This paper treats the effective antiplane shear response of a composite consisting of fibers that interact with the matrix through nonlinear Needleman-type cohesive zones. The first paper (Part I) examines effective axial tension response. The composite cylinders representation of a representative volume element (RVE) is employed throughout. For antiplane shear loading the elastic field solution for a single composite cylinder is found in the form of a series expansion whose coefficients are governed by an infinite set of nonlinear equations. Bounds on the total potential energy and the total complementary energy of an RVE do not coincide although they are shown to differ by a term of order $Oc4$ where c is the fiber volume concentration. Interaction effects due to finite volume concentration, coupled with nonlinear interface characterization, are shown to precipitate instability in composite response. [S0021-8936(00)02104-8]

1.
Needleman
,
A.
,
1987
, “
A Continuum Model for Void Nucleation by Inclusion Debonding
,”
ASME J. Appl. Mech.
,
54
, pp.
525
531
.
2.
Hashin
,
Z.
, and
Rosen
,
B. W.
,
1964
, “
The Elastic Moduli of Fiber Reinforced Materials
,”
ASME J. Appl. Mech.
,
31
, pp.
223
232
.
3.
Hashin
,
Z.
,
1990
, “
Thermoelastic Properties of Fiber Composites With Imperfect Interface
,”
Mech. Mater.
,
8
, pp.
333
348
.
4.
Dong, Z., and Levy, A. J., 2000, “Mean Field Estimates of the Response of Fiber Composites with Nonlinear Interface,” Mech. Mater., to appear.
5.
Benveniste
,
Y.
,
1985
, “
The Effective Mechanical Behavior of Composite Materials With Imperfect Contact Between the Constituents
,”
Mech. Mater.
,
4
, pp.
197
208
.
6.
Aboudi, J., 1991, Mechanics of Composite Materials, Elsevier, Amsterdam.
7.
Gurtin, M. E., 1984, “The Linear Theory of Elasticity,” Mechanics of Solids Vol. 2, C. Truesdell, ed., Springer-Verlag, Heidelberg, pp. 1–273.
8.
Needleman
,
A.
,
1992
, “
Micromechanical Modelling of Interfacial Decohesion
,”
Ultramicroscopy
,
40
, pp.
203
214
.
9.
Levy
,
A. J.
,
1996
, “
The Effective Dilatational Response of Fiber Reinforced Composites With Nonlinear Interface
,”
ASME J. Appl. Mech.
,
63
, pp.
357
364
.
10.
Levy
,
A. J.
, and
Dong
,
Z.
,
1998
, “
Effective Transverse Response of Fiber Composites With Nonlinear Interface
,”
J. Mech. Phys. Solids
,
46
, pp.
1279
1300
.
11.
Levy
,
A. J.
,
1997
, “
On the Nucleation of Cavities in Planar Elasticity
,”
Philos. Trans. R. Soc. London, Ser. A
,
355
, pp.
2417
2458
.
12.
Levy
,
A. J.
,
2000
, “
The Fiber Composite With Nonlinear Interface—Part I: Axial Tension
,”
ASME J. Appl. Mech.
,
67
, pp.
727
732
.
13.
Sangani
,
A. S.
, and
Mo
,
G.
,
1997
, “
Elastic Interactions in Particulate Composites With Perfect as Well as Imperfect Interfaces
,”
J. Mech. Phys. Solids
,
45
, pp.
2001
2031
.