On the elastic-plastic decomposition of crystal deformation at the atomic scale

Given two snapshots of an atomistic system, taken at different stages of the deformation process, one can compute the incremental deformation gradient field, F, as defined by continuum mechanics theory, from the displacements of atoms. However, such a kinematic analysis of the total deformation does not reveal the respective contributions of elastic and plastic deformation. We develop a practical technique to perform the multiplicative decomposition of the deformation field, F = (FFp)-F-e, into elastic and plastic parts for the case of crystalline materials. The described computational analysis method can be used to quantify plastic deformation in a material due to crystal slip-based mechanisms in molecular dynamics and molecular statics simulations. The knowledge of the plastic deformation field, F-p, and its variation with time can provide insight into the number, motion and localization of relevant crystal defects such as dislocations. The computed elastic field, F-e, provides information about inhomogeneous lattice strains and lattice rotations induced by the presence of defects.