Abstract：This paper investigates the anti-plane problem of double-periodic cracks of unequal sizes in a one-dimensional hexagonal piezoelectric quasicrystal material under combined anti-plane mechanical loading and in-plane electrical loading. By employing the elliptic function theory and the conformal mapping techniques, a closed-form analytical solution to the problem is derived. Based on this solution, exact expressions are obtained for the field intensity factors of stress and electric displacement at the crack tips, as well as for the effective electro-elastic moduli of the cracked material. Numerical calculations are conducted to reveal the mechanical-electrical coupling effects induced by multi-crack interactions, particularly the shielding and amplification effects of smaller cracks on the main crack. Furthermore, the degradation of the effective electro-elastic moduli due to micro-crack arrays is quantified. The obtained solution encompasses various typical crack configurations as special cases, such as rectangular arrays with equal crack lengths, rhombic arrays, and staggered row-column cracks, thereby providing a theoretical basis for fracture analysis of one-dimensional hexagonal piezoelectric quasicrystal materials.
2026, Vol. 47 
