A point force and an edge dislocation in an elliptical inclusion embedded in an infinite medium

Abstract

The plane elasticity problem of an infinite plate containing an elliptical inclusion is considered and the solutions for a point force and/or a dislocation located inside the inclusion are derived. By using the complex potential approach of Muskhelishvili, the general solutions are obtained in a form of a certain function plus an infinite series. The numerical convergence of the solutions is found to be better than that of Warren's solutions for the same problem. The proposed solutions are also appropriate for the case of a point force and dislocation acting at a point just on the interface.

Multi-element Metamaterial’s Design Through the Relaxed Micromorphic Model

“…While the concept of ≪ interface models ≫ is well known in classical elasticity interface problems, their use is always limited to treat interfaces induced by damage [13,14,49,124], adhesives between two different media [5,27,60,74,75,97,124,144,150], surface effects in nano-systems [119,120,121], fracture [29,78,106,107,122,127,131,139], delamination [10,52,65,80,108,111], crack growth [22,51,73,116,130,146], bond failure [66,67], screw dislocations [54], grain boundaries [93,110,143], peeling [138]. No applications to mechanical metamaterials can be found until today.…”

Interaction of an edge dislocation with a coated elliptic inclusion

“…A screw dislocation interacting with an elastic elliptical inhomogeneity was studied by Gong and Meguid (1994) based on the Laurent series expansion. Some solutions for the problems of the dislocation (or a point force) inside the inhomogeneity have been also obtained and used to discuss the mobility and the equilibrium position of the dislocation by Chen (1995), Stagni (1999) and Fang et al (2009).…”