Atomistics informed continuum strain field of dislocations

We formulate a novel methodology called the regularized Green's function method for dislocations (RGFMD) for determining the continuum elastic fields of a dislocation at the lattice scales. RGFMD utilizes the quantum mechanical force density (QMFD) to represent atoms within the elastic media without creating any singularities in the elastic fields. QMFD is related to the electron wave functions, which is a fundamental result of density functional theory (DFT) calculations. RGFMD solves the force equilibrium equation where QMFD is used to represent atomic displacements via computationally efficient Fourier transforms. The quasiperiodic nature of dislocations is accounted for by introducing the periodic images of individual atoms along the dislocation line. The advantage of RGFMD over existing classical elasticity solutions and atomistic simulations for dislocations is threefold. First, RGFMD guarantees the production of well-behaving bounded elastic fields, whereas classical elasticity frameworks diverge at the dislocation core. Second, classical elasticity frameworks are built upon the assumption of plane strain conditions, which limits their ability to realistically capture variations in the elastic fields along the dislocation line. RGFMD accurately accounts for the local atomic configuration and does not imply simplifying conditions such as plane strain. Third, atomistic calculations can report elastic quantities such as displacements only at the lattice sites, which precludes their full integration with well-established continuum field theories. RGFMD bridges this gap between atomistic and continuum theories by mapping out continuum elastic fields using the discrete displacement data provided by DFT calculations.