Skip to main content
Erschienen in: Experimental Mechanics 4/2019

06.02.2019

Deformation Field in Diametrically Loaded Soft Cylinders

verfasst von: T.L. Vu, J. Barés, S. Mora, S. Nezamabadi

Erschienen in: Experimental Mechanics | Ausgabe 4/2019

Einloggen

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

search-config
loading …

Abstract

Deformation fields at the surface of diametrically squeezed shallow cylinders in the large deformation regime are measured experimentally and numerically for different material behaviour in the large deformation regime. By means of a digital image correlation method optimized for large displacements, strain fields are measured and compared with finite element simulations. Assuming a neo-Hookean behaviour for cylinders made of rubber silicone, the strain field is found to be in quantitative agreement with non-linear finite element simulations up to the highest deformations reached in our experiments (15%). For materials that follow an elastoplastic constitutive law, agreement is lost after few percents of deformation and location of the strain field differences are identified up to strains as high as 30%. Strain field evolution is also measured for solid foam cylinders up to 60% of global deformation strain. This method that can be applied to a broad variety of materials, even in the occurrence of large deformations, provides a way to study quantitatively local features of the mechanical contact.

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!

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!

Literatur
1.
Zurück zum Zitat Archard JF (1957) Elastic deformation and the laws of friction. In: Proceedings of the royal society of london a: mathematical, physical and engineering sciences, vol 243. The Royal Society, pp 190–205 Archard JF (1957) Elastic deformation and the laws of friction. In: Proceedings of the royal society of london a: mathematical, physical and engineering sciences, vol 243. The Royal Society, pp 190–205
2.
Zurück zum Zitat Lincoln B (1953) Elastic deformation and the laws of friction. Nature 172:169–170CrossRef Lincoln B (1953) Elastic deformation and the laws of friction. Nature 172:169–170CrossRef
3.
Zurück zum Zitat Johnson KL (1987) Contact Mechanics. Cambridge University Press, Cambridge Johnson KL (1987) Contact Mechanics. Cambridge University Press, Cambridge
4.
Zurück zum Zitat Derjaguin B, Muller V, Toporov Y (1975) Effect of contact deformations on the adhesion of particles. J Colloid Interface Sci 53:314–326CrossRef Derjaguin B, Muller V, Toporov Y (1975) Effect of contact deformations on the adhesion of particles. J Colloid Interface Sci 53:314–326CrossRef
5.
Zurück zum Zitat Johnson K, Kendall K, Roberts A (1971) Surface energy and the contact of elastic solids. Proc R Soc London A 324:301–313CrossRef Johnson K, Kendall K, Roberts A (1971) Surface energy and the contact of elastic solids. Proc R Soc London A 324:301–313CrossRef
6.
Zurück zum Zitat Maugis D (2000) Contact, adhesion and rupture of elastic solids springer Maugis D (2000) Contact, adhesion and rupture of elastic solids springer
7.
Zurück zum Zitat Butt HJ, Cappella B, Kappl M (2005) Force measurements with the atomic force microscope: technique, interpretation and applications. Surf Sci Rep 59:1–152CrossRef Butt HJ, Cappella B, Kappl M (2005) Force measurements with the atomic force microscope: technique, interpretation and applications. Surf Sci Rep 59:1–152CrossRef
8.
Zurück zum Zitat Dimitriadis EK, Horkay F, Maresca J, Kachar B, Chadwick RS (2002) Determination of elastic moduli of thin layers of soft material using the atomic force microscope. Biophys J 82:2798–2810CrossRef Dimitriadis EK, Horkay F, Maresca J, Kachar B, Chadwick RS (2002) Determination of elastic moduli of thin layers of soft material using the atomic force microscope. Biophys J 82:2798–2810CrossRef
9.
Zurück zum Zitat Brodu N, Dijksman JA, Behringer RP (2015) Spanning the scales of granular materials through microscopic force imaging. Nat Commun 6:6361CrossRef Brodu N, Dijksman JA, Behringer RP (2015) Spanning the scales of granular materials through microscopic force imaging. Nat Commun 6:6361CrossRef
10.
Zurück zum Zitat Favier de Coulomb A, Bouzid M, Claudin P, Clément E, Andreotti B (2017) Rheology of granular flows across the transition from soft to rigid particles. Physical Review Fluids 2:102301CrossRef Favier de Coulomb A, Bouzid M, Claudin P, Clément E, Andreotti B (2017) Rheology of granular flows across the transition from soft to rigid particles. Physical Review Fluids 2:102301CrossRef
11.
Zurück zum Zitat Majmudar TS, Behringer RP (2005) Contact force measurements and stress-induced anisotropy in granular materials. Nature 435:1079–1082CrossRef Majmudar TS, Behringer RP (2005) Contact force measurements and stress-induced anisotropy in granular materials. Nature 435:1079–1082CrossRef
12.
Zurück zum Zitat O’Sullivan C (2011) Particulate discrete element modelling: a geomechanics perspective. Taylor & Francis O’Sullivan C (2011) Particulate discrete element modelling: a geomechanics perspective. Taylor & Francis
13.
Zurück zum Zitat Radjai F, Jean M, Moreau JJ, Roux S (1996) Force distributions in dense two-dimensional granular systems. Phys Rev Lett 77:274–277CrossRef Radjai F, Jean M, Moreau JJ, Roux S (1996) Force distributions in dense two-dimensional granular systems. Phys Rev Lett 77:274–277CrossRef
14.
Zurück zum Zitat Langston PA, üzün TU, Heyes DM (1995) Discrete element simulation of granular flow in 2d and 3d hoppers: dependence of discharge rate and wall stress on particle interactions. Chem Eng Sci 50:967–987CrossRef Langston PA, üzün TU, Heyes DM (1995) Discrete element simulation of granular flow in 2d and 3d hoppers: dependence of discharge rate and wall stress on particle interactions. Chem Eng Sci 50:967–987CrossRef
15.
Zurück zum Zitat Tutuncu AN, Sharma MM (1992) The influence of fluids on grain contact stiffness and frame moduli in sedimentary rocks. Geophysics 57:1571–1582CrossRef Tutuncu AN, Sharma MM (1992) The influence of fluids on grain contact stiffness and frame moduli in sedimentary rocks. Geophysics 57:1571–1582CrossRef
16.
Zurück zum Zitat Lin DC, Shreiber DI, Dimitriadis EK, Horkay F (2009) Spherical indentation of soft matter beyond the hertzian regime: numerical and experimental validation of hyperelastic models. Biomech Model Mechanobiol 8:345CrossRef Lin DC, Shreiber DI, Dimitriadis EK, Horkay F (2009) Spherical indentation of soft matter beyond the hertzian regime: numerical and experimental validation of hyperelastic models. Biomech Model Mechanobiol 8:345CrossRef
17.
Zurück zum Zitat Tatara Y (1991) On compression of rubber elastic sphere over a large range of displacements—part 1: theoretical study. J Eng Mater Technol 113:285–291CrossRef Tatara Y (1991) On compression of rubber elastic sphere over a large range of displacements—part 1: theoretical study. J Eng Mater Technol 113:285–291CrossRef
18.
Zurück zum Zitat Liu K, Williams D, Briscoe B (1998) The large deformation of a single micro-elastomeric sphere. J Phys D Appl Phys 31:294CrossRef Liu K, Williams D, Briscoe B (1998) The large deformation of a single micro-elastomeric sphere. J Phys D Appl Phys 31:294CrossRef
19.
Zurück zum Zitat Chaudhri M, Hutchings I, Makin P (1984) Plastic compression of spheres. Philos Mag A 49:493–503CrossRef Chaudhri M, Hutchings I, Makin P (1984) Plastic compression of spheres. Philos Mag A 49:493–503CrossRef
20.
Zurück zum Zitat Noyan I (1988) Plastic deformation of solid spheres. Philos Mag A 57:127–141CrossRef Noyan I (1988) Plastic deformation of solid spheres. Philos Mag A 57:127–141CrossRef
21.
Zurück zum Zitat Liu KK (2006) Deformation behaviour of soft particles: a review. J Phys D Appl Phys 39:R189CrossRef Liu KK (2006) Deformation behaviour of soft particles: a review. J Phys D Appl Phys 39:R189CrossRef
22.
Zurück zum Zitat Shull KR (2002) Contact mechanics and the adhesion of soft solids. Materials Science and Engineering: R: Reports 36:1– 45CrossRef Shull KR (2002) Contact mechanics and the adhesion of soft solids. Materials Science and Engineering: R: Reports 36:1– 45CrossRef
23.
Zurück zum Zitat Galindo-Torres SA, Pedroso DM, Williams DJ, Li L (2012) Breaking processes in three-dimensional bonded granular materials with general shapes. Comput Phys Commun 183:266–277CrossRef Galindo-Torres SA, Pedroso DM, Williams DJ, Li L (2012) Breaking processes in three-dimensional bonded granular materials with general shapes. Comput Phys Commun 183:266–277CrossRef
24.
Zurück zum Zitat Menut P, Seiffert S, Sprakel J, Weitz DA (2012) Does size matter? elasticity of compressed suspensions of colloidal-and granular-scale microgels. Soft Matter 8:156–164CrossRef Menut P, Seiffert S, Sprakel J, Weitz DA (2012) Does size matter? elasticity of compressed suspensions of colloidal-and granular-scale microgels. Soft Matter 8:156–164CrossRef
25.
Zurück zum Zitat Ouhbi N, Voivret C, Perrin G, Roux JN (2016) Railway ballast: grain shape characterization to study its influence on the mechanical behaviour. Procedia Eng 143:1120–1127CrossRef Ouhbi N, Voivret C, Perrin G, Roux JN (2016) Railway ballast: grain shape characterization to study its influence on the mechanical behaviour. Procedia Eng 143:1120–1127CrossRef
26.
Zurück zum Zitat Romeo G, Ciamarra MP (2013) Elasticity of compressed microgel suspensions. Soft Matter 9:5401–5406CrossRef Romeo G, Ciamarra MP (2013) Elasticity of compressed microgel suspensions. Soft Matter 9:5401–5406CrossRef
27.
Zurück zum Zitat Lin YL, Wang DM, Lu WM, Lin YS, Tung KL (2008) Compression and deformation of soft spherical particles. Chem Eng Sci 63:195–203CrossRef Lin YL, Wang DM, Lu WM, Lin YS, Tung KL (2008) Compression and deformation of soft spherical particles. Chem Eng Sci 63:195–203CrossRef
28.
Zurück zum Zitat Mora S, Maurini C, Phou T, Fromental J, Audoly B, Pomeau Y (2014) Solid drops: large capillary deformations of immersed elastic rods. Phys Rev Lett 113:178301CrossRef Mora S, Maurini C, Phou T, Fromental J, Audoly B, Pomeau Y (2014) Solid drops: large capillary deformations of immersed elastic rods. Phys Rev Lett 113:178301CrossRef
29.
Zurück zum Zitat Mora S, Pomeau Y (2015) Softening of edges of solids by surface tension. J Phys Condens Matter 27:194112CrossRef Mora S, Pomeau Y (2015) Softening of edges of solids by surface tension. J Phys Condens Matter 27:194112CrossRef
30.
Zurück zum Zitat Mora S, Vu TL, Barés J, Nezamabadi S (2017) Highly deformed grain: from the hertz contact limitation to a new strain field description in 2d. EPJ Web of Conference 140:05011CrossRef Mora S, Vu TL, Barés J, Nezamabadi S (2017) Highly deformed grain: from the hertz contact limitation to a new strain field description in 2d. EPJ Web of Conference 140:05011CrossRef
31.
Zurück zum Zitat Bornert M, Brémand F, Doumalin P, Dupré JC, Fazzini M, Grédiac M, Hild F, Mistou S, Molimard J, Orteu JJ, Robert L, Surrel Y, Vacher P, Wattrisse B (2009) Assessment of digital image correlation measurement errors: methodology and results. Exp Mech 49:353–370CrossRef Bornert M, Brémand F, Doumalin P, Dupré JC, Fazzini M, Grédiac M, Hild F, Mistou S, Molimard J, Orteu JJ, Robert L, Surrel Y, Vacher P, Wattrisse B (2009) Assessment of digital image correlation measurement errors: methodology and results. Exp Mech 49:353–370CrossRef
32.
Zurück zum Zitat Hild F, Roux S (2006) Digital image correlation: from displacement measurement to identification of elastic properties–a review. Strain 42:69–80CrossRef Hild F, Roux S (2006) Digital image correlation: from displacement measurement to identification of elastic properties–a review. Strain 42:69–80CrossRef
33.
Zurück zum Zitat Pan B, Qian K, Xie H, Asundi A (2009) Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Meas Sci Technol 20:062001CrossRef Pan B, Qian K, Xie H, Asundi A (2009) Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Meas Sci Technol 20:062001CrossRef
34.
Zurück zum Zitat Stanier S, Blaber J, Take WA, White D (2016) Improved image-based deformation measurement for geotechnical applications. Can Geotech J 53:727–739CrossRef Stanier S, Blaber J, Take WA, White D (2016) Improved image-based deformation measurement for geotechnical applications. Can Geotech J 53:727–739CrossRef
35.
Zurück zum Zitat Tang Z, Liang J, Xiao Z, Guo C (2012) Large deformation measurement scheme for 3d digital image correlation method. Opt Lasers Eng 50:122–130CrossRef Tang Z, Liang J, Xiao Z, Guo C (2012) Large deformation measurement scheme for 3d digital image correlation method. Opt Lasers Eng 50:122–130CrossRef
36.
Zurück zum Zitat Lagarias JC, Reeds JA, Wright MH, Wright PE (1998) Convergence properties of the nelder–mead simplex method in low dimensions. SIAM J Optim 9:112–147MathSciNetCrossRefMATH Lagarias JC, Reeds JA, Wright MH, Wright PE (1998) Convergence properties of the nelder–mead simplex method in low dimensions. SIAM J Optim 9:112–147MathSciNetCrossRefMATH
38.
Zurück zum Zitat Taforel P, Renouf M, Dubois F, Voivret C (2015) Finite Element-Discrete element coupling strategies for the modelling of Ballast-Soil interaction. Journal of Railway Technology 4:73–95CrossRef Taforel P, Renouf M, Dubois F, Voivret C (2015) Finite Element-Discrete element coupling strategies for the modelling of Ballast-Soil interaction. Journal of Railway Technology 4:73–95CrossRef
39.
Zurück zum Zitat Holzapfel AG (2000) Nonlinear Solid Mechanics: a Continuum Approach for Engineering. Wiley, LondonMATH Holzapfel AG (2000) Nonlinear Solid Mechanics: a Continuum Approach for Engineering. Wiley, LondonMATH
40.
Zurück zum Zitat Nezamabadi S, Zahrouni H, Yvonnet J (2011) Solving hyperelastic material problems by asymptotic numerical method. Comput Mech 47:77–92MathSciNetCrossRefMATH Nezamabadi S, Zahrouni H, Yvonnet J (2011) Solving hyperelastic material problems by asymptotic numerical method. Comput Mech 47:77–92MathSciNetCrossRefMATH
41.
Zurück zum Zitat (2009) ANSYS theory reference for the mechanical APDL and mechanical applications. ANSYS Inc. (2009) ANSYS theory reference for the mechanical APDL and mechanical applications. ANSYS Inc.
42.
Zurück zum Zitat Gong L, Kyriakides S, Triantafyllidis N (2005) On the stability of kelvin cell foams under compressive loads. J Mech Phys Solids 53:771–794CrossRefMATH Gong L, Kyriakides S, Triantafyllidis N (2005) On the stability of kelvin cell foams under compressive loads. J Mech Phys Solids 53:771–794CrossRefMATH
43.
Zurück zum Zitat Pampolini G, Del Piero G (2008) Strain localization in open-cell polyurethane foams: experiments and theoretical model. J Mech Mater Struct 3:969–981CrossRefMATH Pampolini G, Del Piero G (2008) Strain localization in open-cell polyurethane foams: experiments and theoretical model. J Mech Mater Struct 3:969–981CrossRefMATH
Metadaten
Titel
Deformation Field in Diametrically Loaded Soft Cylinders
verfasst von
T.L. Vu
J. Barés
S. Mora
S. Nezamabadi
Publikationsdatum
06.02.2019
Verlag
Springer US
Erschienen in
Experimental Mechanics / Ausgabe 4/2019
Print ISSN: 0014-4851
Elektronische ISSN: 1741-2765
DOI
https://doi.org/10.1007/s11340-019-00477-4

Weitere Artikel der Ausgabe 4/2019

Experimental Mechanics 4/2019 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.