Crack problems in magnetoelectroelastic solids. Part I: exact solution of a crack

• Published in: International journal of engineering science Vol. 41; no. 9; pp. 969 - 981
• Main Authors: Gao, Cun-Fa, Kessler, Hannes, Balke, Herbert
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.05.2003; Elsevier
• Subjects: Crack; Exact sciences and technology; Exact solution; Fracture mechanics (crack, fatigue, damage...); Fracture mechanics, fatigue and cracks; Fundamental areas of phenomenology (including applications); Hole; Magnetoelectroelastic solid; Physics; Solid mechanics; Structural and continuum mechanics; Hole; Magnetoelectroelastic solid; Crack; Exact solution; Eshelby tensor; Singularity; Two dimensional model; Experimental study; Modeling; Electroelasticity; Stroh formalism; Elliptic equation; Magnetoelasticity; Magnetomechanical properties; Electromechanical properties
• ISSN: 0020-7225; 1879-2197
• DOI: 10.1016/S0020-7225(02)00323-3

This paper presents an exact treatment on the problem of an elliptic hole or a crack in a magnetoelectroelastic solid subject to the farfield loadings. First, based on the extended version of Eshelby-Stroh’s formulation, the general solution of an elliptical hole is obtained according to exact boundary conditions at the rim of the hole. Then, when the hole degenerates into a crack, explicit solutions are given for the field intensity factors and electric–magnetic fields inside the crack. It is shown that all the singularities of fields are dependent on the applied mechanical loads, not on the applied electric–magnetic loads. Due to its explicitness, the present solution for a crack can also serve as a benchmark to test the validity of various analysis approaches or assumptions to more complicated crack problems in magnetoelectroelastic media.