A HIGHER-ORDER SUBDOMAIN METHOD FOR FINDING LOCAL STRESS-FIELDS IN COMPOSITES

The problem of finding local and volume averaged stresses in a two-dim ensional heterogeneous solid is formulated in terms of fundamental poi nt load solutions (Green's function) leading to singular integral equa tions. The resulting equations are solved approximately using a subdom ain method in which closed form solutions for a rectangular subdomain are obtained and utilized to find the full field solution. Previously, closed form solutions for a rectangular subvolume had been found, but only for the case of atl assumed constant strain. in the present paye r the solution is obtained for a quadratic form which includes not onl y the usual constant term but also linear and quadratic terms. The adv antages of using the higher order solutions is illustrated by finding the local field in a periodic composite with square fibers. The numeri cal solution takes less than 90 CPU s on a workstation. The solution y ields average properties independent of the reference modulus as would be expected for an accurate solution of the singular integral equatio n and the effective transverse modulus vs volume fraction is close to that from Christensen's model developed for round fibers. (C) 1998 Els evier Science Ltd. All rights reserved.