DDM‐based numerical studies for crack amplification and shielding in magneto‐electro‐elastic solid due to an array of parallel microcracks

The distributed dislocation method (DDM) is meticulously used to numerically study the amplification and shielding effects at the crack tip of a macro‐crack in a semipermeable finite magneto‐electro‐elastic (MEE) solid due to the presence of an array of parallel microcracks. The problem is modeled using an extended Stroh formalism approach in MEE materials and DDM, which is then mathematically formulated into a system of singular integral equations. After that, using the Gauss–Chebyshev quadrature scheme, these equations are solved numerically with great precision. The study considers different distributions of horizontal parallel microcracks aligned parallel to the center macro‐crack in horizontal, vertical, and transverse directions. An algorithm based on the iterative bisection method is elaborated to evaluate the semipermeable crack‐face conditions in MEE material. Also, the issue of implementing exact semipermeable crack‐face conditions for large sizes of parallel microcracks and a comparative analysis of these conditions evaluated based on the iterative bisection method and from the explicit formula of the center crack problem is presented. To analyze the amplification and shielding effects at the tip of the macro‐crack, the effects of the presence of these microcracks in the domain with respect to the distance from the macro‐crack tip have been observed on the stress intensity factors in comparison to stress intensity factors of the center crack problem. The role of geometrical parameters, crack‐face conditions, volume fraction, and number of microcracks in amplification and shielding effects in all the intensity factors (IFs) with respect to the position of the microcracks is discussed graphically and is quantitatively presented for maximum amplification and shielding values.