Hybrid Continuum Mechanics and Atomistic Methods for Simulating Materials Deformation and Failure
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Mechanics and Atomistic Methods for Simulating Materials Deformation and Failure
Ronald E. Miller and Ellad B. Tadmor Abstract Many aspects of materials deformation and failure are controlled by atomic-scale phenomena that can be explored using molecular statics and molecular dynamics simulations. However, many of these phenomena involve processes on multiple length scales with the result that full molecular statics/molecular dynamics simulations of the entire system are too large to be tractable. In this review, we discuss hybrid models that perform molecular statics/molecular dynamics simulations “without all the atoms,” aimed at retaining atomistic detail at a fraction of the computational cost. These methods couple a fully atomistic model in critical regions to regions described by less-expensive continuum methods where they can provide an adequate representation of the important physics. We give an overview of the challenges such models present, with a focus on recent work to address issues of dynamics and finite (non-zero) temperature.
Introduction The field of multiscale modeling has developed out of a recognition that important phenomena in materials science often involve interactions between disparate scales. On the one hand, mechanisms at some fine scale require a model with relatively high complexity and computational cost. On the other hand, appropriate boundary conditions or some important long-range interactions mean that a larger scale is also at play, making it impractical to solve the entire problem using the finescale model. Here, we are specifically interested in the question of what molecular statics (MS) and molecular dynamics (MD)
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methods can teach us about deformation and failure phenomena in ductile materials. Thus, our “fine” scale is the nanoscale of atoms, and our “coarse” scale is on the order of microns, such that we can study deformation phenomena relevant to the microstructure of engineering materials. Figure 1 serves to illustrate the problem with a specific example; a molecular dynamics study of nanoindentation in a Cu-Ni bicrystal. The figure only shows the “interesting” atoms (where plasticity has taken place through dislocation motion). This example leads to two important observations. First, the percentage of atoms that are “interesting” is quite small
(less than 10% of the 500,000 or so atoms in this small example), with the remaining atoms essentially doing what linear elasticity would predict. Second, it is not easy to know in advance which atoms will be the interesting ones. Observations like these have led to the development of a host of “hybrid” methods3–22 with essentially the same goal: to do molecular statics or molecular dynamics simulations without the overhead of explicitly considering all the atoms. These models share the common theme of coupling a fully atomistic region (denoted ΩA) with continuum mechanics* for treating the “un-interesting” regions (denoted ΩC). Thus, the aim is to replace the full molecular dynamics of Figure 1 with a picture like Figure
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