Analytical Solution for Dynamic Fracture of Two Coplanar Limited-Permeable Cracks in Magneto-Electro-Elastic Material

Abstract

Abstract. Two coplanar limited-permeable rectangular cracks in magneto-electro-elastic material are modeled and solved using generalized Almansi's theorem. The mixed boundary value problem is formulated into three pairs of dual integral equations with the help of Fourier transform, in which the unknown functions are the jumps of displacements across the crack-surface. By directly expanding the unknown functions into infinite series form of Jacobi polynomials, the dual integral equations are solved, and the analytical expressions of generalized intensity factors are derived strictly. Based on the generalized intensity factors, the dynamic behaviors of two cracks are estimated under P-wave loads. To show the trends of effects of loading frequency and geometry of cracks on the generalized intensity factors, top finite terms of infinite series are numerically calculated based on the Schmidt method. Numerical results are then drawn graphically. It reveals that the trend of two cracks forming a larger crack by propagating depends strongly on crack geometry and load frequency. This work illuminate the condition inducing different crack propagation patterns, which will benifit the forecast of damage forms of transversely isotropic magneto-electro-elastic material.