A concurrent multiscale micromorphic molecular dynamics

Abstract

Based on a novel concept of multiplicative multiscale decomposition, we have derived a multiscale micromorphic molecular dynamics (MMMD) to extent the (Andersen)-Parrinello-Rahman molecular dynamics to mesoscale and macroscale. The multiscale micromorphic molecular dynamics is a con-current three-scale particle dynamics that couples a fine scale molecular dynamics, a mesoscale particle dynamics of micromorphic medium, and a coarse scale nonlocal particle dynamics of nonlinear continuum together. By choosing proper statistical closure conditions, we have shown that the original Andersen-Parrinello-Rahman molecular dynamics can be rigorously formulated and justified from first principle, and it is a special case of the proposed multiscale micromorphic molecular dynamics. The discovered mutiscale structure and the corresponding multiscale dynamics reveal a seamless transition from atomistic scale to continuum scale and the intrinsic coupling relation among them. The proposed MMMD can be used to solve finite size nanoscale science and engineering problems with arbitrary boundary conditions.

Continuum balances from extended Hamiltonian dynamics

“…In this section, we apply our generalized IKN procedure to an extended Hamiltonian system akin to but more general than that considered by Parrinello & Rahman, 4 whose successful predictions of stress-induced displacive phase transitions in certain crystalline materials initiated an irreversible change in format in the MD simulation of such phenomena. We reiterate that we chose this application not only for its intrinsic importance, but also stimulated by recently proposed multiscale numerical schemes 24,25 for coupling atomistic and continuum models. Importantly, those numerical schemes are based on an APR approach, and we view determining the form of the implied continuum balances to be an endeavor of particular importance and interest.…”

“…On the other hand, the APR approach has the peculiarity of introducing a dynamic generalization of the Cauchy-Born rule, 21,22 which makes it directly relevant to certain recently proposed multiscale computational schemes. [23][24][25] A discussion of how thermostatting techniques can affect the evaluation of transport coefficients in linear response theory (which are related to the balance of linear momentum) is presented by Evans & Morriss. 26 Our goal, however, is to obtain a full set of continuum balances featuring a more accurate account of the macroscopic effects induced by the extended Hamiltonian dynamics.…”

From molecular systems to continuum solids: A multiscale structure and dynamics

“…35. We know that the continuum deformation gradient depends on the relative displacements of all centers of mass, which is…”

Coupling the finite element method and molecular dynamics in the framework of the heterogeneous multiscale method for quasi-static isothermal problems

“…Another attractive method is the so-called perfectly matched multiscale simulation (PMMS) (To and Li, 2005;Li et al, 2006), which was initially derived to reduce spurious phonon reflections at the multiscale interface. Besides, a computational multiscale method to couple thermomechanical equations at the coarse scale with nonequilibrium molecular dynamics at the fine scale was developed (Liu and Li, 2007;Li et al, 2008b;Li and Sheng, 2010;Li and Tong).…”