Extracting continuum-like deformation and stress from molecular dynamics simulations

We present methods that use results from molecular dynamics (MD) simulations to construct continuum parameters, such as deformation gradient and Cauchy stress, from all or any part of an MD system. These parameters are based on the idea of minimizing the difference between MD measures for deformation and traction and their continuum counterparts. The procedures should be applicable to non-equilibrium and inhomogeneous systems, and to any part of a system, such as a polymer chain. The resulting procedures provide methods to obtain first and higher order deformation gradients associated with any subset of the MD system, and associated expressions for the Cauchy and nominal stresses. As these procedures are independent of the type of interactions, they can be used to study any MD simulation in a manner consistent with continuum mechanics and to extract information exploitable at the continuum scale to help construct continuum-level constitutive models.