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 .