A constitutive model is developed to characterize a general class of polymer and polymer-like materials that displays hyperelastic orthotropic mechanical behavior. The strain energy function is derived from the entropy change associated with the deformation of constituent macromolecules and the strain energy change associated with the deformation of a representative orthotropic unit cell. The ability of this model to predict nonlinear, orthotropic elastic behavior is examined by comparing the theory to experimental results in the literature. Simulations of more complicated boundary value problems are performed using the finite element method.
Issue Section:
Technical Papers
1.
Lanir
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, and Fung
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, 1974
, “Two-Dimensional Mechanical Properties of Rabbit Skin—II: Experimental Results
,” J. Biomech.
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.2.
Lanir
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Lanir
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,” Isr. J. Technol.
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.4.
Humphrey
, J. D.
, Strumpf
, R. K.
, and Yin
, F. C. P.
, 1992
, “A Constitutive Theory for Biomembranes: Application to Epicardial Mechanics
,” ASME J. Biomech. Eng.
, 114
, pp. 461
–466
.5.
Rodriguez
, E. K.
, Hoger
, A.
, and McCulloch
, A. D.
, 1994
, “Stress-Dependent Finite Growth in Soft Elastic Tissues
,” J. Biomech.
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), pp. 455
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, Eberlein
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, “Large Strain Analysis of Soft Biological Membranes: Formulation and Finite Element Analysis
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8.
Humphrey
, J. D.
, Strumpf
, R. K.
, and Yin
, F. C. P.
, 1990
, “Determination of a Constitutive Relation for Passive Myocardium—I: A New Functional Form
,” ASME J. Biomech. Eng.
, 112
, pp. 333
–339
.9.
Baumann
, C. G.
, Smith
, S. B.
, Bloomfield
, V. A.
, and Bustamente
, C.
, 1997
, “Ionic Effects on the Elasticity of Single DNA Molecules
,” Proc. Natl. Acad. Sci. U.S.A.
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11.
Kuhn
, W.
, and Gru¨n
, F.
, 1942
, “Beziehungen Zwischen Elastischen Konstanten und Dehnungsdoppelbrechung Hochelastischer Stoffe
,” Kolloid-Z.
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Kellermayer
, M. S. Z.
, Smith
, S. B.
, Bustamente
, C.
, and Granzier
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, 1998
, “Complete Unfolding of the Titin Molecule Under External Force
,” J. Struct. Biol.
, 122
, pp. 197
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.13.
Trombita´s
, K.
, Greaser
, M.
, Labeit
, S.
, Jim
, J.-P.
, Kellermayer
, M.
, Helmes
, M.
, and Granzier
, H.
, 1998
, “Titin Extensibility in situ: Entropic Elasticity of Permanently Folded and Permanently Unfolded Molecular Segments
,” J. Cell Biol.
, 140
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), pp. 853
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Oberhauser
, A. F.
, Marszalek
, P. E.
, Erickson
, H. P.
, and Fernandez
, J. M.
, 1998
, “The Molecular Elasticity of the Extracellular Matrix Protein Tenascin
,” Nature (London)
, 393
, pp. 181
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.15.
Hegner
, M.
, Smith
, S. B.
, and Bustamente
, C.
, 1999
, “Polymerization and Mechanical Properties of Single RecA-DNA Filaments
,” Proc. Natl. Acad. Sci. U.S.A.
, 96
, pp. 10109
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.16.
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
.17.
Spencer, A. J. M., 1984, “Constitutive Theory for Strongly Anisotropic Solids,” CISM Courses and Lectures III, (282), pp. 1–32.
18.
Bischoff
, J. E.
, Arruda
, E. M.
, and Grosh
, K.
, 2001
, “A New Constitutive Model for the Compressibility of Elastomers at Finite Deformations
,” Rubber Chem. Technol.
, 74
(4
), pp. 0541
–0559
.19.
Anand
, L.
, 1996
, “A Constitutive Model for Compressible Elastomeric Solids
,” Comp. Mech.
, 18
, pp. 339
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.20.
Treloar
, L. R. G.
, and Riding
, G.
, 1979
, “A Non-Gaussian Theory for Rubber in Biaxial Strain—I: Mechanical Properties
,” Proc. R. Soc. London, Ser. A
, 369
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Bischoff, J. E., 2001, “Constitutive Modeling and Testing of Biological Soft Tissue,” Ph.D. thesis, University of Michigan.
22.
Wang
, M. C.
, and Guth
, E.
, 1952
, “Statistical Theory of Networks of Non-Gaussian Flexible Chains
,” J. Chem. Phys.
, 20
(7
), pp. 1144
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.23.
Flory
, P. J.
, and Rehner
, J.
, Jr., 1943
, “Statistical Mechanics of Cross-Linked Polymer Networks
,” J. Chem. Phys.
, 11
, pp. 512
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Malvern, L. E., 1969, Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, Englewood Cliffs, NJ.
25.
Smith
, G. F.
, and Rivlin
, R. S.
, 1958
, “The Strain-Energy Function for Anisotropic Elastic Materials
,” Trans. Am. Math. Soc.
, 88
(1
), pp. 175
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.26.
Horowitz
, A.
, Lanir
, Y.
, Yin
, F. C. P.
, Perl
, M.
, Sheinman
, I.
, and Strumpf
, R. K.
, 1988
, “Structural Three-Dimensional Constitutive Law for the Passive Myocardium
,” ASME J. Biomech. Eng.
, 110
, pp. 200
–207
.27.
Billiar
, K. L.
, and Sacks
, M. S.
, 2000
, “Biaxial Mechanical Properties of the Natural and Gluteraldehyde Treated Aortic Valve Cusp—Part II: A Structural Constitutive Model
,” ASME J. Biomech. Eng.
, 122
, pp. 1
–9
.28.
Billiar
, K. L.
, and Sacks
, M. S.
, 2000
, “Biaxial Mechanical Properties of the Natural and Gluteraldehyde Treated Aortic Valve Cusp—Part I: Experimental Results
,” ASME J. Biomech. Eng.
, 122
, pp. 23
–30
.29.
ABAQUS/Standard User’s Manual, Version 5.8, 1999, Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, RI.
Copyright © 2002
by ASME
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