Coupling of Length Scales: Hybrid Molecular Dynamics and Finite Element Approach for Multiscale Nanodevice Simulations
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Coupling of Length Scales: Hybrid Molecular Dynamics and Finite Element Approach for Multiscale Nanodevice Simulations Elefterios Lidorikis1, Martina E. Bachlechner1, Rajiv K. Kalia1, George Z. Voyiadjis2, Aiichiro Nakano1, and Priya Vashishta1 1 Concurrent Computing Laboratory for Materials Simulations and Biological Computation & Visualization Center, Department of Physics & Astronomy and Department of Computer Science Louisiana State University, Baton Rouge, LA 70803, USA 2 Advanced Computational Solid Mechanics Laboratory, Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA 70803, USA ABSTRACT A hybrid molecular-dynamics/finite-element simulation scheme is applied to describe multiscale phenomena in nanodevices. The quality of both static and dynamic coupling between atomistic and continuum regions is studied. The hybrid scheme is used for the Si/Si3N4 interface problem (static coupling), and for the projectile impact on Si problem (dynamic coupling). Excellent agreement is found between hybrid and full molecular dynamics simulation results in the static case, and no wave reflections are found at the atomistic/continuum hand-shake in the dynamic case. The hybrid scheme is thus validated a powerful and cost effective method for performing multiscale simulations of nanodevices. INTRODUCTION Scaling the size of mechanical structures and electronic devices down to the nanometer scale, in order to achieve enhanced mechanical and electro-optical properties, has been of great importance in recent years. In this regime, atomistically-induced stress and strain inhomogeneities, originating at surfaces and interfaces, become increasingly important due to the large surface-to volume ratio [1-3]. A theoretical description for rational design and accurate lifetime prediction of mechanical structures [4,5] in this regime, that goes beyond the traditional continuum approach [3,6,7], is thus necessary [9,10]. Atomistic simulations utilizing the molecular dynamics (MD) method through use of suitable interatomic potentials can provide the necessary atomic level information [11], but cannot reach the desired length scales due to high computational cost. A multiscale scheme, that will efficiently combine atomistic and continuum simulations, is thus needed. The serial multiscale approach is to use atomistic simulations to re-construct the constitutive equations for continuum in regions where atomic resolution is required [12-14]. The concurrent multiscale approach is to spatially decompose the system into an atomic and a continuum region, use atomistic and continuum simulations respectively for their study, and establish a seamless hand shaking (HS) between the two schemes [15-17]. In this work, we use the concurrent multiscale approach and study the quality of the hand shaking in the static coupling between atomistics and continuum (atomistically-induced stress patterns that extend into the continuum) as well as their dynamic coupling (stress waves that propagate from the atomistics region
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