Simulation of the mechanical behavior of soft tissues is critical for many physiological and medical device applications. Accurate mechanical test data is crucial for both obtaining the form and robust parameter determination of the constitutive model. For incompressible soft tissues that are either membranes or thin sections, planar biaxial mechanical testing configurations can provide much information about the anisotropic stress–strain behavior. However, the analysis of soft biological tissue planar biaxial mechanical test data can be complicated by in-plane shear, tissue heterogeneities, and inelastic changes in specimen geometry that commonly occur during testing. These inelastic effects, without appropriate corrections, alter the stress-traction mapping and violates equilibrium so that the stress tensor is incorrectly determined. To overcome these problems, we presented an analytical method to determine the Cauchy stress tensor from the experimentally derived tractions for tethered testing configurations. We accounted for the measured testing geometry and compensate for run-time inelastic effects by enforcing equilibrium using small rigid body rotations. To evaluate the effectiveness of our method, we simulated complete planar biaxial test configurations that incorporated actual device mechanisms, specimen geometry, and heterogeneous tissue fibrous structure using a finite element (FE) model. We determined that our method corrected the errors in the equilibrium of momentum and correctly estimated the Cauchy stress tensor. We also noted that since stress is applied primarily over a subregion bounded by the tethers, an adjustment to the effective specimen dimensions is required to correct the magnitude of the stresses. Simulations of various tether placements demonstrated that typical tether placements used in the current experimental setups will produce accurate stress tensor estimates. Overall, our method provides an improved and relatively straightforward method of calculating the resulting stresses for planar biaxial experiments for tethered configurations, which is especially useful for specimens that undergo large shear and exhibit substantial inelastic effects.

References

References
1.
Sacks
,
M.
,
2000
, “
Biaxial Mechanical Evaluation of Planar Biological Materials
,”
J. Elast.
,
61
(
1–3
), pp.
199
246
.10.1023/A:1010917028671
2.
Sun
,
W.
,
Sacks
,
M. S.
,
Sellaro
,
T. L.
,
Slaughter
,
W. S.
, and
Scott
,
M. J.
,
2003
, “
Biaxial Mechanical Response of Bioprosthetic Heart Valve Biomaterials to High In-Plane Shear
,”
ASME J. Biomech. Eng.
,
125
(
3
), pp.
372
380
.10.1115/1.1572518
3.
Stella
,
J. A.
,
Liao
,
J.
, and
Sacks
,
M. S.
,
2007
, “
Time-Dependent Biaxial Mechanical Behavior of the Aortic Heart Valve Leaflet
,”
J. Biomech.
,
40
(
14
), pp.
3169
3177
.10.1016/j.jbiomech.2007.04.001
4.
Sacks
,
M. S.
,
1999
, “
A Method for Planar Biaxial Mechanical Testing That Includes In-Plane Shear
,”
ASME J. Biomech. Eng.
,
121
(
5
), pp.
551
555
.10.1115/1.2835086
5.
Freed
,
A. D.
,
Einstein
,
D. R.
, and
Sacks
,
M. S.
,
2010
, “
Hypoelastic Soft Tissues: Part II: In-Plane Biaxial Experiments
,”
Acta Mech.
,
213
(
1–2
), pp.
205
222
.10.1007/s00707-010-0357-y
6.
Fomovsky
,
G. M.
, and
Holmes
,
J. W.
,
2010
, “
Evolution of Scar Structure, Mechanics, and Ventricular Function After Myocardial Infarction in the Rat
,”
Am. J. Physiol. Heart Circ. Physiol.
,
298
(
1
), pp.
H221
228
.10.1152/ajpheart.00495.2009
7.
Sun
,
W.
,
Sacks
,
M. S.
, and
Scott
,
M. J.
,
2003
, “
Numerical Simulations of the Planar Biaxial Mechanical Behavior of Biological Materials
,”
ASME Summer Bioengineering
,
L. J.
Soslowsky
, ed.,
ASME
,
Miami, FL
, pp.
875
876
.
8.
Jor
,
J. W.
,
Nash
,
M. P.
,
Nielsen
,
P. M.
, and
Hunter
,
P. J.
,
2011
, “
Estimating Material Parameters of a Structurally Based Constitutive Relation for Skin Mechanics
,”
Biomech. Model. Mechanobiol.
,
10
(
5
), pp.
767
778
.10.1007/s10237-010-0272-0
9.
Bellini
,
C.
,
Glass
,
P.
,
Sitti
,
M.
, and
Di Martino
,
E. S.
,
2011
, “
Biaxial Mechanical Modeling of the Small Intestine
,”
J. Mech. Behav. Biomed. Mater.
,
4
(
8
), pp.
1727
1740
.10.1016/j.jmbbm.2011.05.030
10.
Azadani
,
A. N.
,
Chitsaz
,
S.
,
Matthews
,
P. B.
,
Jaussaud
,
N.
,
Leung
,
J.
,
Tsinman
,
T.
,
Ge
,
L.
, and
Tseng
,
E. E.
,
2012
, “
Comparison of Mechanical Properties of Human Ascending Aorta and Aortic Sinuses
,”
Ann. Thorac. Surg.
,
93
(
1
), pp.
87
94
.10.1016/j.athoracsur.2011.08.002
11.
Kamenskiy
,
A. V.
,
Pipinos
,
I. I.
,
Dzenis
,
Y. A.
,
Lomneth
,
C. S.
,
Kazmi
,
S. A. J.
,
Phillips
,
N. Y.
, and
MacTaggart
,
J. N.
,
2014
, “
Passive Biaxial Mechanical Properties and In Vivo Axial Pre-Stretch of the Diseased Human Femoropopliteal and Tibial Arteries
,”
Acta Biomater.
,
10
(
3
), pp.
1301
1313
.10.1016/j.actbio.2013.12.027
12.
Gregory
,
D. E.
, and
Callaghan
,
J. P.
,
2011
, “
A Comparison of Uniaxial and Biaxial Mechanical Properties of the Annulus Fibrosus: A Porcine Model
,”
ASME J. Biomech. Eng.
,
133
(
2
), p.
024503
.10.1115/1.4003327
13.
Sun
,
W.
,
Sacks
,
M. S.
, and
Scott
,
M. J.
,
2005
, “
Effects of Boundary Conditions on the Estimation of the Planar Biaxial Mechanical Properties of Soft Tissues
,”
ASME J. Biomech. Eng.
,
127
(
4
), pp.
709
715
.10.1115/1.1933931
14.
O'Connell
,
G.
,
Sen
,
S.
, and
Elliott
,
D.
,
2012
, “
Human Annulus Fibrosus Material Properties From Biaxial Testing and Constitutive Modeling Are Altered With Degeneration
,”
Biomech. Model. Mechanobiol.
,
11
(
3–4
), pp.
493
503
.10.1007/s10237-011-0328-9
15.
Sommer
,
G.
,
Eder
,
M.
,
Kovacs
,
L.
,
Pathak
,
H.
,
Bonitz
,
L.
,
Mueller
,
C.
,
Regitnig
,
P.
, and
Holzapfel
,
G. A.
,
2013
, “
Multiaxial Mechanical Properties and Constitutive Modeling of Human Adipose Tissue: A Basis for Preoperative Simulations in Plastic and Reconstructive Surgery
,”
Acta Biomater.
,
9
(
11
), pp.
9036
9048
.10.1016/j.actbio.2013.06.011
16.
Hu
,
J. J.
,
Chen
,
G. W.
,
Liu
,
Y. C.
, and
Hsu
,
S. S.
,
2014
, “
Influence of Specimen Geometry on the Estimation of the Planar Biaxial Mechanical Properties of Cruciform Specimens
,”
Exp. Mech.
,
54
(
4
), pp.
615
631
.10.1007/s11340-013-9826-2
17.
Simón-Allué
,
R.
,
Cordero
,
A.
, and
Peña
,
E.
,
2014
, “
Unraveling the Effect of Boundary Conditions and Strain Monitoring on Estimation of the Constitutive Parameters of Elastic Membranes by Biaxial Tests
,”
Mech. Res. Commun.
57
(
0
), pp.
82
89
.10.1016/j.mechrescom.2014.01.009
18.
Lanir
,
Y.
,
1979
, “
A Structural Theory for the Homogeneous Biaxial Stress-Strain Relationships in Flat Collagenous Tissues
,”
J. Biomech.
,
12
(
6
), pp.
423
436
.10.1016/0021-9290(79)90027-7
19.
Lanir
,
Y.
, and
Fung
,
Y. C.
,
1974
, “
Two-Dimensional Mechanical Properties of Rabbit Skin. II. Experimental Results
,”
J. Biomech.
,
7
(
2
), pp.
171
182
.10.1016/0021-9290(74)90058-X
20.
Fan
,
R.
, and
Sacks
,
M. S.
,
2014
, “
Simulation of Planar Soft Tissues Using a Structural Constitutive Model: Finite Element Implementation and Validation
,”
J. Biomech
,
47
(9), pp.
2043
2054
.
21.
Sacks
,
M. S.
,
2000
, “
A Structural Constitutive Model for Chemically Treated Planar Connective Tissues Under Biaxial Loading
,”
Comput. Mech.
,
26
(
3
), pp.
243
249
.10.1007/s004660000175
22.
Sacks
,
M. S.
,
Lam
,
T. V.
, and
Mayer
,
J. E. Jr.
,
2004
, “
A Structural Constitutive Model for the Native Pulmonary Valve
,” 26th Annual International Conference of the
IEEE
Engineering in Medicine and Biology Society (IEMBS), San Francisco, CA, Sept. 1–5, Vol. 2, pp.
3734
3736
.10.1109/IEMBS.2004.1404048
23.
Sacks
,
M. S.
,
Merryman
,
W. D.
, and
Schmidt
,
D. E.
,
2009
, “
On the Biomechanics of Heart Valve Function
,”
J. Biomech.
,
42
(
12
), pp.
1804
1824
.10.1016/j.jbiomech.2009.05.015
24.
Lee
,
C. H.
,
Amini
,
R.
,
Gorman
,
R. C.
,
Gorman
,
J. H.
, III
, and
Sacks
,
M. S.
,
2014
, “
An Inverse Modeling Approach for Stress Estimation in Mitral Valve Anterior Leaflet Valvuloplasty for In-Vivo Valvular Biomaterial Assessment
,”
J. Biomech.
,
47
(
9
), pp.
2055
2063
.10.1016/j.jbiomech.2013.10.058
25.
Billiar
,
K. L.
, and
Sacks
,
M. S.
,
2000
, “
Biaxial Mechanical Properties of the Natural and Glutaraldehyde Treated Aortic Valve Cusp—Part I: Experimental Results
,”
ASME J. Biomech. Eng.
,
122
(
1
), pp.
23
30
.10.1115/1.429624
26.
Billiar
,
K. L.
, and
Sacks
,
M. S.
,
2000
, “
Biaxial Mechanical Properties of the Native and Glutaraldehyde-Treated Aortic Valve Cusp: Part II—A Structural Constitutive Model
,”
ASME J. Biomech. Eng.
,
122
(
4
), pp.
327
335
.10.1115/1.1287158
27.
Sacks
,
M. S.
,
Hamamoto
,
H.
,
Connolly
,
J. M.
,
Gorman
,
R. C.
,
Gorman
,
J. H.
, III
, and
Levy
,
R. J.
,
2007
, “
In Vivo Biomechanical Assessment of Triglycidylamine Crosslinked Pericardium
,”
Biomaterials
,
28
(
35
), pp.
5390
5398
.10.1016/j.biomaterials.2007.08.021
28.
Sun
,
W.
, and
Sacks
,
M. S.
,
2005
, “
Finite Element Implementation of a Generalized Fung-Elastic Constitutive Model for Planar Soft Tissues
,”
Biomech. Model. Mechanobiol.
,
4
(
2–3
), pp.
190
199
.10.1007/s10237-005-0075-x
29.
Fung
,
Y. C.
,
1993
,
Biomechanics: Mechanical Properties of Living Tissues
,
Springer Verlag
,
New York
.
30.
Hanabusa
,
Y.
,
Takizawa
,
H.
, and
Kuwabara
,
T.
,
2013
, “
Numerical Verification of a Biaxial Tensile Test Method Using a Cruciform Specimen
,”
J. Mater. Process. Technol.
,
213
(
6
), pp.
961
970
.10.1016/j.jmatprotec.2012.12.007
31.
Zhao
,
X.
,
Berwick
,
Z. C.
,
Krieger
,
J. F.
,
Chen
,
H.
,
Chambers
,
S.
, and
Kassab
,
G. S.
,
2014
, “
Novel Design of Cruciform Specimens for Planar Biaxial Testing of Soft Materials
,”
Exp. Mech.
,
54
(
3
), pp.
343
356
.10.1007/s11340-013-9808-4
32.
Ramault
,
C.
,
Makris
,
A.
,
Van Hemelrijck
,
D.
,
Lamkanfi
,
E.
, and
Van Paepegem
,
W.
,
2011
, “
Comparison of Different Techniques for Strain Monitoring of a Biaxially Loaded Cruciform Specimen
,”
Strain
,
47
, pp.
210
217
.10.1111/j.1475-1305.2010.00760.x
33.
Makris
,
A.
,
Vandenbergh
,
T.
,
Ramault
,
C.
,
Van Hemelrijck
,
D.
,
Lamkanfi
,
E.
, and
Van Paepegem
,
W.
,
2010
, “
Shape Optimisation of a Biaxially Loaded Cruciform Specimen
,”
Polym. Test.
,
29
(
2
), pp.
216
223
.10.1016/j.polymertesting.2009.11.004
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