Connecting discrete and continuum dislocation mechanics: a non-singular spectral framework

In this paper, we present an improved framework of the spectral-based Discrete Dislocation Dynamics (DDD) approach introduced in [1,2], that establishes a direct connection with the continuum Field Dislocation Mechanics (FDM) approach. To this end, an analytical method to convert a discrete dislocation network to its continuous dislocation density tensor representation is first developed. From there, the mechanical fields are evaluated using a FDM-based spectral framework, while submesh resolution elastic interactions are accounted for via the introduction of a rigorous stress splitting procedure that leverages properties of non-singular dislocation theories. The model results in a computationally efficient approach for DDD simulations that enables the use of elastic anisotropy and heterogeneities, while being fully compatible with recently developed subcycling time-integrators. As an example, the model is used to perform a work-hardening simulation, and potential applications that take advantage of the full-field nature of the method are explored, such as informing FDM models, and efficiently calculating virtual diffraction patterns.