Jt. Cheng et al., A HIGHER-ORDER SUBDOMAIN METHOD FOR FINDING LOCAL STRESS-FIELDS IN COMPOSITES, International journal of solids and structures, 35(36), 1998, pp. 5189-5203
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.