This paper is concerned with the constitutive behavior of a particular orthogonal fiber network under biaxial dead loading. We also describe a new kind of biaxial, dead-loading machine which is applicable to anisotropic materials. The machine does not require that the loads are exerted along symmetry axes of the material. A specimen of the cloth was loaded by different loading paths to the same equibiaxial dead-load, and two different final deformations were observed. A related observation was reported by Treloar for rubber in 1948. In order to understand this instability, we experimentally determined the energy function for the cloth. The energy function is then used in a variational calculation to explain this instability.

1.
Ball
J. M.
, and
Schaeffer
D. G.
,
1983
, “
Bifurcation and Stability of Homogeneous Equilibrium Configurations of an Elastic Body under Dead-Load Tractions
,”
Mathematical Proceeding Cambridge Philosophical Society
, Vol.
94
, pp.
315
339
.
2.
Chadwick, P., 1976, Continuum Mechanics: Concise theory and problems, George Allen & Unwin, London, pp. 22, 138.
3.
Chen
Y. C.
,
1987
, “
Stability of Homogeneous Deformations of an Incompressible Elastic Body under Dead-Load Surface Tractions
,”
Journal of Elasticity
, Vol.
17
, pp.
223
248
.
4.
Kearsley
E. A.
,
1986
, “
Asymmetric Stretching of a Symmetrically Loaded Elastic Sheet
,”
International Journal of Solids and Structures
, Vol.
22
, pp.
111
119
.
5.
MacSithigh
G. P.
,
1986
, “
Energy-Minimal Finite Deformations of a Symmetrically Loaded Elastic Sheet
,”
Quarterly Journal of Mechanics and Applied Mathematics
, Vol.
39
, pp.
111
123
.
6.
Pipkin
A. C.
,
1974
, “
Generalized Plane Deformations of Ideal Fiber-Reinforced Materials
,”
Quarterly Applied Mathematics
, Vol.
32
, pp.
253
263
.
7.
Pipkin
A. C.
,
1974
, “
Infinitesimal Plane Wrinkling of Inextensible Networks
,”
Journal of Elasticity
, Vol.
17
, pp.
35
52
.
8.
Pipkin
A. C.
, and
Rivlin
R. S.
,
1963
, “
Minimum-Weight Design for Pressure Vessels Reinforced with Inextensible Fibers
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
30
, pp.
103
108
.
9.
Rivlin
R. S.
,
1955
, “
Plane Strain of a Net Formed by Inextensible Cords
,”
Journal of Rational Mechanics and Analysis
, Vol.
4
, pp.
951
974
.
10.
Rivlin
R. S.
,
1948
, “
Large Elastic Deformations of Isotropic Materials II: Some Uniqueness Theorems for Pure Homogeneous Deformation
,”
Philosophical Transactions, Royal Society of Lond.
, Vol.
A240
, pp.
491
508
.
11.
Rivlin
R. S.
,
1974
, “
Stability of Pure Homogeneous Deformation of an Elastic Cube under Dead Loading
,”
Quarterly Applied Mechanics
, Vol.
32
, pp.
265
271
.
12.
Rivlin
R. S.
, and
Saunders
D. W.
,
1951
, “
Large Elastic Deformations of Isotropic Materials VII: Experiments on the Deformation of Rubber
,”
Philosophical Transactions, Royal Society of Lond.
, Vol.
A243
, pp.
251
288
.
13.
Treloar
L. R. G.
,
1948
, “
Stress and Birefringence in Rubber Subjected to General Homogeneous Strain
,”
Proceedings, Physics Society
, Vol.
60
, pp.
135
144
.
14.
Treloar, L. R. G., 1949, Physics of Rubber Elasticity, Oxford University Press, London, pp. 116.
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