In this first effort, a partially-debonded circular inclusion in a one-dimensional quasicrystal material with piezoelectric effect is studied. This mixed boundary value problem of a circular interface crack is reduced to solving three Riemann–Hilbert problems with the use of analytical continuation theory. The crack-tip singularity of the circular interface crack is investigated and the intensity factors of the stresses in the phonon and the phason fields and electric displacements are derived explicitly. Some particular cases are provided to show the effect of the crack angle, material properties and loadings on the field singularities at the tips of the circular interface crack.

首先，研究具有压电效应的一维准晶体材料中部分剥离的圆形夹杂物。圆形界面裂纹的混合边值问题被简化为使用解析连续理论来解决三个Riemann-Hilbert问题。研究了圆形界面裂纹的裂纹尖端奇异性，并明确推导了声子和声子场中应力的强度因子以及电位移。提供了一些特殊情况，以显示裂纹角度，材料特性和载荷对圆形界面裂纹尖端处的场奇异性的影响。