Jt. Cheng et al., GAUSS INTEGRATION APPLIED TO A GREENS-FUNCTION FORMULATION FOR CYLINDRICAL FIBER COMPOSITES, Mechanics of materials, 26(4), 1997, pp. 247-267
The stress in an elastic two phase material is formulated in terms of
eigenstrains and Green's functions leading to a singular integral equa
tion. The singularity is dealt with by a subtraction technique and con
tour integrations, one of which corresponds to the Eshelby solution. T
he remaining non-singular integration is evaluated numerically using a
Gauss rule. The calculated local stresses are within 1% of the analyt
ical solution for an isolated inclusion problem. Also, the effective p
roperties as a function of volume fraction are in good agreement with
Christensen's analytical result. The method is then used to study rect
angular versus square packing. The volume averaged stiffness for recta
ngular packing may be either higher or lower than that for square pack
ing, depending on the loading direction. The stress concentration fact
or is shown to increase with fiber volume fraction. The stress concent
ration factor also increases at a decreasing rate as the fiber to matr
ix stiffness ratio is increased. All changes examined that an increase
in the stiffness, whether by increased fiber volume fraction, increas
ed fiber stiffness or an alternate packing arrangement, also increase
the fiber stress concentration factor. (C) 1997 Elsevier Science Ltd.