Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Computational Mechanics
Erschienen in: Computational Mechanics 6/2018

02.05.2018 | Original Paper

A model-adaptivity method for the solution of Lennard-Jones based adhesive contact problems

verfasst von: Hachmi Ben Dhia, Shuimiao Du

Erschienen in: Computational Mechanics | Ausgabe 6/2018

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The surface micro-interaction model of Lennard-Jones (LJ) is used for adhesive contact problems (ACP). To address theoretical and numerical pitfalls of this model, a sequence of partitions of contact models is adaptively constructed to both extend and approximate the LJ model. It is formed by a combination of the LJ model with a sequence of shifted-Signorini (or, alternatively, -Linearized-LJ) models, indexed by a shift parameter field. For each model of this sequence, a weak formulation of the associated local ACP is developed. To track critical localized adhesive areas, a two-step strategy is developed: firstly, a macroscopic frictionless (as first approach) linear-elastic contact problem is solved once to detect contact separation zones. Secondly, at each shift-adaptive iteration, a micro-macro ACP is re-formulated and solved within the multiscale Arlequin framework, with significant reduction of computational costs. Comparison of our results with available analytical and numerical solutions shows the effectiveness of our global strategy.
Vorheriger Artikel An enrichment-based approach for the simulation of fretting problems
Nächster Artikel Scalable parallel elastic–plastic finite element analysis using a quasi-Newton method with a balancing domain decomposition preconditioner

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
Anciaux G, Ramisetti SB, Molinari JF (2012) A finite temperature bridging domain method for md-fe coupling and application to a contact problem. Comput Methods Appl Mech Eng 205:204–212CrossRef
2.
3.
Belgacem FB, Hild P, Laborde P (1998) The mortar finite element method for contact problems. Math Comput Model 28(4–8):263–271MathSciNetCrossRef
4.
Ben Dhia H (1988) Modelling and solution by penalty duality method of unilateral contact problems. Calcul Struct Intell Artif 2:3–18
5.
Ben Dhia H (1995) Mathematical analysis of non-linear thin plate problems of mindlin-naghdi-reissner type existence of solutions under optimal hypotheses. C R Acad Sci 1(1):1545–1552MathSciNetMATH
6.
Ben Dhia H (1997) Plaques en grandes transformations élastiques sous contact hyperélastique. In: Actes du 3ème Colloque National de Calcul des Structures, Giens, vol 1, pp 465–470
7.
Ben Dhia H (1998) Multiscale mechanical problems: the Arlequin method. C R Acad Sci Ser IIB Mech Phys Astron 326(12):899–904MATH
8.
Ben Dhia H (1999) Numerical modelling of multiscale problems: the Arlequin method. In: CD Proceedings of ECCM’99, Munchen
9.
Ben Dhia H (2003) Aspects géométriques numériques micro-macro des interfaces. In: Modèles et Lois d’Interface pour le Contact. LMA-Marseilles
10.
Ben Dhia H (2006) Global-local approaches: the Arlequin framework. Eur J Comput Mech 15(1–3):67–80CrossRef
11.
Ben Dhia H (2008) Further insights by theoretical investigations of the multiscale Arlequin method. Int J Multiscale Comput Eng 6(3):215–232CrossRef
12.
Ben Dhia H, Elkhodja N, Roux FX (2008) Multimodeling of multi-alterated structures in the Arlequin framework: solution with a domain-decomposition solver. Eur J Comput Mech 17(5–7):969–980CrossRef
13.
Ben Dhia H, Rateau G (2001) Mathematical analysis of the mixed Arlequin method. C R Acad Sci Ser I Math 332(7):649–654MathSciNetMATH
14.
Ben Dhia H, Rateau G (2005) The Arlequin method as a flexible engineering design tool. Int J Numer Meth Eng 62(11):1442–1462CrossRef
15.
Ben Dhia H, Torkhani M (2011) Modeling and computation of fretting wear of structures under sharp contact. Int J Numer Meth Eng 85(1):61–83CrossRef
16.
Ben Dhia H, Torkhani M, Zammali C (2005) Modèle d’interface multi-niveau pour les problèmes de contact. In: Colloque National de Calcul des Structures, Giens 2005, vol 1. Hermès Lavoisier, pp 63–68
17.
Ben Dhia H, Zammali C (2004) Level-sets and Arlequin framework for dynamic contact problems. Rev Eur Elem 13(5–7):403–414MATH
18.
Ben Dhia H, Zammali C (2007) Level-sets fields, placement and velocity based formulations of contact-impact problems. Int J Numer Meth Eng 69(13):2711–2735MathSciNetCrossRef
19.
Ben Dhia H, Zarroug M (2002) Contact in the Arlequin framework. In: Contact mechanics. Springer, pp 403–410
20.
Ben Dhia H, Zarroug M (2002) Hybrid frictional contact particles-in elements. Rev Eur Elem 11(2–4):417–430MATH
21.
Boussinesq J (1885) Application des potentiels à l’étude de l’équilibre et du mouvement des solides élastiques. Gauthier-Villars, Paris
22.
Bradley RS (1932) Lxxix. The cohesive force between solid surfaces and the surface energy of solids. Philos Mag J Sci 13(86):853–862CrossRef
23.
Brezzi F (1974) On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. Rev Fr Automat Inf Rech Oper Anal Numer 8(R2):129–151MathSciNetMATH
24.
Cappella B, Dietler G (1999) Force-distance curves by atomic force microscopy. Surf Sci Rep 34(1–3):15–3104
25.
Derjaguin BV (1934) Untersuchungen über die reibung und adhäsion, iv. Colloid Polym Sci 69(2):155–164
26.
Derjaguin BV, Muller VM, Toporov YP (1975) Effect of contact deformations on the adhesion of particles. J Colloid Interface Sci 53(2):314–326CrossRef
27.
Dimitri R, De Lorenzis L, Scott M, Wriggers P, Taylor R, Zavarise G (2014) Isogeometric large deformation frictionless contact using t-splines. Comput Methods Appl Mech Eng 269:394–414MathSciNetCrossRef
28.
Feng JQ (2000) Contact behavior of spherical elastic particles: a computational study of particle adhesion and deformations. Colloids Surf A 172(1):175–198CrossRef
29.
Feng JQ (2001) Adhesive contact of elastically deformable spheres: a computational study of pull-off force and contact radius. J Colloid Interface Sci 238(2):318–323CrossRef
30.
31.
Greenwood J, Williamson JP (1966) Contact of nominally flat surfaces. Proc R Soc Lond A Math Phys Eng Sci 295:300–319CrossRef
32.
Hoang TV, Wu L, Paquay S, Golinval JC, Arnst M, Noels L (2017) A computational stochastic multiscale methodology for mems structures involving adhesive contact. Tribol Int 110:401–425CrossRef
33.
Johnson K (1987) Contact mechanics. Cambridge University Press, Cambridge
34.
35.
Johnson K, Kendall K, Roberts A (1971) Surface energy and the contact of elastic solids. Proc R Soc Lond A Math Phys Eng Sci 324(1558):301–313CrossRef
36.
Kloosterman G, van Damme RM, van den Boogaard AH, Huetink J (2001) A geometrical-based contact algorithm using a barrier method. Int J Numer Meth Eng 51(7):865–882MathSciNetCrossRef
37.
Konyukhov A, Schweizerhof K (2008) On the solvability of closest point projection procedures in contact analysis: analysis and solution strategy for surfaces of arbitrary geometry. Comput Methods Appl Mech Eng 197(33):3045–3056MathSciNetCrossRef
38.
Laursen TA (2003) Computational contact and impact mechanics: fundamentals of modelling interfacial phenomena in nonlinear finite element analysis. Springer, BerlinCrossRef
39.
Maday Y, Mavriplis C, Patera A (1989) Nonconforming mortar element methods: application to spectral discretizations. In: Chan T, Glowinski R, Periaux J, Widlund OB (eds) Domain decomposition methods. SIAM, Philadelphia, pp 392–418
40.
Maugis D (1992) Adhesion of spheres: the jkr-dmt transition using a dugdale model. J Colloid Interface Sci 150(1):243–269CrossRef
41.
Medina S, Dini D (2014) A numerical model for the deterministic analysis of adhesive rough contacts down to the nano-scale. Int J Solids Struct 51(14):2620–2632CrossRef
42.
Muller V, Yushchenko V, Derjaguin B (1980) On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane. J Colloid Interface Sci 77(1):91–101CrossRef
43.
Puso MA, Laursen TA (2004) A mortar segment-to-segment contact method for large deformation solid mechanics. Comput Methods Appl Mech Eng 193(6):601–629CrossRef
44.
Qian D, Wagner GJ, Liu WK, Yu MF, Ruoff RS (2002) Mechanics of carbon nanotubes. Appl Mech Rev 55(6):495–533CrossRef
45.
Sauer RA (2011) Enriched contact finite elements for stable peeling computations. Int J Numer Methods Eng 87(6):593–616MathSciNetCrossRef
46.
Sauer RA (2016) A survey of computational models for adhesion. J Adhes 92(2):81–120CrossRef
47.
Sauer RA, Li S (2007) An atomic interaction-based continuum model for adhesive contact mechanics. Finite Elem Anal Des 43(5):384–396MathSciNetCrossRef
48.
Sauer RA, Li S (2007) An atomic interaction-based continuum model for computational multiscale contact mechanics. PAMM 7(1):4080,029–4080,030CrossRef
49.
Tabor D (1977) Surface forces and surface interactions. J Colloid Interface Sci 58(1):2–13CrossRef
50.
Tur M, Giner E, Fuenmayor F, Wriggers P (2012) 2d contact smooth formulation based on the mortar method. Comput Methods Appl Mech Eng 247:1–14MathSciNetCrossRef
51.
Wellmann C, Wriggers P (2011) A concurrent multiscale approach to non-cohesive granular materials. In: Recent developments and innovative applications in computational mechanics. Springer, pp 257–264
52.
53.
Wriggers P (2006) Computational contact mechanics, 2nd edn. Springer, BerlinCrossRef
54.
55.
Wu JJ (2006) Nanoadhesion between a rigid circular disc and an infinite elastic surface. Int J Solids Struct 43(6):1624–1637CrossRef
56.
Zavarise G, Wriggers P, Schrefler B (1998) A method for solving contact problems. Int J Numer Methods Eng 42(3):473–498CrossRef
Metadaten
Titel
A model-adaptivity method for the solution of Lennard-Jones based adhesive contact problems
verfasst von
Hachmi Ben Dhia
Shuimiao Du
Publikationsdatum
02.05.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 6/2018
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-018-1578-5

Weitere Artikel der Ausgabe 6/2018

Computational Mechanics 6/2018 Zur Ausgabe

Original Paper

Meshfree truncated hierarchical refinement for isogeometric analysis

Original Paper

Scalable parallel elastic–plastic finite element analysis using a quasi-Newton method with a balancing domain decomposition preconditioner

Original Paper

An enrichment-based approach for the simulation of fretting problems

Original Paper

Stochastic hyperelastic modeling considering dependency of material parameters

Original Paper

Modelling multiple cycles of static and dynamic recrystallisation using a fully implicit isotropic material model based on dislocation density

Original Paper

Numerical evaluation of discontinuous and nonconforming finite element methods in nonlinear solid mechanics

Neuer Inhalt

    Bildnachweise