3.1 Case study and verification
In the elliptical coordinate system, the major and minor axis and axis
ratio of any ellipse can be calculated by Eq (3). To simplify the
problem, the focal length of the ellipse is taken as a =1m. The
four cases of radial coordinate ξ = 0.1, 0.2, 0.5, 1.5 are
determined to study the influence of different axial ratio on the
scattering of incident SH wave around the elliptical inclusion. The
smaller ξ , the larger the elliptical axis ratio and the closer
the shape is to crack. The larger ξ , the smaller the elliptical
axis ratio, and the closer the shape is to circle. The parameter
settings of the radial coordinate are illustrated in Table 1.
In this study, the wave velocity cs was set as
2300 m/s, the incident wave numbers (k ) were predetermined to be
0.2, 0.5 and 1, respectively. The range of stress wave numbers generated
by earthquake, engineering blasting and mostly impacts was covered here
in.14 The difference in the material properties of the
medium and elliptical inclusion additionally affected the scattering of
incident SH wave around the elliptical inclusion.26This study set up three cases for calculation, as shown in Table 2.
In Table 2,k* =k 2/k 1,μ* =μ 1/μ 2 and three
cases correspond to the inclusion being stiffer, softer and much softer
than the medium, respectively.
Subsequently, the case was computed when the material properties
parameters of the inclusion and medium were the same to verify the
correctness of the derivation. When
the inclusion and medium possessed the identical material properties
parameters, the propagation of SH wave in the inclusion was the same as
the propagation in the medium, and dynamic stress concentration was only
related to the phase difference in the stress wave. Therefore, incident
SH wave only produced the incident wave, and not generated the scattered
and standing waves, leading to αDSCF determined
only by the incident wave. According to the definition ofαηDSCF , the maximum value ofαηDSCF was 1. The numerical
results are shown in Fig. 3.
In Fig. 3, as the incident wave number and axial ratio changed,αηDSCF had a maximum value at
the angle perpendicular to the incident direction (both ends of the
elliptical minor axis), and a minimum value at the angle of incidence
(both ends of the elliptical major axis). The maximum and minimum values
of αηDSCF were 1 and 0.αηDSCF gradually increased with
the angle from 0° to 90°, and distribution ofαηDSCF was symmetrical about
the x and y axes. To verify the correctness of the
theoretical derivation, the numerical results were compared with those
available in literature. As expected, the verification exhibited
excellent agreement between the results of the present study and those
available in the literature.10