Multiscale Modeling of Multiphysics: From Atoms to Continuum Open Access
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Nowadays, computer simulation has emerged as a powerful tool for material modeling, a research field noted for the depth of its intellectual development and its wide range of applications. Basically, there exist two fundamental physical models that provide foundations for almost all material behavioral simulations: microscopic discrete atomistic models and macroscopic continuum models. The difference between these two descriptions, atoms versus continuum, is like day and night. Atomistic model considers the material system as a collection of discrete particles, while continuum model considers the material system as a continuous media. Our goal is to bridge the gap between these two distinct models and allow these two models to communicate with each other within a unified theoretical framework.Among various kinds of atomistic models, molecular dynamics (MD) simulation has established itself as a widely adopted simulation tool to investigate the material properties and to predict the structural responses at nanoscale. Continuum theory powered by finite element method (FEM) has been demonstrated and tested throughout the history of science in explaining and predicting various physical phenomena. In this work, we further include environmental influence, including thermal and electromagnetic effects, into the theoretical framework of MD and FEM, to investigate the multi-physics, i.e., thermal-mechanical-electromagnetic coupling effects. These allow us to study heat conduction at nanoscale, electromagnetic effects on nanocrystalline materials, and thermal-mechanical coupling phenomena in a thermal-visco-elastic-plastic solid.A concurrent atomistic/continuum theory is constructed based on Molecular Dynamics and Coarse-Grained Molecular Dynamics (CGMD). By following the idea of classical FEM, a force-based CGMD method and a stiffness-based CGMD method are developed as the foundation of the proposed multiple length scale modeling. The philosophy is that the solution region can be and should be decomposed into two kinds of sub-regions in space. For the critical region, molecular dynamics with a relatively smaller time step is adopted to capture the key phenomena of that region; for the far field, the proposed coarse-grained method with a relatively large time step is used to reduce the computational efforts and lead to an acceleration of such simulation. As a benchmark test, a wave propagation problem is studied. Numerical results draw conclusions that our theory on multiscale modeling of multi-physics allows a seamless connection between atomistic description and continuum description, and is able to capture the thermal-mechanical-electromagnetic coupling multi-physics phenomena happened during the complex nano-manufacturing process and in the material service life.