基于原子模型的非局域连续模型

Abstract

In traditional continuum theories, constitutive relations such as generalized Hooke’s law and the Fourier law for heat conduction, are representations of macroscopic phenomenons. These theories have severe limitations as the length scale of the structure becomes close to the atomistic dimensions. The failure of the traditional continuum theories at atomistic scale can be attribute to the ignoring of the length scale induced by intrinsic non-locality of atomistic interactions. The primary objective of this work is to construct a coupled atomistic-continuum model strictly based on the atomistic model bypassing any empirical constitutive law and any local homogeneous assumption such as Cauchy-Born rule. The intrinsic non-locality of the atomistic interactions are explicitly built into the model. Inhomogeneous deformation at atomistic scale can be efficiently represented by this model.