Multiscale modeling of nano/micro systems by a multiscale continuum field theory

Abstract

This paper presents a multiscale continuum field theory and its application in modeling and simulation of nano/micro systems. The theoretical construction of the continuum field theory will be briefly introduced. In the simulation model, a single crystal can be discretized into finite element mesh as in a continuous medium. However, each node is a representative unit cell, which contains a specified number of discrete and distinctive atoms. Governing differential equations for each atom in all nodes are obtained. Material behaviors of a given system subject to the combination of mechanical loadings and temperature field can be obtained through numerical simulations. In this work, the nanoscale size effect in single crystal bcc iron is studied, the phenomenon of wave propagation is simulated and wave speed is obtained. Also, dynamic crack propagation in a multiscale model is simulated to demonstrate the advantage and applicability of this multiscale continuum field theory.

Dynamic behaviour of solids and granular materials: a force potential-based particle method

“…The approach can be applied to problems ranging from the (i) very microscopic one, such as in the so‐called ab initio approach (multi‐body electronic structure theory, density functional theory, quantum chemistry, …) in which the force field arising between atoms, electrons and nuclei is considered ; (ii) the atomistic dynamics and statistics approaches (referred to as molecular dynamics, MD or kinetic Monte Carlo models, suitable to describe kinetically dominated mechanisms) in which the effective bonds between molecules are properly described through potentials and (iii) the mesoscale approaches based on the mean field rate theoretical methods (that typically mimic average dynamical properties ), up to the (iv) macroscopic scale, such as the continuum‐based thermodynamics or constitutive kinetic models, typically formulated by using variational methods. Multiscale analysis of solids has also been proposed in recent papers .…”

“…The approach can be applied to problems ranging from the (i) very microscopic one, such as in the socalled ab initio approach (multi-body electronic structure theory, density functional theory, quantum chemistry, : : :) in which the force field arising between atoms, electrons and nuclei is considered [2]; (ii) the atomistic dynamics and statistics approaches (referred to as molecular dynamics, MD or kinetic Monte Carlo models, suitable to describe kinetically dominated mechanisms) in which the effective bonds between molecules are properly described through potentials [3,4] and (iii) the mesoscale approaches based on the mean field rate theoretical methods (that typically mimic average dynamical properties [6]), up to the (iv) macroscopic scale, such as the continuum-based thermodynamics or constitutive kinetic models, typically formulated by using variational methods. Multiscale analysis of solids has also been proposed in recent papers [7,8].On the other hand, such a discrete nature is well evident for some classes of materials, such as the granular one, that consist of several low deformable particles, usually interacting each other through elastic contact, cohesive and friction forces [9][10][11][12][13]. Among the different problems involving the simulation of mechanical materials response, geomechanical and powders, one can be naturally studied by exploiting their significant granular nature [14][15][16][17].At the macroscale, the discrete methods have relevant applications in mineral processing, rock blasting, crushing, phenomena involving sand mechanics, powders technology, failure of compact or granular bodies [15,17].…”

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

“…It is based on standard finite elements and constitutive equations derived from atomistic interactions. Next to that, there are the bridging-scale method and the multiscale continuum field theory (Zeng et al, 2011). The coarse-grained molecular dynamics (CGMD) Broughton, 1998, 2000) approach produces equations of motion for the nodal fields of a finite element model, which are derived from an underlying atomistic model at thermodynamic equilibrium.…”