The force on a moving dislocation

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Abstract
There is a close formal similarity between the equations of elasticity with anti-plane strain and the equations of electrodynamics in two dimensions, the screw dislocation being the counterpart of the line charge. This similarity has led to the suggestion that there is a specific 'Lorentzian' force on a dislocation which moves through a medium which is itself in motion. This is the analogue of the magnetic force on a moving charge. The equations of a linear continuum can be satisfied whether such a force exists or not. A nonlinear model based on that of Peierls is constructed, and an approximate solution of a problem is presented which, if the approximations made are justified, demonstrates that this 'Lorentzian' force on a dislocation does not exist.

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