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Fig. 1 | Materials Theory

Fig. 1

From: GD3: generalized discrete defect dynamics

Fig. 1

Dislocation eigenstrain formalism. a Schematic of a dislocation loop L defined as the boundary of a cut introduced over a surface S within a continuous material. A dislocation with Burgers vector b is introduced when the crystal in domain S+ above surface S is slipped by an amount b=b in the direction of b/b with respect to the crystal in domain S below surface S, thereby generating a displacement jump [u]=b across surface S. b In the eigenstrain theory, dislocations are considered as plate-like Eshelbian inclusions of thickness t. Surface S corresponding to the slip plane of the dislocation is defined by the plane formed by the Burgers vector b and the line direction t such that \(\mathbf {n} = \frac {\mathbf {b} \times \mathbf {t}}{\|\mathbf {b} \times \mathbf {t}\|}\). For a dislocation, t corresponds to the inter-atomic distance associated with its slip plane

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