It is advantageous in mechanics to identify experiments that correspond to tractable boundary value problems—this facilitates data reduction and interpretation. Increasingly more situations are arising, however, wherein experimentalists cannot dictate the geometry or applied loads during testing. Inverse finite element methods are, therefore, becoming essential tools for calculating material parameters. In this paper, we present numerical and experimental results that show that one such inverse finite element method is very useful in characterizing the mechanical behavior of neo-Hookean (rubber) membranes subjected to axisymmetric and nonaxisymmetric finite inflations.

1.
Bylski
D. I.
,
Kriewall
T. J.
,
Akkas
N.
, and
Melvin
J. W.
,
1986
, “
Mechanical Behavior of Fetal Dura Mater Under Large Deformation Biaxial Tension
,”
Journal of Biomechanics
, Vol.
19
, pp.
19
26
.
2.
Charrier
J. M.
,
Shrivastava
S.
, and
Wu
R.
,
1989
, “
Free and Constrained Inflation of Elastic Membranes in Relation to Thermoforming—Non-axisymmetric Problems
,”
Journal of Strain Analysis
, Vol.
34
, pp.
55
74
.
3.
Green, A. E., and Adkins, J. E., 1970, Large Elastic Deformations, Clarendon Press, Oxford.
4.
Gruttmann
F.
, and
Taylor
R. L.
,
1992
, “
Theory and Finite Element Formulation of Rubberlike Membrane Shells Using Principal Stretches
,”
International Journal for Numerical Methods in Engineering
, Vol.
35
, pp.
111
1126
.
5.
Hsu
F. P. K.
,
Schwab
C.
,
Rigamonti
D.
, and
Humphrey
J. D.
,
1994
, “
Identification of Response Functions for Nonlinear Membranes via Axisymmetric Inflation Tests: Implications for Biomechanics
,”
International Journal of Solids and Structures
, Vol.
31
, pp.
3375
3386
.
6.
Hsu
F. P. K.
,
Downs
J.
,
Liu
A. M. C.
,
Rigamonti
D.
, and
Humphrey
J. D.
,
1995
, “
A Triplane Video-Based Experimental System for Studying Axisymmetrically Inflated Biomembranes
,”
IEEE Transactions for Biomedical Engineering
, Vol.
42
, pp.
442
449
.
7.
Humphrey
J. D.
,
Strumpf
R. K.
, and
Yin
F. C. P.
,
1990
, “
Determination of a Constitutive Relation for Passive Myocardium: II. Parameter Estimation
,”
ASME Journal of Biomechanical Engineering
, Vol.
112
, pp.
340
346
.
8.
Humphrey
J. D.
,
Strumpf
R. K.
, and
Yin
F. C. P.
,
1992
, “
A Constitutive Theory for Biomembranes: Application to Epicardium
,”
ASME Journal of Biomechanical Engineering
, Vol.
114
, pp.
461
466
.
9.
Kavanagh
K. T.
, and
Clough
R. W.
,
1971
, “
Finite Element Applications in the Characterization of Elastic Solids
,”
International Journal of Solids and Structures
, Vol.
7
,
11
23
.
10.
Kyriacou
S. K.
, and
Humphrey
J. D.
,
1996
, “
Influence of Size, Shape, and Properties on the Mechanics of Axisymmetric Saccular Aneurysms
,”
Journal of Biomechanics
, Vol.
29
, pp.
1015
1022
.
11.
Kyriacou
S. K.
,
Schwab
C.
, and
Humphrey
J. D.
,
1996
, “
Finite Element Analysis of Nonlinear Orthotropic Hyperelastic Membranes
,”
Computational Mechanics
, Vol.
18
, pp.
269
278
.
12.
Ling
Y.
,
Engel
P. A.
,
Brodskey
W. L.
, and
Guo
Y.
,
1993
, “
Finding the Constitutive Relation for a Specific Elastomer
,”
ASME Journal of Electronic Packaging
, Vol.
115
, pp.
329
336
.
13.
Miller
C. E.
,
Lavery
J. P.
, and
Donnelly
T. A.
,
1979
, “
Determination of Elastic Parameters for Human Fetal Membranes
,”
Journal of Rheology
, Vol.
23
, pp.
57
78
.
14.
Nied
H. F.
,
Taylor
C. A.
, and
Delorenzi
H. G.
,
1990
, “
Three-dimensional Finite Element Simulation of Thermoforming
,”
Polymer Engineering and Science
, Vol.
30
, pp.
1314
1322
.
15.
Pipkin
A. C.
,
1968
, “
Integration of an Equation in Membrane Theory
,”
ZAMP
, Vol.
19
, pp.
818
819
.
16.
Rivlin
R. S.
, and
Saunders
D. W.
,
1951
, “
Large Elastic Deformations of Isotropic Materials. VII, Experiments on the Deformation of Rubber
,”
Philosophical Transactions of the Royal Society, Series A
, Vol.
243
, pp.
251
288
.
17.
Treloar
L. R. G.
,
1944
, “
Strains in an Inflated Rubber Sheet, and the Mechanism of Bursting
,”
Institute of Rubber Industry Transactions
, Vol.
19
, pp.
201
212
.
18.
Twizell
E. H.
, and
Ogden
R. W.
,
1983
, “
Non-linear Optimization of the Material Constants in Ogden’s Stress-deformation Function for Incompressible Isotropic Elastic Materials
,”
Journal of the Australian Mathematics Society
, Vol.
B24
, pp.
424
434
.
19.
Wineman
A.
,
Wilson
D.
, and
Melvin
J. W.
,
1979
, “
Material Identification of Soft Tissue Using Membrane Inflation
,”
Journal of Biomechanics
, Vol.
12
, pp.
841
850
.
20.
Xu
P.
, and
Mark
J. E.
,
1990
, “
Biaxial Extension Studies Using Inflation of Sheets of Unimodal Model Networks
,”
Rubber Chemistry and Technology
, Vol.
63
, pp.
276
284
.
21.
Yongxiang
G.
, and
Jisheng
L.
,
1994
, “
The Study on Mechanical Parameters of Finite Deformation of Membranes
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
61
, pp.
202
204
.
22.
Zamani
N. G.
,
Watt
D. F.
, and
Esteghamatian
M.
,
1989
, “
Status of the Finite Element Method in the Thermoforming Process
,”
International Journal of Numerical Methods in Engineering
, Vol.
28
, pp.
2681
2693
.
This content is only available via PDF.
You do not currently have access to this content.