Indentation has been widely used to characterize the mechanical properties of biopolymers. Besides Hertzian solution, Sneddon's solution is frequently adopted to interpret the indentation data to deduce the elastic properties of biopolymers, e.g., elastic modulus. Sneddon's solution also forms the basis to develop viscoelastic contact models for determining the viscoelastic properties of materials from either conical or flat punch indentation responses. It is worth mentioning that the Sneddon's solution was originally proposed on the basis of linear elastic contact theory. However, in both conical and flat punch indentation of compliant materials, the indented solid may undergo finite deformation. In this case, the extent to which the Sneddon's solution is applicable so far has not been systematically investigated. In this paper, we use the combined theoretical, computational, and experimental efforts to investigate the indentation of hyperelastic compliant materials with a flat punch or a conical tip. The applicability of Sneddon's solutions is examined. Furthermore, we present new models to determine the elastic properties of nonlinear elastic biopolymers.

References

References
1.
Engler
,
A. J.
,
Sen
,
S.
,
Sweeney
,
H. L.
, and
Discher
,
D. E.
,
2006
, “
Matrix Elasticity Directs Stem Cell Lineage Specification
,”
Cell
,
126
(
4
), pp.
677
689
.10.1016/j.cell.2006.06.044
2.
Lee
,
J.
,
Abdeen
,
A. A.
,
Zhang
,
D.
, and
Kilian
,
K. A.
,
2013
, “
Directing Stem Cell Fate on Hydrogel Substrates by Controlling Cell Geometry, Matrix Mechanics and Adhesion Ligand Composition
,”
Biomaterials
,
34
(
33
), pp.
8140
8148
.10.1016/j.biomaterials.2013.07.074
3.
Chen
,
J.
,
Irianto
,
J.
,
Inamdar
,
S.
,
Pravincumar
,
P.
,
Lee
,
D.
,
Bader
,
D. L.
, and
Knight
,
M.
,
2012
, “
Cell Mechanics, Structure, and Function are Regulated by the Stiffness of the Three-Dimensional Microenvironment
,”
Biophys. J.
,
103
(
6
), pp.
1188
1197
.10.1016/j.bpj.2012.07.054
4.
Chen
,
J.
,
Wright
,
K.
, and
Birch
,
M.
,
2014
, “
Nanoscale Viscoelastic Properties and Adhesion of Polydimethylsiloxane for Tissue Engineering
,”
Acta Mech. Sin.
,
30
(
1
), pp.
2
6
.10.1007/s10409-014-0022-0
5.
Evans
,
E. A.
,
1983
, “
Bending Elastic Modulus of Red Blood Cell Membrane Derived From Buckling Instability in Micropipet Aspiration Tests
,”
Biophys. J.
,
43
(
1
), pp.
27
30
.10.1016/S0006-3495(83)84319-7
6.
Sato
,
M.
,
Theret
,
D.
,
Wheeler
,
L.
,
Ohshima
,
N.
, and
Nerem
,
R.
,
1990
, “
Application of the Micropipette Technique to the Measurement of Cultured Porcine Aortic Endothelial Cell Viscoelastic Properties
,”
ASME J. Biomech. Eng.
,
112
(
3
), pp.
263
268
.10.1115/1.2891183
7.
Aoki
,
T.
,
Ohashi
,
T.
,
Matsumoto
,
T.
, and
Sato
,
M.
,
1997
, “
The Pipette Aspiration Applied to the Local Stiffness Measurement of Soft Tissues
,”
Ann. Biomed. Eng.
,
25
(
3
), pp.
581
587
.10.1007/BF02684197
8.
Guilak
,
F.
,
Jones
,
W. R.
,
Ting-Beall
,
H. P.
, and
Lee
,
G. M.
,
1999
, “
The Deformation Behavior and Mechanical Properties of Chondrocytes in Articular Cartilage
,”
Osteoarthrotis Cartilage
,
7
(
1
), pp.
59
70
.10.1053/joca.1998.0162
9.
Kauer
,
M.
,
2001
, “
Inverse Finite Element Characterization of Soft Tissues With Aspiration Experiments
,” ETH Zürich, Swiss Federal Institute of Technology, Zürich, Switzerland.
10.
Boudou
,
T.
,
Ohayon
,
J.
,
Arntz
,
Y.
,
Finet
,
G.
,
Picart
,
C.
, and
Tracqui
,
P.
,
2006
, “
An Extended Modeling of the Micropipette Aspiration Experiment for the Characterization of the Young's Modulus and Poisson's Ratio of Adherent Thin Biological Samples: Numerical and Experimental Studies
,”
J. Biomech.
,
39
(
9
), pp.
1677
1685
.10.1016/j.jbiomech.2005.04.026
11.
Guevorkian
,
K.
,
Colbert
,
M.-J.
,
Durth
,
M.
,
Dufour
,
S.
, and
Brochard-Wyart
,
F.
,
2010
, “
Aspiration of Biological Viscoelastic Drops
,”
Phys. Rev. Lett.
,
104
(
21
), p.
218101
.10.1103/PhysRevLett.104.218101
12.
Zhao
,
R.
,
Sider
,
K. L.
, and
Simmons
,
C. A.
,
2011
, “
Measurement of Layer-Specific Mechanical Properties in Multilayered Biomaterials by Micropipette Aspiration
,”
Acta Biomater.
,
7
(
3
), pp.
1220
1227
.10.1016/j.actbio.2010.11.004
13.
Cao
,
Y. P.
,
Li
,
G. Y.
,
Zhang
,
M. G.
, and
Feng
,
X. Q.
,
2014
, “
Determination of the Reduced Creep Function of Viscoelastic Compliant Materials Using Pipette Aspiration Method
,”
ASME J. Appl. Mech.
,
81
(
7
), p.
071006
.10.1115/1.4027159
14.
Zhang
,
M. G.
,
Cao
,
Y. P.
,
Li
,
G. Y.
, and
Feng
,
X. Q.
,
2014
, “
Pipette Aspiration of Hyperelastic Compliant Materials: Theoretical Analysis, Simulations and Experiments
,”
J. Mech. Phys. Solids
, 68(8), pp. 179–196.10.1016/j.jmps.2014.03.012
15.
Koay
,
E. J.
,
Shieh
,
A. C.
, and
Athanasiou
,
K. A.
,
2003
, “
Creep Indentation of Single Cells
,”
ASME J. Biomech. Eng.
,
125
(
3
), pp.
334
341
.10.1115/1.1572517
16.
Cheng
,
Y. T.
, and
Cheng
,
C. M.
,
2004
, “
Scaling, Dimensional Analysis, and Indentation Measurements
,”
Mater. Sci. Eng., R
,
44
(
4
), pp.
91
149
.10.1016/j.mser.2004.05.001
17.
Oyen
,
M.
,
2006
, “
Analytical Techniques for Indentation of Viscoelastic Materials
,”
Philos. Mag.
,
86
(
33–35
), pp.
5625
5641
.10.1080/14786430600740666
18.
Tweedie
,
C. A.
, and
van Vliet
,
K. J.
,
2006
, “
Contact Creep Compliance of Viscoelastic Materials Via Nanoindentation
,”
J. Mater. Res.
,
21
(
6
), pp.
1576
1589
.10.1557/jmr.2006.0197
19.
Kranenburg
,
J. M.
,
Tweedie
,
C. A.
,
van Vliet
,
K. J.
, and
Schubert
,
U. S.
,
2009
, “
Challenges and Progress in High-Throughput Screening of Polymer Mechanical Properties by Indentation
,”
Adv. Mater.
,
21
(
35
), pp.
3551
3561
.10.1002/adma.200803538
20.
Ladjal
,
H.
,
Hanus
,
J.-L.
,
Pillarisetti
,
A.
,
Keefer
,
C.
,
Ferreira
,
A.
, and
Desai
,
J. P.
,
2009
, “
Atomic Force Microscopy-Based Single-Cell Indentation: Experimentation and Finite Element Simulation
,”
IEEE/RSJ International Conference on Proceedings of Intelligent Robots and Systems
(
IROS 2009
), St. Louis, MO, October 10–15, pp.
1326
1332
10.1109/IROS.2009.5354351.
21.
Hu
,
Y.
,
Zhao
,
X.
,
Vlassak
,
J. J.
, and
Suo
,
Z.
,
2010
, “
Using Indentation to Characterize the Poroelasticity of Gels
,”
Appl. Phys. Lett.
,
96
(
12
), p.
121904
.10.1063/1.3370354
22.
Hu
,
Y.
,
Chen
,
X.
,
Whitesides
,
G. M.
,
Vlassak
,
J. J.
, and
Suo
,
Z.
,
2011
, “
Indentation of Polydimethylsiloxane Submerged in Organic Solvents
,”
J. Mater. Res.
,
26
(
6
), pp.
785
795
.10.1557/jmr.2010.35
23.
Zhang
,
M. G.
,
Cao
,
Y. P.
,
Li
,
G. Y.
, and
Feng
,
X. Q.
,
2014
, “
Spherical Indentation Method for Determining the Constitutive Parameters of Hyperelastic Soft Materials
,”
Biomech. Model Mechanobiol.
,
13
(
1
), pp.
1
11
.10.1007/s10237-013-0481-4
24.
Lindström
,
S. B.
,
Kulachenko
,
A.
,
Jawerth
,
L. M.
, and
Vader
,
D. A.
,
2013
, “
Finite-Strain, Finite-Size Mechanics of Rigidly Cross-Linked Biopolymer Networks
,”
Soft Matter
,
9
(
30
), pp.
7302
7313
.10.1039/c3sm50451d
25.
Barenblatt
,
G. I.
,
1996
,
Scaling, Self-Similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics
,
Cambridge University
,
New York
.
26.
Mooney
,
M.
,
1940
, “
A Theory of Large Elastic Deformation
,”
J. Appl. Phys.
,
11
(
9
), pp.
582
592
.10.1063/1.1712836
27.
Rivlin
,
R. S.
,
1949
, “
Large Elastic Deformations of Isotropic Materials. V. The Problem of Flexure
,”
Philos. Trans. R. Soc., A
,
195
(
1043
), pp.
463
473
.10.1098/rspa.1949.0004
28.
Arruda
,
E. M.
, and
Boyce
,
M. C.
,
1993
, “
A Three-Dimensional Constitutive Model for the Large Stretch Behavior of Rubber Elastic Materials
,”
J. Mech. Phys. Solids
,
41
(
2
), pp.
389
412
.10.1016/0022-5096(93)90013-6
29.
DS Simulia Corp.
,
2010
, “
ABAQUS User's Manual
,” Version 6.10, Dassault Systemes, Providence, RI.
30.
Lim
,
Y. Y.
, and
Chaudhri
,
M. M.
,
2004
, “
Indentation of Elastic Solids With Rigid Cones
,”
Philos. Mag.
,
84
(27), pp.
2877
2903
.10.1080/14786430410001716782
31.
Liu
,
Y.
,
Kerdok
,
A. E.
, and
Howe
,
R. D.
,
2004
, “
A Nonlinear Finite Element Model of Soft Tissue Indentation
,”
Medical Simulation
,
Springer
,
Berlin
, pp.
67
76
.
32.
Zaeimdar
,
S.
,
2014
, “
Mechanical Characterization of Breast Tissue Constituents for Cancer Assessment
,” Ph.D. thesis, School of Mechatronic Systems Engineering, Surrey, BC, Canada.
33.
Farine
,
M.
,
2013
, “
Instrumented Indentation of Soft Materials and Biological Tissues
,” Ph. D. thesis, Eidgenössische Technische Hochschule ETH Zürich, Zürich, Switzerland.
34.
Cao
,
Y. P.
, and
Lu
,
J.
,
2004
, “
Depth-Sensing Instrumented Indentation With Dual Sharp Indenters: Stability Analysis and Corresponding Regularization Schemes
,”
Acta Mater
,
52
(
5
), pp.
1143
1153
.10.1016/j.actamat.2003.11.001
35.
Weisenhorn
,
A. L.
,
Khorsandi
,
M.
,
Kasas
,
S.
,
Gotzos
,
V.
, and
Butt
,
H. J.
,
1993
, “
Deformation and Height Anomaly of Soft Surfaces Studied With an AFM
,”
Nanotechnology
,
4
(
2
), pp.
106
–113.10.1088/0957-4484/4/2/006
36.
Vinckier
,
A.
, and
Semenza
,
G.
,
1998
, “
Measuring Elasticity of Biological Materials by Atomic Force Microscopy
,”
FEBS Lett.
,
430
(
1
), pp.
12
16
.10.1016/S0014-5793(98)00592-4
37.
A-Hassan
,
E.
,
Heinz
,
W. F.
,
Antonik
,
M. D.
,
D'Costa
,
N. P.
,
Nageswaran
,
S.
,
Schoenenberger
,
C.-A.
, and
Hoh
,
J. H.
,
1998
, “
Relative Microelastic Mapping of Living Cells by Atomic Force Microscopy
,”
Biophys. J.
,
74
(
3
), pp.
1564
1578
.10.1016/S0006-3495(98)77868-3
38.
Collinsworth
,
A. M.
,
Zhang
,
S.
,
Kraus
,
W. E.
, and
Truskey
,
G. A.
,
2002
, “
Apparent Elastic Modulus and Hysteresis of Skeletal Muscle Cells Throughout Differentiation
,”
Am. J. Physiol. Cell Physiol.
,
283
(
4
), pp.
C1219
C1227
.10.1152/ajpcell.00502.2001
39.
Kuznetsova
,
T. G.
,
Starodubtseva
,
M. N.
,
Yegorenkov
,
N. I.
,
Chizhik
,
S. A.
, and
Zhdanov
,
R. I.
,
2007
, “
Atomic Force Microscopy Probing of Cell Elasticity
,”
Micron
,
38
(
8
), pp.
824
833
.10.1016/j.micron.2007.06.011
40.
McKee
,
C. T.
,
Last
,
J. A.
,
Russell
,
P.
, and
Murphy
,
C. J.
,
2011
, “
Indentation Versus Tensile Measurements of Young's Modulus for Soft Biological Tissues
,”
Tiss. Eng.
,
17
(
3
), pp.
155
164
.10.1089/ten.teb.2010.0520
41.
Thomas
,
G.
,
Burnham
,
N. A.
,
Camesano
,
T. A.
, and
Wen
,
Q.
,
2013
, “
Measuring the Mechanical Properties of Living Cells Using Atomic Force Microscopy
,”
J. Vis. Exp.
,
76
, p.
e50497
.10.3791/50497
42.
Cao
,
Y. P.
,
Ji
,
X. Y.
, and
Feng
,
X. Q.
,
2010
, “
Geometry Independence of the Normalized Relaxation Functions of Viscoelastic Materials in Indentation
,”
Philos. Mag.
,
90
(
12
), pp.
1639
1655
.10.1080/14786430903439826
43.
Cao
,
Y. P.
,
Zhang
,
M. G.
, and
Feng
,
X. Q.
,
2013
, “
Indentation Method for Measuring the Viscoelastic Kernel Function of Nonlinear Viscoelastic Soft Materials
,”
J. Mater. Res.
,
28
(
6
), pp.
806
816
.10.1557/jmr.2012.431
You do not currently have access to this content.