A deformation gradient tensor and strain tensors for atomistic simulations

A kinematical algorithm is proposed for the construction of strain tensors from atomistic simulation data. Local strain tensors such as the Almansi and Green strain tensors suitable for use in large deformation molecular dynamics/statics simulations are computed directly from a discrete form of the deformation gradient. The discrete, incremental form of the deformation gradient emerges from a weighted least squares minimization that includes a length scale relating the distance from the atom in question with a particular radius. This region defines the nonlocal domain of the strain at that atom. The local atomic strain tensors are then computed using continuum definitions in terms of the deformation gradient. The results of molecular dynamics simulations are presented that compare the Almansi and Green strain tensors under inhomogeneous deformation and indicate that the small-strain approximation should not be used to determine large atomic strains.