We consider a large deformation plane-strain problem involving a compressible orthotropic solid subjected to uniaxial compressive loading along one of the principle directions which is aligned with the boundary of a half-space. An exact solution for the displacement field is obtained and a condition for the smallest compressive load corresponding to the onset of a surface instability is determined. It is shown that when the compression occurs along the stiffest direction this condition is expressible in terms of a cubic polynomial, and that the corresponding critical load is lower than the well-known estimate which determines the critical load to be equal to the inplane shear modulus.

1.
Ben-chin
K.
, and
Pipkin
A. C.
,
1972
, “
Finite Buckling of Fiber-Reinforced Columns
,”
Acta Mechanica
, Vol.
13
, pp.
265
280
.
2.
Biot, M. A., 1965, Mechanics of Incremental Deformations, John Wiley and Sons, New York.
3.
Budiansky
B.
,
1983
, “
Micromechanics
,”
Computers and Structures
, Vol.
16
, pp.
3
12
.
4.
Christensen
R. M.
,
1994
, “
Material Instability for Fiber Composites
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
61
, pp.
476
477
.
5.
Geymonat
G.
,
Mu¨ller
S.
, and
Triantafyllidis
N.
,
1993
, “
Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity
,”
Arch. Rational Mech. Anal.
, Vol.
121
, pp.
231
290
.
6.
Hill
R.
, and
Hutchinson
J. W.
,
1975
, “
Bifurcation phenomena in the plane tension test
,”
J. Mech. Phys. Solids
, Vol.
23
, pp.
239
264
.
7.
Kyriakides
S.
,
Arseculeratne
R.
,
Perry
E. J.
, and
Liechti
K. M.
,
1995
, “
On the compressive failure of fiber reinforced composites
,”
Int. J. Solids Structures
, Vol.
32
, pp.
689
738
.
8.
Malvem, L. E., 1969, Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, Englewood Cliffs, NJ.
9.
Rosen, B. W., 1965, “Mechanics of composite strengthening,” Fiber Composite Materials, Am. Soc. Metals Seminar.
10.
Shield
T. W.
,
Kim
K. S.
, and
Shield
R. T.
,
1994
, “
The Buckling of an Elastic Layer Bonded to an Elastic Substrate in Plane Strain
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
61
, pp.
231
235
.
11.
Steif
P. S.
,
1987
, “
An exact two-dimensional approach to fiber micro-buckling
,”
Int. J. Solids Struct
, Vol.
23
, pp.
1235
1246
.
12.
Steif
P. S.
,
1988
, “
A simple model for the compressive failure of weakly bonded, fiber reinforced composites
,”
J. Composite Materials
, Vol.
22
, pp.
818
828
.
13.
Triantafyllidis
N.
, and
Maker
B. N.
,
1985
, “
On the Comparison Between Microscopic and Macroscopic Instability Mechanisms in a Class of Fiber-Reinforced Composites
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
52
, pp.
794
800
.
This content is only available via PDF.
You do not currently have access to this content.