An iterative approach for analysis of cracks with exact boundary conditions in finite magnetoelectroelastic solids

摘要

An iteration approach in combination with the boundary element method is proposed to analyze a crack with exact crack face boundary conditions (BCs) in a finite magnetoelectroelastic solid. The crack opens under an applied load and the opened cavity is considered as a single domain filled with air or vacuum. The electric and magnetic fields inside a crack cavity affect the crack opening displacement (COD), which is a geometrically nonlinear problem. When establishing a boundary integral equation for inner and outer domains bounded by opening crack faces, nearly singular integrals occur due to the very thin domain of a crack cavity. However, the nearly singular integrals require no special treatment by employing intelligent adaptive algorithms in software Mathematica. The proposed approach is based on iteration of boundary elements for a crack-cavity domain and sub-region boundary elements for an outer magnetoelectroelastic solid with the crack faces changing during the iterative process. In this approach, exact crack face BCs are used in iteration, and the exact electric displacement and magnetic induction across the crack face as well as the COD can be determined. Furthermore, extended stress intensity factors are calculated and finally, the effects of BCs and the crack size are discussed.