Abstract：The problem of a doubly periodic array of cracks and rigid line inclusions in an infinite medium under far-field antiplane shear is investigated. By employing the conformal mapping technique and the elliptical function theory, an exact solution of the whole-field stress is obtained. The closed form formulae for the stress intensity factor at the tips of cracks and rigid line inclusions are presented. The interaction of the tip fields between cracks and rigid line inclusions is discussed. The major results are: (a) the tip fields of cracks and rigid line inclusions show different laws with the change of horizontal and vertical distribution periods; (b) with the increase of the length of cracks 2a (0≤a/ω1≤0.5), the stress intensity factor of cracks increases monotonously, whereas the tip field of rigid line inclusions show almost unchanged; (c) when the length of rigid line inclusions 2d (0≤d/ω2≤1) increases, the stress intensity factor of rigid line inclusions gradually decreases from 1 to 0, whereas the tip field of cracks is only slightly increased.
2014, Vol. 35 
