Asymptotics of multiple crack interactions and prediction of effective modulus

An asymptotic analysis for crack interactions is performed to solve the doubly periodic array of unbridged/ bridged cracks under unidirectional tension. The solution leads to a closed-form expression for the e€ective Youngʹs modulus of the cracked body. It is a function of the geometry of the crack array and the bridging sti€ness. A comparison with numerical results obtained previously, shows that the closed-form expression yields accurate results at low to moderate levels of crack density and relative crack length, for both unbridged and bridged cracks