The three-dimensional elastodynamic solution for dislocation plasticity and its implementation in discrete dislocation dynamics simulations

An analytical solution for the elastodynamic displacement field of non-uniformly moving Volterra dislocations is derived using the Green's function approach. The elastodynamics strain and stress fields can then be evaluated by numerically differentiating the displacement field. Qualitative comparisons are made with molecular dynamic simulations, and the analytical solution is shown to capture the same features. The plane waves that emanate from, and are parallel to, the slip plane during the instantaneous injection process of edge or screw dislocations are captured by the analytical solution. This was not captured by previously proposed elastodynamic solutions. A computationally efficient swept-area-tracking algorithm is then developed and implemented into three-dimensional discrete dislocation dynamics simulations to compute the elastodynamic field induced by dislocation movements and interactions. This approach provides a way forward for modeling deformation of materials under shock loading or quantifying the dynamics effects that dominate during dislocation avalanches during deformation of metals.