Dynamic stress intensity factors of two 3D rectangular cracks in a transversely isotropic elastic material under a time-harmonic elastic P-wave

• The dynamic behavior of two 3D rectangular cracks in elasticity is studied.
• The dynamic stress intensity factors near the rectangular crack edges is obtained.
• Generalized Almansi’s theorem and the Schmidt method are used.
• Numerical examples are provided to show the influence of factors on the DSIFs.

The dynamic stress intensity factors (DSIFs) of two 3D rectangular cracks in a transversely isotropic elastic material under an incident harmonic stress wave are investigated by generalized Almansi’s theorem and the Schmidt method in the present paper. Using 2D Fourier transform and defining the jumps of displacement components across the crack surface as the unknown functions, three pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement components across the crack surfaces are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the geometric shape of the rectangular crack, the characteristics of the harmonic wave and the distance between two rectangular cracks on the DSIFs of the transversely isotropic elastic material.