Concurrent Multiscale Modeling of Embedded Nanomechanics
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Concurrent Multiscale Modeling of Embedded Nanomechanics Robert E. Rudd Lawrence Livermore National Laboratory Condensed Matter Physics, L-415 Livermore, CA 94551 USA ABSTRACT We discuss concurrent multiscale simulations of dynamic and temperature-dependent processes found in nanomechanical systems coupled to larger scale surroundings. We focus on the behavior of sub-micron Micro-Electro-Mechanical Systems (MEMS), especially micro-resonators. The coupling of length scales methodology we have developed for MEMS employs an atomistic description of small but key regions of the system, consisting of millions of atoms, coupled concurrently to a finite element model of the periphery. The result is a model that accurately describes the behavior of the mechanical components of MEMS down to the atomic scale. This paper reviews some of the general issues involved in concurrent multiscale simulation, extends the methodology to metallic systems and describes how it has been used to identify atomistic effects in sub-micron resonators. INTRODUCTION The mechanics and mechanical dynamics of nanoscale systems is often very different from their macroscopic counterparts [1]. Large enough systems behave as if they were composed of continuous media. Whether a particular system is large enough depends on how its size compares to the largest microscopic features of the material. Microstructure matters, or at least it can matter if the length scale of the microstructure is comparable to macroscopic length scales, such as those set by strain gradients. In pure single crystals, materials already begin to appear continuous in many ways at the length scale of tens of lattice spacings. Nevertheless, at sufficiently small length scales the fact that the material is composed of atoms and is not a continuous medium will become apparent. This effect is one reason that mechanics at the nanoscale is not simply macroscopic mechanics reduced in size. Nanomechanics is a separate, and as yet only vaguely understood, field. Another distinction of nanomechanics is the fact that nanoscale systems often have a large surface area-to-volume ratio. In general, this ratio grows as the size of a system is reduced, and the emergence of surface effects in sub-micron systems has become a recurrent theme in nanoscience. For example, surface effects have a large impact on the structure and morphology of quantum dots [2]. In this Article, we examine some of the new phenomena of nanomechanics based on our computations and in light of recent experimental results from other groups. We also describe new computational tools we have developed in order to compute nanomechanical effects. Of particular interest to us are nanomechanical systems that are strongly coupled to their surroundings, which are typically micron scale or larger. The nanoscale system may be on the surface of a substrate to which it is coupled, or it may be completely surrounded by material. This particular kind of multiscale system, whether on the surface
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Figure 1: Three dimensional model of the microreso
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