Based on complex conformal mapping and Duhamel’s integral method the steady and transient dynamic stress distribution around an elliptical cavity subjected to plane P-wave was obtained. The influence of incident angle(θ0), axial ratio(k) and normalized wave length (t0) on the dynamic stress concentration factor (DSCF) was evaluated. Further, the finite element method (FEM) software LS-DYNA was utilized to validate the analytical solution. The results indicated that the maximum compression DSCF increased with θ0, except θ0=0, and decreased with k. When θ0=0 the maximum tensile DSCF increase with the decrease of k. The position of maximum compression and tensile DSCF varied with incident θ0. Under the transient incident condition DSCF was affected by normalized wave length t0, with the increasing of t0 the DSCF gone up then down finally gone closed to the static stress concentration factor. Further, the stress state around the elliptical cavity under transient impact loading was compared with the experimental results of elastic stress distribution and plastic failure and got a good agreement, and possible dynamic failure modes of elliptical cavity were discussed.

The complex boundary of the elliptical inclusion rendered it difficult to solve the problem of wave scattering. In this study, the steady-state response was analyzed using the wave function expansion method. Subsequently, the Ricker wavelet was employed as the transient disturbance and Fourier transform was used to determine the distribution of transient dynamic stress concentration around the elliptical inclusion. The effects of wave number, elliptical axial ratio and difference in material properties on the distribution of the dynamic stress concentration around the elliptical inclusion were evaluated. The numerical results revealed that the dynamic stress concentration always appeared at both ends of the major axis and minor axis of the elliptical inclusion, and the difference in material properties between the inclusion and medium influenced the variations in the dynamic stress concentration factor with the wave number and elliptical axial ratio.