The solid angle and the Burgers formula in the theory of gradient elasticity: Line integral representation

• Using gradient elasticity the solid angle is given as line integral.
• Gradient version of the Eshelby–deWit form of the Burgers formula is derived.
• Such a form is suitable for the simulation of 3D dislocation dynamics.

A representation of the solid angle and the Burgers formula as line integral is derived in the framework of the theory of gradient elasticity of Helmholtz type. The gradient version of the Eshelby–deWit representation of the Burgers formula of a closed dislocation loop is given. Such a form is suitable for the numerical implementation in 3D dislocation dynamics (DD).