Submitted Paper

Inserted: 16 mar 2026
Last Updated: 3 sep 2026

Year: 2026

Abstract:

We present a numerical formulation for the resolution of finite systems of interacting edge dislocations and wedge disclinations. The approach is based on a finite element discretization of a fourth-order elliptic boundary value problem arising from the mechanical equilibrium equations of plane-strain linear elasticity in the presence of kinematic incompatibilities. The numerical implementation follows a continuous interior penalty discontinuous Galerkin framework and relies on the solution of a finite set of local cell problems. Our method is validated against analytical benchmarks and used to explore several non-trivial dislocation-disclination configurations, illustrating how translational and rotational incompatibilities shape the stress state of the body.

Keywords: linearized elasticity, edge dislocations, Finite element method, Wedge Disclinations, Airy Stress Function, discontinuous Galerkin method

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