Abstract
This article studies the effective constitutive relations of brittle and ductile solids containing either aligned or randomly oriented penny-shaped cracks. The matrix material considered is linear before yielding and behaves with a pure power-law after yielding. An explicit yield function is obtained for the cracked body under general external loading conditions, and the effective stress potential is given in a simple optimization procedure. The results show that the presence of microcracks inside solids significantly lowers the strength of materials.
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