Current techniques for measuring the bulk shear or elastic modulus of small samples of soft materials are usually limited by materials handling issues. This paper describes a nondestructive testing method based on embedded spherical inclusions. The technique simplifies materials preparation and handling requirements and is capable of continuously monitoring changes in stiffness. Exact closed form derivations of as functions of the inclusion force-displacement relationship are presented. Analytical and numerical analyses showed that size effects are significant for medium dimensions up to several times those of the inclusion. Application of the method to DNA-crosslinked gels showed good agreement with direct compression tests.
Issue Section:
Cell
1.
Horkay
, F.
, and Zrinyi
, M.
, 1982, “Studies on the Mechanical and Swelling Behavior of Polymer Networks Based on the Scaling Concept. 4. Extension of the Scaling Approach to Gels Swollen to Equilibrium in a Diluent of Arbitrary Activity
,” Macromolecules
0024-9297, 15
(5
), pp. 1306
–1310
.2.
Zhang
, X.
, Zhibing
, H.
, and Li
, Y.
, 1998, “Rubber Elasticity of Polyacrylamide Gels in High Network Concentration
,” Polymer
0032-3861, 39
(13
), pp. 2783
–2788
.3.
Peng
, M.
, Ping Gong
, J.
, and Osada
, Y.
, 2003, “Substrate Effect on the Formation of Hydrogels with Heterogeneous Network Structure
,” Chem. Rev. (Washington, D.C.)
0009-2665, 3
(1
), pp. 40
–50
.4.
Wong
, J. Y.
, Velasco
, A.
, Rajagopalan
, P.
, and Pham
, Q.
, 2003, “Directed Movement of Vascular Smooth Muscle Cells on Gradient-Compliant Hydrogels
,” Langmuir
0743-7463, 19
(5
), pp. 1908
–1913
.5.
Lee
, J.
, Leonard
, M.
, Oliver
, T.
, Ishihara
, A.
, and Jacobson
, K.
, 1994, “Traction Forces Generated by Locomoting Keratocytes
,” J. Cell Biol.
0021-9525, 127
(6 Pt 2), pp. 1957
–1964
.6.
Pelham
, R. J.
, Jr., and Wang
, Y.
, 1997, “Cell Locomotion and Focal Adhesions Are Regulated by Substrate Flexibility
,” Proc. Natl. Acad. Sci. U.S.A.
0027-8424, 94
(25
), pp. 13661
–13665
.7.
Lo
, C. M.
, Wang
, H. B.
, Dembo
, M.
, and Wang
, Y. L.
, 2000, “Cell Movement Is Guided by the Rigidity of the Substrate
,” Biophys. J.
0006-3495, 79
(1
), pp. 144
–152
.8.
Wang
, H. B.
, Dembo
, M.
, and Wang
, Y. L.
, 2000, “Substrate Flexibility Regulates Growth and Apoptosis of Normal but Not Transformed Cells
,” Am. J. Physiol.
0002-9513, 279
(5
), pp. C1345
–C1350
.9.
Radmacher
, M.
, Tillmann
, R. W.
, Fritz
, M.
, and Gaub
, H. E.
, 1992, “From Molecules to Cells: Imaging Soft Samples with the Atomic Force Microscope
,” Science
0036-8075, 257
(5078
), pp. 1900
–1905
.10.
Radmacher
, M.
, Fritz
, M.
, and Hansma
, P. K.
, 1995, “Imaging Soft Samples with the Atomic Force Microscope: Gelatin in Water and Propanol
,” Biophys. J.
0006-3495, 69
(1
), pp. 264
–270
.11.
Tao
, N. J.
, Lindsay
, S. M.
, and Lees
, S.
, 1992, “Measuring the Microelastic Properties of Biological Material
,” Biophys. J.
0006-3495, 63
(4
), pp. 1165
–1169
.12.
Shao
, Z.
, Mou
, J.
, Czajkowsky
, D. M.
, Yang
, J.
, and Yuan
, J.
, 1996, “Biological Atomic Force Microscopy: What Is Achieved and What Is Needed
,” Adv. Phys.
0001-8732, 45
(1
), pp. 1
–86
.13.
Laurent
, V. M.
, Henon
, S.
, Planus
, E.
, Fodil
, R.
, Balland
, M.
, Isabey
, D.
, and Gallet
, F.
, 2002, “Assessment of Mechanical Properties of Adherent Living Cells by Bead Micromanipulation: Comparison of Magnetic Twisting Cytometry vs Optical Tweezers
,” ASME J. Biomech. Eng.
0148-0731, 124
(4
), pp. 408
–421
.14.
Ziemann
, F.
, Radler
, J.
, and Sackmann
, E.
, 1994, “Local Measurements of Viscoelastic Moduli of Entangled Actin Networks Using an Oscillating Magnetic Bead Micro-Rheometer
,” Biophys. J.
0006-3495, 66
(6
), pp. 2210
–2216
.15.
Keller
, M.
, Schilling
, J.
, and Sackmann
, E.
, 2001, “Oscillatory Magnetic Bead Rheometer for Complex Fluid Microrheometry
,” Rev. Sci. Instrum.
0034-6748, 72
(9
), pp. 3626
–3634
.16.
Wilhelm
, C.
, Elias
, F.
, Browaeys
, J.
, Ponton
, A.
, and Bacri
, J. C.
, 2002, “Local Rheological Probes for Complex Fluids: Application to Laponite Suspensions
,” Phys. Rev. E
1063-651X, 66
, p. 021502
.17.
Amblard
, F.
, Maggs
, A. C.
, Yurke
, B.
, Pargellis
, A.
, and Leibler
, S.
, 1996, “Subdiffusion and Anomalous Local Viscoelasticity in Actin Networks
,” Phys. Rev. Lett.
0031-9007, 77
(21
), pp. 4470
–4473
.18.
Amblard
, F.
, Yurke
, B.
, Pargellis
, A.
, and Loibler
, S.
, 1996, “A Magnetic Manipulator for Studying Local Rheology and Micromechanical Properties of Biological Systems
,” Rev. Sci. Instrum.
0034-6748, 67
, pp. 818
–827
.19.
Hunkeler
, D.
, and Hamielic
, A. E.
, 1991, “Mechanism and Kinetics of the Persulfate-Initiated Polymerization of Acrylamide
,” Water-Soluble Polymers: Synthesis, Solution Properties, and Applications
, S. W.
Shalaby
, C. L.
McCormick
, and G. B.
Butler
, eds., American Chemical Society
, Washington, D.C., pp. 82
–104
.20.
Billmeyer
, F. W.
, Jr., 1984, Textbook of Polymer Science
, Wiley
, New York.21.
Panikkar
, B.
, Hari
, P. R.
, and Sharma
, C. P.
, 1997, “Modified Polyacrylamide Microspheres as Immunosorbent
,” Artif. Cells Blood Substit Immobil Biotechnol.
1073-1199, 25
(6
), pp. 541
–550
.22.
Rieben
, R.
, Korchagina
, E. Y.
, von Allmen
, E.
, Hovinga
, J. K.
, Lammle
, B.
, Jungi
, T. W.
, Bovin
, N. V.
, and Nydegger
, U. E.
, 1995, “In Vitro Evaluation of the Efficacy and Biocompatibility of New, Synthetic Abo Immunoabsorbents
,” Transplantation
0041-1337, 60
(5
), pp. 425
–430
.23.
Grigoryan
, A. S.
, Volozhin
, A. I.
, Ahmar
, N. A.
, and Titov
, M. N.
, 1998, “Experimental and Morphological Study of Biomedical Efficacy of Two Variants of Composites Based on Polyacrylamide Gel and Hydroxyapatite Used for Repair of Bone Defects
,” Stomatologie
1220-1898, 77
(4
), pp. 9
–13
.24.
Gelfi
, C.
, and Righetti
, P. G.
, 1981, “Polymerization Kinetics of Polyacrylamide Gels I. Effect of Different Cross-Linkers
,” Electrophoresis
0173-0835, 2
, pp. 213
–219
.25.
Patras
, G.
, Qiao
, G. G.
, and Solomon
, D. H.
, 2000, “Characterization of thePore Structure of Aqueous Three-Dimensional Polyacrylamide Gels with a Novel Cross-Linker
,” Electrophoresis
0173-0835, 21
(17
), pp. 3843
–3850
.26.
Sperling
, L. H.
, 2001, Introduction to Physical Polymer Science
, Wiley
, New York.27.
Lin
, D. C.
, Yurke
, B.
, and Langrana
, N. A.
, 2004, “Mechanical Properties of a Reversible, DNA-Crosslinked Polyacrylamide Hydrogel
,” ASME J. Biomech. Eng.
0148-0731, 126
(1
), pp. 104
–110
.28.
Lin
, D. C.
, Yurke
, B.
, and Langrana
, N. A.
, 2002, “Viscosity Sensitivity in a Reversible Polyacrylamide Gel with DNA Crosslinks
,” in Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology
, IEEE
, 1
, pp. 627
–628
.29.
Landau
, L. D.
, and Lifshitz
, E. M.
, 1986, Theory of Elasticity
, Pergamon
, Oxford.30.
Barber
, J. R.
, 2002, Elasticity
, Kluwer Academic
, Dordrecht.31.
Rahman
, M.
, 2000, “Point Singularities and the Singularity Method in Classical Elastodynamics
,” Proc. R. Soc. London, Ser. A
1364-5021, 456
, pp. 2021
–2042
.32.
Phan-Thien
, N.
, 1993, “Rigid Spherical Inclusion: The Multipole Expansion
,” J. Elast.
0374-3535, 32
, pp. 243
–252
.33.
Lur’e
, A. I.
, 1967, “The Roben Elastostatic Problem for a Three-Axis Ellipsoid
,” Inzh. Zh., Mekh. Tverd. Tela
0541-4180, 2
(1
), pp. 80
–83
.Copyright © 2005
by American Society of Mechanical Engineers
You do not currently have access to this content.
