Mechanical behavior of nanomaterials: Modeling and simulation
Abstract
A semi-continuum model is proposed for nanomaterials that possess a plate-like geometry, such as ultra-thin films. In contrast to the classical continuum theory, the current model accounts for the discrete nature in the thickness direction directly. In-plane Young's modulus, in-plane and out-of-plane Poisson's ratios are investigated with this model. It is found that the values of the Young's modulus and Poisson's ratios depend on the number of atomic layers in the thickness direction and approach the respective bulk values as the number of atomic layers increases. Based on the semi-continuum model, a nanoplate model is also developed for plate-like nanomaterials. Equations of motion are derived with Hamilton's Principle. The dispersion relations of a three-layered nanomaterial are analyzed with both the nanoplate model and the lattice model to show the effectiveness of this nanoplate model. Cylindrical bending of a three-atom-layered nanoplate is analyzed with the nanoplate model, the lattice model, and the continuum Mindlin plate theory. It is found that the nanoplate model predicts the deflection in good agreement with the lattice model. The continuum Mindlin plate theory tends to underpredict the deflection. This result indicates that, if the continuum plate theory is used to extract the Young's modulus of a nanomaterial, the value could be significantly underestimated. An approach to realize simple tension stress state in molecular statics simulation is proposed and used to analyze the size-dependent mechanical behavior of FCC single crystal Ni nanoplates, Ni nanowires and Ni/Ag nanolaminates. For nanoplates, the simulations show that the Young's modulus and the Poisson's ratios are highly size-dependent at nanoscale. The Young's modulus of nanowires decreases as the characteristic sizes decrease. For Ag/Ni nanolaminates, it is found that elastic constants, c11, c33, and biaxial modulus Y, all show a decrease as the number of monolayers in each lamina decreases.
Degree
Ph.D.
Advisors
Sun, Purdue University.
Subject Area
Materials science|Mechanics
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