Multiple interacting three-dimensional flaws in electromagnetothermoelastic coupled multiphase composites by extended hypersing

This work presents extended hypersingular integral equation (E-HIE) method to analyze the multiple interacting three-dimensional mixed-mode flaws problem in electromagnetothermoelastic coupled multiphase composites (EMTE-CMCs) under extended electro-magneto-thermo-elastic coupled loads through intricate theoretical analysis and numerical simulations. Using the Green’s functions,  the multiple interacting three-dimensional flaws problem are reduced to solving a set of E-HIEs coupled with extended boundary integral equations, in which the unknown functions are the extended displacement discontinuities. Then, the behavior of the extended displacement discontinuities around the multiple flaws front terminating at the interface are analyzed by the extended main-part analysis method of E-HIEs. Analytical solutions for the extended singular stresses, the extended stress intensity factors and the extended energy release rate near the flaws front in EMTE-CMCs are provided. Also, a numerical method of the E-HIEs for multiple interacting three-dimensional flaws subjected to extended coupled loads is put forward with the extended displacement discontinuities approximated by the product of basic density functions and polynomials. In addition, distributions of extended stress intensity factors (E-SIFs) varying with the shape of flaws and the vertical spacing are presented. The relationship between E-SIF and the shape of flaw (b/a), the distance between two interface flaws (h/a), the properties of the materials and the electro-magneto-elastic coupling effects is discussed. The effect of flaws orientation, interaction and shielding are analyzed.