Multiresolution Molecular Mechanics: Dynamics

Abstract

A new static concurrent atomistic/continuum coupling method under the Multiresolution Molecular Mechanics (MMM) framework has been presented in the first part of this paper (Yang et al., 2013 [28]). The present paper presents the dynamic coupling method under the MMM framework called the Multiresolution Molecular Dynamics (MMD) method. First, the derivation of the governing MMD equations from a Hamiltonian that approximates the energy of the original system of atoms under the MMM framework is presented. The method is then tested numerically with these four problems: (i) 1-D wave propagation; (ii) 2-D wave propagation; (iii) 2-D crack propagation; and (iv) modal analysis. Numerical results obtained from MMD compare favorably with the true solutions obtained through full-atomistic simulations, even without any special handshake zone design to eliminate spurious wave reflections. A convergence study is run through the modal analysis of a 2-D beam. Overall, the proposed method demonstrates very good accuracy and convergence in numerical tests.