Application of X-FEM to study two-unequal-collinear cracks in 2-D finite magnetoelectoelastic specimen

A quasi-static and propagating analysis is simulated for two-unequal-collinear cracks in a 2-D finite magnetoelectroelastic specimen using X-FEM. The intensity factors (IFs) are calculated using interaction integral in conjugation with the near tip behavior given by the Stroh formalism. In quasi-static case energy release rate (ERR) variations are investigated with respect to inter-crack space, crack lengths and mechanical/electrical/magnetic loads. Two-collinear-unequal cracks in an infinite domain problem are simulated, analyzed and validated. Further, effects of asymmetric orientation and symmetric orientation of quasi-static two-unequal-collinear cracks vis-à-vis specimen boundaries on total energy release rate (TERR) and mechanical energy release rate (MERR) are investigated. The case of one edge and one internal quasi-static crack is obtained as a corollary and the case study is presented. Next, the crack growth study for two-unequal-collinear edge cracks is simulated using maximum modified hoop stress intensity factor criterion and considering anisotropic fracture toughness behavior of polarized ceramics. The effect of volume fraction, electrical and magnetic loadings are similar to the strain energy density function criterion of crack propagation for magnetoelectroelastic ceramics. Lastly dependence of volume fraction and material constants of magnetoelectroelastic ceramics are observed on the set of standard eight basis functions for these ceramics. Hence, a more generalized set of basis functions is also defined here for these ceramics.