4.2 Transient response of radial stress
The transient response of radial stress with different axial ratios and different ωp in the three cases was evaluated in the case study. The numerical results were shown in Figs. 19-23. The distribution of transientαξDSCF was similar to that of steady-state αξDSCF . When the shape of inclusion was close to circle and the incident wave was highωp , transientαξDSCF exhibited multiple extreme values. Distribution ofαξDSCF on the front wave surface was different from that on the back wave surface, but distribution of αξDSCF was symmetric about the x -axis. In Fig. 19,αξDSCF always had the largest value at both ends of the elliptical major axis, with the maximum value reaching 7.869, and the minimum value of 0 at both ends of the elliptical minor axis. The value of transientαξDSCF in Figs. 20 and 21 was much smaller than the value in Fig. 19, and a majority of the maximum values were around 1. At a small ωp , distribution of transient αξDSCF was similar to Fig.19. At a large ωp , the maximum and minimum values did not always appear at both ends of the major and minor axes of ellipse, while multiple extreme values did.
Fig. 22 indicated that when the elliptical axial ratio andωp were constant, transientαξDSCF for the inclusion was stiffer than the medium decrease upon reducing the elliptical axial ratio, from 7.214 to 2.710. For the inclusion was softer than the medium, transient αξDSCFincreased upon decreasing the elliptical axial ratio, from 0.597 to 1.156. Numerical results demonstrated that as the inclusion was stiffer than the medium, the radial stress concentration for the shape of inclusion close to crack was more significant than that for the shape of inclusion close to circle. But for the inclusion was softer than the medium, the radial stress concentration for shape of inclusion approaching circle was more significant than that as shape of inclusion approaching crack. The difference in material properties between the inclusion and medium also affected the changes in transientαξDSCF with elliptical axial ratio, which was consistent with transientαηDSCF . In addition, at the small radial coordinate, the shape of elliptical inclusion was close to crack, the distribution shape of transientαξDSCF around both ends of the elliptical major axis was similar to crack tip, and the value of transient αξDSCF changed drastically. However, at the lager radial coordinate, the shape of elliptical inclusion was close to circle, the distribution shape of transient αξDSCF around both ends of the elliptical major axis was approximate to the circle, and the value of transient αξDSCFvaried slightly. This behavior was consistent with the distribution of stead-state αξDSCF .
Fig. 23 demonstrated that at the constant elliptical axial ratio andωp , the transientαξDSCF with the inclusion stiffer than the medium was much larger than the transientαξDSCF for the inclusion softer than the medium. The numerical findings indicated that the radial stress concentration of the stiff inclusion was more significant than that of soft inclusion, and the stiffer the inclusion, the greater the possibility of failure at both ends of the major axis. The value of transient αξDSCF in case 2 was higher than that in case 3, which confirmed that the greater the difference in material properties between the medium and inclusion, the more significant the dynamic stress concentration. This behavior was in accordance with the changes in transientαηDSCF .