Research Papers

Specific Adhesion of Finite Soft Elastic Solid

[+] Author and Article Information
Zibin Zhang

Key Laboratory of Mechanics on Disaster
and Environment in Western China,
College of Civil Engineering and Mechanics,
Ministry of Education,
Lanzhou University,
Lanzhou 730000, Gansu, China

Jizeng Wang

Key Laboratory of Mechanics on Disaster
and Environment in Western China,
College of Civil Engineering and Mechanics,
Ministry of Education,
Lanzhou University,
Lanzhou 730000, Gansu, China
e-mail: jzwang@lzu.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 17, 2018; final manuscript received September 10, 2018; published online October 1, 2018. Editor: Yonggang Huang.

J. Appl. Mech 86(1), 011001 (Oct 01, 2018) (9 pages) Paper No: JAM-18-1477; doi: 10.1115/1.4041471 History: Received August 17, 2018; Revised September 10, 2018

Specific adhesion of soft elastic half spaces via molecular bond clusters has been extensively studied in the past ten years. In this study, the adhesion of a soft elastic solid with finite size is considered aiming to investigate how their size and shape may affect the adhesion strength. To model this problem, plane strain assumption is adopted to describe the deformation of the elastic solid. This deformation couples the stochastic behavior of adhesive bonds, for which we have considered the mean field treatment based on the classical Bell theory. Numerical solutions have revealed that, besides the elastic modulus, size of the elastic solid and spatial arrangement of the bond clusters are all crucial factors in mediating the adhesion strength. Most interestingly, there clearly exists an optimal size/shape of the elastic solid that corresponds to the largest adhesion strength. These findings provide new insights and inspirations in understanding various phenomena of cellular adhesion and designing advanced functional biomaterials.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


Chen, X. , and Gumbiner, B. M. , 2006, “ Crosstalk Between Different Adhesion Molecules,” Curr. Opin. Cell Biol., 18(5), pp. 572–578. [CrossRef] [PubMed]
Qian, J. , Wang, J. Z. , and Gao, H. J. , 2008, “ Lifetime and Strength of Adhesive Molecular Bond Clusters Between Elastic Media,” Langmuir, 24(4), pp. 1262–1270. [CrossRef] [PubMed]
Chen, L. , and Chen, S. H. , 2015, “ Adhesion of a Gas-Filled Membrane on a Stretched Substrate,” Int. J. Solids Struct., 69, pp. 189–194. [CrossRef]
Maître, J. L. , and Heisenberg, C. P. , 2011, “ The Role of Adhesion Energy in Controlling Cell-Cell Contacts,” Curr. Opin. Cell Biol., 23(5), pp. 508–514. [CrossRef] [PubMed]
Tozeren, A. , 1990, “ Cell-Cell, Cell-Substrate Adhesion: Theoretical and Experimental Considerations,” ASME J. Biomech. Eng., 112 (3), pp. 311–318. [CrossRef]
Alberts, B. , Johnson, A. , Lewis, J. , Raff, M. , Roberts, K. , and Walter, P. , 2002, Molecular Biology of the Cell, Garland Science, New York.
Okegawa, T. , Pong, R. C. , Li, Y. , and Hsieh, J. T. , 2004, “ The Role of Cell Adhesion Molecule in Cancer Progression and Its Application in Cancer Therapy,” Acta Biochim. Polym., 51(2), pp. 445–458 https://www.ncbi.nlm.nih.gov/pubmed/15218541.
Chien, S. , and Sung, L. A. , 1987, “ Physicochemical Basis and Clinical Implications of Red Cell Aggregation,” Clin. Hemorheol. Microcirc., 7(1), pp. 71–91. [CrossRef]
Sung, K. L. , Sung, L. A. , Crimmins, M. , Burakoff, S. J. , and Chien, S. , 1986, “ Determination of Junction Avidity of Cytolytic T Cell and Target Cell,” Science, 234(4782), pp. 1405–1408. [CrossRef] [PubMed]
Tozeren, A. , Sung, K. L. , and Chien, S. , 1989, “ Theoretical and Experimental Studies on Cross-Bridge Migration During Cell Disaggregation,” Biophys. J., 55(3), pp. 479–487. [CrossRef] [PubMed]
Bell, G. I. , 1978, “ Models for the Specific Adhesion of Cells to Cells,” Science, 200(4342), pp. 618–627. [CrossRef] [PubMed]
Erdmann, T. , and Schwarz, U. S. , 2004, “ Stability of Adhesion Clusters Under Constant Force,” Phys. Rev. Lett., 92(10), p. 108102. [CrossRef] [PubMed]
Erdmann, T. , and Schwarz, U. S. , 2004, “ Stochastic Dynamics of Adhesion Clusters Under Shared Constant Force and With Rebinding,” J. Chem. Phys., 121(18), pp. 8997–9017. [CrossRef] [PubMed]
Wang, J. Z. , and Huang, Q. Z. , 2015, “ A Stochastic Description on Adhesion of Molecular Bond Clusters Between Rigid Media With Curved Interfaces,” Int. J. Appl. Mech., 7(5), p. 1550071. [CrossRef]
Wang, J. Z. , and Gao, H. J. , 2010, “ Size and Shape Dependent Steady-State Pull-Off Force in Molecular Adhesion Between Soft Elastic Materials,” Int. J. Fract., 166(1–2), pp. 13–19. [CrossRef]
Qian, J. , Wang, J. Z. , Lin, Y. , and Gao, H. J. , 2009, “ Lifetime and Strength of Periodic Bond Clusters Between Elastic Media Under Inclined Loading,” Biophys. J., 97(9), pp. 2438–2445. [CrossRef] [PubMed]
Gao, H. J. , Qian, J. , and Chen, B. , 2011, “ Probing Mechanical Principles of Focal Contacts in Cell-Matrix Adhesion With a Coupled Stochastic-Elastic Modelling Framework,” J. R. Soc. Interface, 8(62), pp. 1217–1232. [CrossRef] [PubMed]
Wang, J. Z. , and Gao, H. J. , 2008, “ Clustering Instability in Adhesive Contact Between Elastic Solids Via Diffusive Molecular Bonds,” J. Mech. Phys. Solids, 56(1), pp. 251–266. [CrossRef]
Zhang, W. L. , Lin, Y. , Qian, J. , Chen, W. Q. , and Gao, H. J. , 2013, “ Tuning Molecular Adhesion Via Material Anisotropy,” Adv. Funct. Mater., 23(37), pp. 4729–4738.
Zhang, W. L. , Qian, J. , Yao, H. M. , Chen, W. Q. , and Gao, H. J. , 2012, “ Effects of Functionally Graded Materials on Dynamics of Molecular Bond Clusters,” Sci. China Phys. Mech., 55(6), pp. 980–988. [CrossRef]
Li, L. , Zhang, W. Y. , and Wang, J. Z. , 2016, “ A Viscoelastic-Stochastic Model of the Effects of Cytoskeleton Remodelling on Cell Adhesion,” Roy. Soc. Open Sci., 3(10), p. 160539. [CrossRef]
Wang, J. Z. , Yao, J. Y. , and Gao, H. J. , 2012, “ Specific Adhesion of a Soft Elastic Body on a Wavy Surface,” Theor. Appl. Mech. Lett., 2(1), p. 014002. [CrossRef]
Jin, F. , and Guo, X. , 2013, “ Mechanics of Axisymmetric Adhesive Contact of Rough Surfaces Involving Power-Law Graded Materials,” Int. J. Solids Struct., 50(20–21), pp. 3375–3386. [CrossRef]
Zhang, W. , Jin, F. , Zhang, S. , and Guo, X. , 2014, “ Adhesive Contact on Randomly Rough Surfaces Based on the Double-Hertz Model,” ASME J. Appl. Mech., 81(5), p. 051008. [CrossRef]
Jin, F. , Wan, Q. , and Guo, X. , 2015, “ Plane Contact and Partial Slip Behaviors of Elastic Layers With Randomly Rough Surfaces,” ASME J. Appl. Mech., 82(9), p. 091006. [CrossRef]
Nicolas, A. , and Safran, S. A. , 2006, “ Limitation of Cell Adhesion by the Elasticity of the Extracellular Matrix,” Biophys. J., 91(1), pp. 61–73. [CrossRef] [PubMed]
He, S. J. , Su, Y. W. , Ji, B. H. , and Gao, H. J. , 2014, “ Some Basic Questions on Mechanosensing in Cell-Substrate Interaction,” J. Mech. Phys. Solids, 70, pp. 116–135. [CrossRef]
Gao, Z. W. , and Gao, Y. F. , 2016, “ Why Do Receptor-Ligand Bonds in Cell Adhesion Cluster Into Discrete Focal-Adhesion Sites,” J. Mech. Phys. Solids, 95, pp. 557–574. [CrossRef]
Erdmann, T. , and Schwarz, U. S. , 2006, “ Bistability of Cell-Matrix Adhesions Resulting From Nonlinear Receptor-Ligand Dynamics,” Biophys. J., 91(6), pp. L60–L62. [CrossRef] [PubMed]
Timoshenko, S. , and Goodier, J. N. , 1970, Theory of Elasticity, McGraw-Hill, New York.
Sadd, M. H. , 2009, Elasticity: Theory, Applications, and Numerics, Academic Press, Burlington, MA.


Grahic Jump Location
Fig. 2

Distribution of the normalized interfacial traction within the adhesion region. Hollow circles and triangles are results on the adhesion of finite elastic solids, while the solid line refers to the elastic half-space [2,15].

Grahic Jump Location
Fig. 4

The normalized pull-off force as a function of nondimensional parameter α for (a) a = 0.5 μm, l = 5 μm and (b) a = 0.5 μm, h = 2 μm

Grahic Jump Location
Fig. 1

The plane strain problem of a rectangular elastic solid adhered on a rigid substrate via ligand–receptor bonds, where width and thickness of the elastic solid is 2l and h, molecular bonds occupy the area [−a, a] within [−l, l]

Grahic Jump Location
Fig. 11

A plane-strain problem of the rectangular elastic solid under two symmetrical loads

Grahic Jump Location
Fig. 3

The distribution of normalized interfacial traction under different values of nondimensional parameter α for (a) h = 5 μm, (b) h = 0.5 μm. Other parameters are l = 5 μm, μ = 0.495, a = 0.5 μm, F = 0.01 pN, respectively.

Grahic Jump Location
Fig. 5

Distribution of the normalized interfacial traction under different values of the ratio, h/a, where E = 15 kPa, μ = 0.495, l = 5 μm, F = 0.01 pN, and a = 0.5 μm

Grahic Jump Location
Fig. 6

Distribution of the normalized interfacial traction under different values of the ratio, l/a, where E = 15 kPa, μ = 0.495, F = 0.01 pN, h/a = 4, and a = 0.5 μm

Grahic Jump Location
Fig. 12

The iteration scheme for solving the coupled nonlinear system of integral-differential Eqs. (10)(12), where δ denotes a prescribed error tolerance

Grahic Jump Location
Fig. 7

The normalized pull-off force as a function of the normalized thickness under different values of parameter α, where a = 0.5 μm, and l = 5 μm

Grahic Jump Location
Fig. 8

The adhesion strength as a function of the normalized thickness under different cluster spacing, where E = 15 kPa

Grahic Jump Location
Fig. 9

Schematic plot on the adhesion of a cell-shaped elastic solid, where the aspect ratio is about 4

Grahic Jump Location
Fig. 10

The normalized pull off force as a function of (a) cluster size and (b) cluster spacing, under different values of Young's modulus



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In