Towards multi-scale continuum elasticity theory

We propose a new method of constructing a series of nested quasicontinuum models, which describe linear elastic behavior of crystal lattices at successively smaller scales. The relevant scales are dictated by the interatomic interactions and are not arbitrary. The novelty of the model is in the use of a decomposition of the displacement field into the coarse part and the micro-level corrections. The coarse contribution is the conventional homogenized displacement field used in classical continuum elasticity. The micro-level corrections are sub-continuum fields representing the fine structure of the boundary layers exhibited by the discrete equilibrium configuration. The model is based on a multi-point Padé approximation in the Fourier space of the discrete Green’s function. We systematically compare the new model with the conventional strain gradient model.