It is well known that end effects in a composite material do not always decay as they do in a homogeneous and isotropic material, but there is no unified explanation for this difference. We note that the stress field in a composite material can be resolved into two kinds: one is the stress distribution in an isotropic and homogeneous reference system where Saint-Venant’s principle is satisfied and the other is the internal stress field induced by the incompatibility. Considering that the incompatibility is proportional to the difference between the elastic compliances of the components or to the deviation from isotropy, we propose, based on an argument concerning the dislocations associated with the incompatibility, a reason why end effects may survive to a long distance in a composite material.

1.
Arimitsu
Y.
,
Nishioka
K.
, and
Senda
T.
,
1994
, “
Analysis of Anisotropic Elasticity by Means of Internal Stress in Reference Isotropic Elastic Body
,”
Z. Angew. Math. Mech.
, Vol.
74
, pp.
465
473
.
2.
Choi
I.
, and
Horgan
C. O.
,
1977
, “
Saint-Venant’s Principle and End Effects in Anisotropic Elasticity
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
44
, pp.
424
430
.
3.
Choi
I.
, and
Horgan
C. O.
,
1978
, “
Saint-Venant End Effects for Plane Deformation of Sandwich Strips
,”
Int. J. of Solid Structures
, Vol.
14
, pp.
187
195
4.
Dong
S. B.
, and
Goetschel
D. B.
,
1982
, “
Edge Effect in Laminated Composite Plates
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
49
, pp.
129
135
.
5.
Fung, Y. C., 1965, Foundations of Solid Mechanics, Prentice-Hall, Englewood Cliffs, NJ.
6.
Goodier
J. N.
,
1937
, “
A General Proof of Saint-Venant’s Principle
,”
Phil. Mag. Ser. 7
, Vol.
23
, pp.
607
609
.
7.
Hoff
N. J.
,
1945
, “
The Applicability of Saint-Venant’s Principle to Airplane Structures
,”
J. Aeronautical Sci.
, Vol.
12
, pp.
455
460
.
8.
Horgan
C. O.
,
1972
a, “
On Saint-Venant’s Principle in Plane Anisotropic Elasticity
,”
J. of Elasticity
, Vol.
2
, pp.
169
180
.
9.
Horgan
C. O.
,
1972
b, “
Some Remarks on Saint-Venant’s Principle for Transversely Isotropic Composites
,”
J. of Elasticity
, Vol.
2
, pp.
335
339
.
10.
Horgan
C. O.
,
1982
, “
Saint-Venant End Effects in Composites
,”
J. Compos. Mater.
, Vol.
16
, pp.
411
422
.
11.
Horgan
C. O.
,
1989
, “
Recent Developments Concerning Saint-Venant’s Principle: An Update
,”
Applied Mechanics Reviews
, Vol.
42
, pp.
295
303
.
12.
Horgan, C. O., and Knowles, J. K. 1983, “Recent Developments Concerning Saint-Venant’s Principle,” Advances in Applied Mechanics, Vol. 23, Academic Press, San Diego, CA, pp. 179–269.
13.
Kro¨ner, E., 1958, Kontinuumstheorie der Versetzungen und Eigenspannungen, Springer-Verlag, Berlin.
14.
Mura, T., 1982, Micromechanics of Defects in Solids, Martinus Nijhoff, The Hague, The Netherlands.
15.
Nishioka
K.
,
Takai
T.
,
Arimitsu
Y.
, and
Ohashi
T.
,
1987
, “
A Method of Analyzing Elastic Constraints due to Grain or Interphase Boundaries
,”
Mechanics of Materials
, Vol.
6
, pp.
139
145
.
16.
Nye, J. F., 1967, Physical Properties of Crystals, Oxford University Press, London.
17.
Okumura, H., Watanabe K., and Yamada, Y., 1985, “Finite-Element Analyses of Saint-Venant End Effects for Composite Materials,” ASTM Spec. Tech. Publ., pp. 225–235.
18.
de Saint-Venant, B., 1855, Me´moire sur la Torsion des Prismes, Me´m. des Savants e´trangers, Paris.
19.
Sternberg
E.
,
1954
, “
On Saint-Venant’s Principle
,”
Quart. Appl. Math.
, Vol.
11
, pp.
393
402
.
20.
Timoshenko, S. P., and Goodier, J. N., 1970, Theory of Elasticity, 3rd ed., McGraw-Hill, New York.
21.
von Mises
R.
,
1945
, “
On Saint-Venant’s Principle
,”
Bull. Amer. Math. Soc.
, Vol.
51
, pp.
555
562
.
22.
Zanaboni
O.
,
1937
, “
Dimostrazione General del Principio del de Saint-Venant
,”
Atti. Accad. Lincei, Roma
, Vol.
25
, pp.
117
121
.
This content is only available via PDF.
You do not currently have access to this content.