Accurate evaluations of strain and stress in atomistic simulations of crystalline solids

In this paper, we study the accuracy of Hardy-type formulas for the approximation of continuum quantities from atomistic simulations. Such formulas are derived by expressing the displacement, deformation gradient and stress in terms of certain kernel functions. We propose three criteria for choosing appropriate kernel functions to significantly improve the sampling accuracy. We present a simple procedure to construct kernel functions that meet these criteria. Furthermore, numerical tests on homogeneous and non-homogeneous systems provide validations for our analysis.