Computationally efficient method for determining limiting velocities of edge dislocations in anisotropic crystals

The continuum-limit theory of dislocations in crystals predicts divergences in the elastic energy at crystal-geometry dependent limiting velocities $v_L$. The $v_L$ separate subsonic, transonic, and supersonic dislocation glide regimes and are therefore important for material strength models at high strain rates. Although it is known how to calculate these limiting velocities, there is one special case - edge dislocations with reflection symmetry, but non-vanishing elastic constants $c_{16}^{\mathrm{\prime }}$ or $c_{26}^{\mathrm{\prime }}$ - where previous methods have been notoriously slow. In this letter, we address this deficiency by deriving a computationally efficient method for determining the $v_L$ of edge dislocations with reflection symmetry which is two orders of magnitude faster than the previous method.