Abstract
This paper aims to a more fundamental understanding of multiple defects (cracks and rigid-line inclusions) on the fracture behavior of magnetoelectroelastic (MEE) materials. A theoretical study is conducted on a MEE solid weakened by a doubly periodic array of cracks and rigid-line inclusions under anti-plane mechanical and in-plane electric and magnetic loadings. By using the elliptic function theory, the conformal mapping technique and the analytic function boundary value theory, a rigorous analytical solution to the MEE heterogeneous material are obtained. The closed form formulae for the MEE field intensity factors and the energy release rates at crack tips and rigid-line tips are presented. Numerical examples of electrically and magnetically impermeable cracks and rigid-line inclusions are studied to reveal the relationship of the energy release rates with the period ratio of the microstructure, the length of the cracks, the length of the rigid-line inclusions and the applied mechanical loading, electrical loading and magnetic loading. The analytical solution obtained is general and many other results can be regarded as degenerated cases. The present analytical solution can provide theoretical benchmark results for the multiphysics fracture problem of MEE solid with a large number of defects.
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