https://orcid.org/0000-0001-7421-0500
Abstract
Contact interactions play an important role in the tribological behavior of engineering materials. This paper develops a finite element model to investigate the contact mechanics and stress distribution of auxetic materials, i.e., materials with negative Poisson’s ratio. The model results are compared with numerical and mathematical models for isotropic auxetic polymers. The indentation of auxetic materials is analyzed for the effects of friction, plasticity and allowing separation after contact with a spherical indenter using a commercial software, abaqus. The results are discussed in terms of stress profiles, force-indentation depth curves, plasticity, friction, internal energy, compressibility, sink-in, and the pile-up of material. It is concluded that for purely elastic contact, the indentation resistance increases for auxetic materials and the inclusion of friction shifts subsurface stresses closer to the surface. However, the introduction of plasticity negates the improvement of increased indentation resistance. The pile-up of material around the indent reduces for auxetic materials which makes them more suitable for rolling/sliding contacts. The internal strain energy decreases for purely elastic contact and increases for an elastic/plastic contact.
Issue Section:
Contact Mechanics
References
1.
Kumar
, N.
, Khaderi
, S. N.
, and Tirumala Rao
, K.
, 2020
, “Elasto-Plastic Indentation of Auxetic and Metal Foams
,” ASME J. Appl. Mech.
, 87
(1
), p. 011006
. 10.1115/1.40450022.
Lakes
, R.
, 1987
, “Foam Structures With a Negative Poisson’s Ratio
,” Science
, 235
(4792
), pp. 1038
–1040
. 10.1126/science.235.4792.10383.
Argatov
, I. I.
, Guinovart-Díaz
, R.
, and Sabina
, F. J.
, 2012
, “On Local Indentation and Impact Compliance of Isotropic Auxetic Materials From the Continuum Mechanics Viewpoint
,” Int. J. Eng. Sci.
, 54
, pp. 42
–57
. 10.1016/j.ijengsci.2012.01.0104.
Carneiro
, V. H.
, Meireles
, J.
, and Puga
, H.
, 2013
, “Auxetic Materials—A Review
,” Mater. Sci. Pol.
, 31
(4
), pp. 561
–571
. 10.2478/s13536-013-0140-65.
Ali
, M. N.
, Busfield
, J. J. C.
, and Rehman
, I. U.
, 2014
, “Auxetic Oesophageal Stents: Structure and Mechanical Properties
,” J. Mater. Sci. Mater. Med.
, 25
(2
), pp. 527
–553
. 10.1007/s10856-013-5067-26.
Kuribayashi
, K.
, Tsuchiya
, K.
, You
, Z.
, Tomus
, D.
, Umemoto
, M.
, Ito
, T.
, and Sasaki
, M.
, 2006
, “Self-Deployable Origami Stent Grafts as a Biomedical Application of Ni-Rich TiNi Shape Memory Alloy Foil
,” Mater. Sci. Eng. A
, 419
(1–2
), pp. 131
–137
. 10.1016/j.msea.2005.12.0167.
Bianchi
, M.
, Scarpa
, F. L.
, and Smith
, C. W.
, 2008
, “Stiffness and Energy Dissipation in Polyurethane Auxetic Foams
,” J. Mater. Sci.
, 43
(17
), pp. 5851
–5860
. 10.1007/s10853-008-2841-58.
Bezazi
, A.
, Boukharouba
, W.
, and Scarpa
, F.
, 2009
, “Mechanical Properties of Auxetic Carbon/Epoxy Composites: Static and Cyclic Fatigue Behaviour
,” Phys. Status Solidi Basic Res.
, 246
(9
), pp. 2102
–2110
. 10.1002/pssb.2009820429.
Donoghue
, J. P.
, Alderson
, K. L.
, and Evans
, K. E.
, 2009
, “The Fracture Toughness of Composite Laminates With a Negative Poisson’s Ratio
,” Phys. Status Solidi Basic Res.
, 246
(9
), pp. 2011
–2017
. 10.1002/pssb.20098203110.
Lakes
, R. S.
, and Elms
, K.
, 1993
, “Indentability of Conventional and Negative Poisson’s Ratio Foams
,” J. Compos. Mater.
, 27
(12
), pp. 1193
–1202
. 10.1177/00219983930270120311.
Alderson
, K. L.
, Fitzgerald
, A.
, and Evans
, K. E.
, 2000
, “The Strain Dependent Indentation Resilience of Auxetic Microporous Polyethylene
,” J. Mater. Sci.
, 35
(16
), pp. 4039
–4047
. 10.1023/A:100483010341112.
Yang
, W.
, Li
, Z. M.
, Shi
, W.
, Xie
, B. H.
, and Yang
, M. B.
, 2004
, “On Auxetic Materials
,” J. Mater. Sci.
, 39
(10
), pp. 3269
–3279
. 10.1023/B:JMSC.0000026928.93231.e013.
Photiou
, D.
, Prastiti
, N.
, Sarris
, E.
, and Constantinides
, G.
, 2016
, “On the Conical Indentation Response of Elastic Auxetic Materials: Effects of Poisson’s Ratio, Contact Friction and Cone Angle
,” Int. J. Solids Struct.
, 81
, pp. 33
–42
. 10.1016/j.ijsolstr.2015.10.02014.
Alderson
, K. L.
, Simkins
, V. R.
, Coenen
, V. L.
, Davies
, P. J.
, Alderson
, A.
, and Evans
, K. E.
, 2005
, “How to Make Auxetic Fibre Reinforced Composites
,” Phys. Status Solidi Basic Res.
, 242
(3
), pp. 509
–518
. 10.1002/pssb.20046037115.
Yang
, S.
, Qi
, C.
, Wang
, D.
, Gao
, R.
, Hu
, H.
, and Shu
, J.
, 2013
, “A Comparative Study of Ballistic Resistance of Sandwich Panels With Aluminum Foam and Auxetic Honeycomb Cores
,” Adv. Mech. Eng.
, 5
, pp. 1
–15
.16.
Prawoto
, Y.
, 2012
, “Seeing Auxetic Materials From the Mechanics Point of View: A Structural Review on the Negative Poisson’s Ratio
,” Comput. Mater. Sci.
, 58
, pp. 140
–153
. 10.1016/j.commatsci.2012.02.01217.
Mir
, M.
, Ali
, M. N.
, Sami
, J.
, and Ansari
, U.
, 2014
, “Review of Mechanics and Applications of Auxetic Structures
,” Adv. Mater. Sci. Eng.
, 2014
, pp. 1
–17
. 10.1155/2014/75349618.
Strek
, T.
, Maruszewski
, B.
, Narojczyk
, J. W.
, and Wojciechowski
, K. W.
, 2008
, “Finite Element Analysis of Auxetic Plate Deformation
,” J. Non-Cryst. Solids
, 354
(35–39
), pp. 4475
–4480
. 10.1016/j.jnoncrysol.2008.06.08719.
Ge
, Z.
, Hu
, H.
, and Liu
, Y.
, 2013
, “A Finite Element Analysis of a 3D Auxetic Textile Structure for Composite Reinforcement
,” Smart Mater. Struct.
, 22
(8
), p. 084005
. 10.1088/0964-1726/22/8/08400520.
Taljat
, B.
, and Pharr
, G. M.
, 2004
, “Development of Pile-Up During Spherical Indentation of Elastic-Plastic Solids
,” Int. J. Solids Struct.
, 41
(14
), pp. 3891
–3904
. 10.1016/j.ijsolstr.2004.02.03321.
Taljat
, B.
, Zacharia
, T.
, and Pharr
, G. M.
, 1998
, “Pile-Up Behavior of Spherical Indentations in Engineering Materials
,” Mater. Res. Soc. Symp.—Proc.
, 522
, pp. 33
–38
. 10.1557/PROC-522-3322.
Dirrenberger
, J.
, Forest
, S.
, and Jeulin
, D.
, 2012
, “Elastoplasticity of Auxetic Materials
,” Comput. Mater. Sci.
, 64
, pp. 57
–61
. 10.1016/j.commatsci.2012.03.03623.
Zhang
, J.
, Lu
, G.
, Ruan
, D.
, and Wang
, Z.
, 2018
, “Tensile Behavior of an Auxetic Structure: Analytical Modeling and Finite Element Analysis
,” Int. J. Mech. Sci.
, 136
, pp. 143
–154
. 10.1016/j.ijmecsci.2017.12.02924.
Liu
, S.
, Lu
, G.
, Chen
, Y.
, and Leong
, Y. W.
, 2015
, “Deformation of the Miura-Ori Patterned Sheet
,” Int. J. Mech. Sci.
, 99
, pp. 130
–142
. 10.1016/j.ijmecsci.2015.05.00925.
Bianchi
, M.
, Scarpa
, F.
, Banse
, M.
, and Smith
, C. W.
, 2011
, “Novel Generation of Auxetic Open Cell Foams for Curved and Arbitrary Shapes
,” Acta Mater.
, 59
(2
), pp. 686
–691
. 10.1016/j.actamat.2010.10.00626.
Duncan
, O.
, Shepherd
, T.
, Moroney
, C.
, Foster
, L.
, Venkatraman
, P. D.
, Winwood
, K.
, Allen
, T.
, and Alderson
, A.
, 2018
, “Review of Auxetic Materials for Sports Applications: Expanding Options in Comfort and Protection
,” Appl. Sci.
, 8
(6
), p. 941
. 10.3390/app806094127.
Needleman
, A.
, Tvergaard
, V.
, and Van der Giessen
, E.
, 2015
, “Indentation of Elastically Soft and Plastically Compressible Solids
,” Acta Mech. Sin.
, 31
(4
), pp. 473
–480
. 10.1007/s10409-015-0467-928.
Deshpande
, V. S.
, and Fleck
, N. A.
, 2000
, “Isotropic Constitutive Models for Metallic Foams
,” J. Mech. Phys. Solids
, 48
(6
), pp. 1253
–1283
. 10.1016/S0022-5096(99)00082-429.
Ghaednia
, H.
, Wang
, X.
, Saha
, S.
, Xu
, Y.
, Sharma
, A.
, and Jackson
, R. L.
, 2017
, “A Review of Elastic-Plastic Contact Mechanics
,” ASME Appl. Mech. Rev.
, 69
(6
), p. 060804
. 10.1115/1.403818730.
Cheng
, C. M.
, and Cheng
, Y. T.
, 1997
, “On the Initial Unloading Slope in Indentation of Elastic-Plastic Solids by an Indenter With an Axisymmetric Smooth Profile
,” Appl. Phys. Lett.
, 71
(18
), pp. 2623
–2625
. 10.1063/1.12015931.
Johnson
, K. L.
, and Keer
, L. M.
, 2011
, “Contact Mechanics of Nanometer-Scale Molecular Contacts: Correlation Between Adhesion, Friction, and Hydrogen Bond Thermodynamics
,” J. Am. Chem. Soc.
, 133
(22
), pp. 8625
–8632
. 10.1021/ja201114332.
Mossakovskii
, V. I.
, 1963
, “Compression of Elastic Bodies Under Conditions of Adhesion (Axisymmetric Case)
,” J. Appl. Math. Mech.
, 27
(3
), pp. 630
–643
. 10.1016/0021-8928(63)90150-333.
Ramírez
, M.
, Nava-Gómez
, G. G.
, Sabina
, F. J.
, Camacho-Montes
, H.
, Guinovart-Díaz
, R.
, Rodríguez-Ramos
, R.
, and Bravo-Castillero
, J.
, 2012
, “Enhancement of Young’s Moduli and Auxetic Windows in Laminates With Isotropic Constituents
,” Int. J. Eng. Sci.
, 58
, pp. 95
–114
. 10.1016/j.ijengsci.2012.03.02934.
Argatov
, I. I.
, 2006
, “The Solution of the Hertz Axisymmetric Contact Problem
,” J. Appl. Math. Mech.
, 70
(4
), pp. 621
–635
. 10.1016/j.jappmathmech.2006.09.01335.
Lakes
, R. S.
, 1993
, “Design Considerations for Negative Poisson’s Ratio Materials
,” ASME J. Mech. Des.
, 115
(4
), pp. 696
–700
. 10.1115/1.291925636.
Borodich
, F. M.
, and Keer
, L. M.
, 2004
, “Contact Problems and Depth-Sensing Nanoindentation for Frictionless and Frictional Boundary Conditions
,” Int. J. Solids Struct.
, 41
(9–10
), pp. 2479
–2499
. 10.1016/j.ijsolstr.2003.12.01237.
Borodich
, F. M.
, and Keer
, L. M.
, 2004
, “Evaluation of Elastic Modulus of Materials by Adhesive (No-Slip) Nano-Indentation
,” Proc. R. Soc. A Math. Phys. Eng. Sci.
, 460
(2042
), pp. 507
–514
. 10.1098/rspa.2003.122438.
Huber
, M. T.
, 1904
, “Zur Theorie Der Berührung Fester Elastischer Körper
,” Ann. Phys.
, 319
(6
), pp. 153
–163
. 10.1002/andp.1904319061139.
Struchtrup
, H.
, 2014
, “The First Law of Thermodynamics,” Thermodynamics and Energy Conversion
, Springer
, Berlin/Heidelberg
, pp. 33
–53
.40.
SIMULIA
, 2011
, ABAQUS Analysis User’s Manual (version 6.11)
, Dassault Systèmes Simulia Corp
, Providence, RI
. http://130.149.89.49:2080/v6.11/index.html41.
Stepanov
, I. A.
, 2013
, “The First Law of Thermodynamics for Auxetic Materials
,” J. Non-Cryst. Solids
, 367
(1
), pp. 51
–52
. 10.1016/j.jnoncrysol.2013.02.01742.
Yan
, W.
, and Pun
, C. L.
, 2010
, “Spherical Indentation of Metallic Foams
,” Mater. Sci. Eng. A
, 527
(13–14
), pp. 3166
–3175
. 10.1016/j.msea.2010.01.06843.
Baroutaji
, A.
, Arjunan
, A.
, Niknejad
, A.
, Tran
, T.
, and Olabi
, A.-G.
, 2019
, “Application of Cellular Material in Crashworthiness Applications: An Overview
,” Reference Module in Materials Science and Materials Engineering
. 10.1016/B978-0-12-803581-8.09268-744.
Wang
, J. G.
, Sun
, W.
, and Anand
, S.
, 2008
, “A Microstructural Analysis for Crushable Deformation of Foam Materials
,” Comput. Mater. Sci.
, 44
(1
), pp. 195
–200
. 10.1016/j.commatsci.2008.01.01445.
Ineos Olefins & Polymers USA
, 2010
, “Typical Engineering Properties of Polypropylene
,” Ineos Olefin. Polym. USA, p. 2, https://www.ineos.com/globalassets/ineos-group/businesses/ineos-olefins-and-polymers-usa/products/technical-information--patents/ineos-engineering-properties-of-p.pdf, Accessed October 5, 2020.46.
Ahmed
, R.
, 2002
, “Rolling Contact Fatigue,” ASM Handbook Volume 11: Failure Analysis and Prevention
, W. T.
Becker
, and R. J.
Shipley
, eds., ASM International
, OH
, pp. 941
–956
.47.
SIMULIA
, 2013
, “Controlling Result Averaging,” ABAQUS Analysis User’s Manual (version 6.13)
, Dassault Systèmes Simulia Corp
, Providence, RI
. http://130.149.89.49:2080/v6.13/index.html48.
Ahmed
, R.
, and Sutcliffe
, M. P. F.
, 2001
, “An Experimental Investigation of Surface Pit Evolution During Cold-Rolling or Drawing of Stainless Steel Strip
,” ASME J. Tribol.
, 123
(1
), pp. 1
–7
. 10.1115/1.132758049.
Oliver
, W. C.
, and Pharr
, G. M.
, 1992
, “An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments
,” J. Mater. Res.
, 7
(6
), pp. 1564
–1583
. 10.1557/JMR.1992.1564Copyright © 2020 by ASME
You do not currently have access to this content.
