Crack-tip amplification and shielding by micro-cracks in piezoelectric solids – Part II: Dynamic case

The crack-tip dynamic amplification and shielding by micro-cracks in an unbounded, two-dimensional, homogeneous and linear piezoelectric solid are studied in this paper using a time-domain boundary element method (BEM). The BEM is based on the time-domain hypersingular traction boundary integral equations (BIEs). A quadrature formula for the temporal discretization is adopted to approximate the convolution integrals and a collocation method for the spatial discretization. Quadratic quarter-point elements are implemented at all crack-tips. A novel definition of the dynamic amplification ratios of the dynamic field intensity factors and the mechanical strain or electrical energy release rate is introduced. Then the influences of various loading conditions, the location and orientation of the micro-cracks on the dynamic amplification ratios are investigated. Compared with the corresponding static amplification ratios as presented in Part I, some interesting and useful findings are presented together with a simple method which is very feasible for engineering applications.