The Coupled Atomistic/Discrete-Dislocation method in 3d part I: Concept and algorithms

The Coupled Atomistic/Discrete-Dislocation (CADD) method is a concurrent multiscale technique that couples atomistic and discrete dislocation domains with the ability to pass dislocations seamlessly between domains. CADD has been demonstrated only in 2d plane-strain problems, for which each individual dislocation is either entirely atomistic or entirely discrete. Here, a full 3d implementation of CADD is presented, with emphasis on the algorithms for handling the description of dislocation lines that span both atomistic and continuum domains, so-called hybrid dislocations. The key new features of the method for 3d are (i) the use of an atomistic template of the dislocation core structure to transmit the proper atomistic environment of a continuum dislocation to the atomistic domain for hybrid dislocations and (ii) a staggered solution procedure enabling evolution of the hybrid dislocations. The method naturally requires calibration of discrete-dislocation Peierls stresses and mobilities to their atomistic values, implementation of a dislocation detection algorithm to identify atomistic dislocations, and computation of continuum dislocation displacement fields that provide boundary conditions for the atomistic problem. The method is implemented using the atomistic code LAMMPS and the discrete dislocation code ParaDiS within the LibMultiscale environment developed by the lead authors, and so has all the advantages of these widely-used high-performance open-source codes. Validation and application of CADD-3d are presented in companion papers. (C) 2018 Elsevier Ltd. All rights reserved.