GAUSS INTEGRATION APPLIED TO A GREENS-FUNCTION FORMULATION FOR CYLINDRICAL FIBER COMPOSITES

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.