Effective stiffness of a periodically cracked 3-D solid

Abstract

This paper studies the effective elastic stiffness of 3-D periodically cracked solids. A direct approach is used to solve the transition problem to obtain the effective stiffness from the details of the microstructure. A specific class of periodically cracked solids is then considered. The crack opening volume for these periodic configurations were obtained using a specialized Boundary Element Method (BEM). The BEM involves special techniques for evaluating finite-part integrals and for approximating the periodic Green function. Finally, results for the effective stiffness of particular configurations of periodically cracked 3-D solids are presented and compared with approximate methods. These results indicate that, in general, the crack density parameter is not sufficient to characterize a damaged solid.