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

Abstract

We present an improved framework of the spectral-based Discrete Dislocation Dynamics (DDD) approach introduced in (Bertin et al., 2015; Bertin and Capolungo, 2018), that establishes a direct connection with the continuum Field Dislocation Mechanics (FDM) approach. First, an analytical method to convert a discrete dislocation network to its continuous dislocation density tensor representation is 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 compatible with recently developed subcycling time-integrators. As examples, 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.