Dynamic stress concentration and failure characteristics around elliptical cavity subjected to impact loading

Wave function expansion method is used to solve the scattering and dynamic stress concentration around the elliptic cavity in the full plane under steady state linear elastic stationary incident SH wave with arbitrary angle. Under the elliptical coordinate system, Mathieu equation is obtained by separating variables from Helmholtz equation. Considering the simplicity of Mathieu function in solving elliptic boundary problem, the incident plane wave is expanded into the series of Mathieu function, and the full wave function is obtained from the stress boundary condition of the elliptic cavity, then the response of the elliptic cavity subjected to the steady state linear elastic stationary incident SH wave is obtained. Through the Fourier integral transformation of transient impact, the dynamic stress concentration of transient incident SH wave around an elliptical cavity can be obtained. In addition, the finite element method (FEM) numerical simulation software LS-DYNA is used to calculate the dynamic stress concentration and plastic deformation around the elliptical cavity with transient impact. Furthermore, the influence of the initial stress on plastic deformation is obtained. The results show that the incident angel, wave number and the ellipse axis ratio have great influence on the distribution of dynamic stress concentration and the failure of the elliptical cavity.