A Boundary Element Analysis of Quasi-Brittle Solids Containing Cracks

Abstract

Quasi-brittle solids usually contain many cracks. When numerical methods are used, it is difficult to simulate all the cracks’ behaviors, especially when the crack propagation is included. To surmount the difficulty, a new procedure combining the subdomain boundary element method and the generalized self-consistent scheme is presented. The behavior of a single crack is analyzed first. The obtained information is then used to predict the overall behavior of the cracked solids. The relationship between the overall response of the cracked solids and the growth of wing cracks is established numerically. A cohesive-crack model is used to simulate the fracture process zone of the quasi-brittle solids. Besides, the advancement of the wing crack tip is used as a control variable. An incremental iteration algorithm is developed to trace the growth of the wing (secondary) cracks, which is not known a priori. The influence of the crack angle and the friction coefficient on the effective moduli is also investigated. Finally, a gypsum square plate containing orderly distributed cracks is analyzed to illustrate the adequacy and efficiency of the present procedure.