Multiresolution Molecular Mechanics: Dynamics
E Biyikli and QC Yang and AC To, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 274, 42-55 (2014).
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. (c) 2014 Elsevier B.V. All rights reserved.
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