0034.26602
    • Mindlin R D. Compliance of elastic bodies in contact. Journal of Applied Mechanics 16: 259–268 (1949)
    • (1949) Journal of Applied Mechanics , vol.16 , pp. 259-268
    • Mindlin, R.D.1
  • 35
    • 0029368532 scopus 로고
    • Axi-symmetric bodies of equal material in contact under torsion or shift
    • 0846.73056, 10.1007/BF00835661
    • Jäger J. Axi-symmetric bodies of equal material in contact under torsion or shift. Archive of Applied Mechanics 65: 478–487 (1995)
    • (1995) Archive of Applied Mechanics , vol.65 , pp. 478-487
    • Jäger, J.1
  • 39
    • 0000588215 scopus 로고
    • Viscoelastic stress analysis
    • 92453, 0125.13505
    • Radok J R M. Viscoelastic stress analysis. Q Appl Math 15: 198–202 (1957)
    • (1957) Q Appl Math , vol.15 , pp. 198-202
    • Radok, J.R.M.1
  • 40
    • 0000827365 scopus 로고
    • Contact of nominally flat surfaces
    • 10.1098/rspa.1966.0242
    • Greenwood J A, Williamson J B P. Contact of nominally flat surfaces. Proc R Soc A 295: 300–319 (1966)
    • (1966) Proc R Soc A , vol.295 , pp. 300-319
    • Greenwood, J.A.1    Williamson, J.B.P.2
  • 41
    • 34548226545 scopus 로고    scopus 로고
    • Elastic contact between rough surfaces: Effect of roughness at large and small wavelengths
    • 10.1016/j.triboint.2007.02.003
    • Hyun S, Robbins M O. Elastic contact between rough surfaces: Effect of roughness at large and small wavelengths. Tribol Intern 40: 1413–1422 (2007)
    • (2007) Tribol Intern , vol.40 , pp. 1413-1422
    • Hyun, S.1    Robbins, M.O.2
  • 42
    • 33747595437 scopus 로고    scopus 로고
    • Practical Green’s function approach to the simulation of elastic semi-infinite solids
    • 10.1103/PhysRevB.74.075420
    • Campana C, Müser M H. Practical Green’s function approach to the simulation of elastic semi-infinite solids. Phys Rev B 74: 075420 (2006)
    • (2006) Phys Rev B , vol.74 , pp. 075420
    • Campana, C.1    Müser, M.H.2
  • 43
    • 79960635299 scopus 로고    scopus 로고
    • Stiffness of contacts between rough surfaces
    • 10.1103/PhysRevLett.106.204301
    • Akarapu S, Sharp T, Robbins M O. Stiffness of contacts between rough surfaces. Phys Rev Lett 106: 204301 (2011)
    • (2011) Phys Rev Lett , vol.106 , pp. 204301
    • Akarapu, S.1    Sharp, T.2    Robbins, M.O.3
  • 44
    • 79951799771 scopus 로고    scopus 로고
    • Transverse and normal interfacial stiffness of solids with randomly rough surfaces
    • 10.1088/0953-8984/23/8/085001
    • Campana C, Persson B N J., Müser M H. Transverse and normal interfacial stiffness of solids with randomly rough surfaces. J Phys: Condens Matter 23: 085001 (2011)
    • (2011) J Phys: Condens Matter , vol.23 , pp. 085001
    • Campana, C.1    Persson, B.N.J.2    Müser, M.H.3
  • 45
    • 84857878808 scopus 로고    scopus 로고
    • Normal contact stiffness of elastic solids with fractal rough surfaces
    • 10.1103/PhysRevLett.108.104301
    • Pohrt R, Popov V L. Normal contact stiffness of elastic solids with fractal rough surfaces. Phys Rev Lett 108: 104301 (2012)
    • (2012) Phys Rev Lett , vol.108 , pp. 104301
    • Pohrt, R.1    Popov, V.L.2
  • 46
    • 84865325445 scopus 로고    scopus 로고
    • Normal contact stiffness of elastic solids with fractal rough surfaces for one- and three-dimensional systems
    • 10.1103/PhysRevE.86.026710
    • Pohrt R, Popov V L, Filippov A E. Normal contact stiffness of elastic solids with fractal rough surfaces for one- and three-dimensional systems. Phys Rev E 86: 026710 (2012)
    • (2012) Phys Rev E , vol.86 , pp. 026710
    • Pohrt, R.1    Popov, V.L.2    Filippov, A.E.3
  • 47
    • 84976284073 scopus 로고    scopus 로고
    • Contact mechanics of randomly rough self-affine surfaces
    • Pohrt R, Popov V L. Contact mechanics of randomly rough self-affine surfaces. Tribology International, 2013, in press.
    • (2013) Tribology International
    • Pohrt, R.1    Popov, V.L.2
  • 50
    • 77956725245 scopus 로고    scopus 로고
    • Adhesive contribution to the coefficient of friction between rough surfaces
    • 10.1007/s11249-010-9617-1
    • Heise R, Popov V L. Adhesive contribution to the coefficient of friction between rough surfaces. Tribology Letters 39: 247–250 (2010)
    • (2010) Tribology Letters , vol.39 , pp. 247-250
    • Heise, R.1    Popov, V.L.2
  • 51
    • 0001797224 scopus 로고
    • The relation between the friction and viscoelastic properties of rubber
    • 10.1098/rspa.1963.0112
    • Grosch K A. The relation between the friction and viscoelastic properties of rubber. Proc R Soc Lond A 274: 21–39 (1963)
    • (1963) Proc R Soc Lond A , vol.274 , pp. 21-39
    • Grosch, K.A.1
  • 52
    • 79960664443 scopus 로고    scopus 로고
    • Static friction coefficient is not a material constant
    • 10.1103/PhysRevLett.106.254301
    • Ben-David O, Fineberg J. Static friction coefficient is not a material constant. Phys Rev Lett 106: 254301 (2011)
    • (2011) Phys Rev Lett , vol.106 , pp. 254301
    • Ben-David, O.1    Fineberg, J.2
  • 53
    • 0034186935 scopus 로고    scopus 로고
    • Contact modeling — forces
    • 10.1016/S0301-679X(00)00063-3
    • Adams G G, Nosonovsky M. Contact modeling — forces. Tribology International 33: 431–442 (2000)
    • (2000) Tribology International , vol.33 , pp. 431-442
    • Adams, G.G.1    Nosonovsky, M.2
  • 54
    • 84876529827 scopus 로고    scopus 로고
    • Mesoscopic nature of friction and numerical simulation methods in tribology
    • Psakhie S G, Popov V L. Mesoscopic nature of friction and numerical simulation methods in tribology. Physical Mesomechanics 15: 251–253 (2012)
    • (2012) Physical Mesomechanics , vol.15 , pp. 251-253
    • Psakhie, S.G.1    Popov, V.L.2
  • 55
    • 33847264875 scopus 로고    scopus 로고
    • Fractal Tomlinson model for mesoscopic friction: From microscopic velocity-dependent damping to macroscopic Coulomb friction
    • 10.1103/PhysRevE.75.027103
    • Filippov A E, Popov V L. Fractal Tomlinson model for mesoscopic friction: From microscopic velocity-dependent damping to macroscopic Coulomb friction. Physical Review E 75: 027103 (2007)
    • (2007) Physical Review E , vol.75 , pp. 027103
    • Filippov, A.E.1    Popov, V.L.2
  • 56
    • 84976498354 scopus 로고
    • Ein Gedankenmodell zur kinetischen Theorie der festen Körper
    • JFM 54.0847.04, 10.1002/zamm.19280080202
    • Prandtl L. Ein Gedankenmodell zur kinetischen Theorie der festen Körper. ZAMM 8: 85–106 (1928). English translation: Popov V L, Gray J A T. Prandtl-Tomlinson model: History and applications in friction, plasticity, and nanotechnologies. ZAMM 92: 683–708 (2012)
    • (1928) ZAMM , vol.8 , pp. 85-106
    • Prandtl, L.1
  • 57
    • 0033689705 scopus 로고    scopus 로고
    • A theory of the transition from static to kinetic friction in boundary lubrication layers
    • 10.1016/S0038-1098(00)00179-4
    • Popov V L. A theory of the transition from static to kinetic friction in boundary lubrication layers. Solid State Commun 115: 369–373 (2000)
    • (2000) Solid State Commun , vol.115 , pp. 369-373
    • Popov, V.L.1
  • 60
    • 84870336924 scopus 로고    scopus 로고
    • Elastic contact of rough surfaces: A simple criterion to make 2D isotropic roughness equivalent to 1D one
    • 10.1016/j.wear.2012.10.004
    • Scaraggi M, Putignano C, Carbone G. Elastic contact of rough surfaces: A simple criterion to make 2D isotropic roughness equivalent to 1D one. Wear 297: 811–817 (2013)
    • (2013) Wear , vol.297 , pp. 811-817
    • Scaraggi, M.1    Putignano, C.2    Carbone, G.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.