Stochastic homogenization of nano-thickness thin films including patterned holes using structural perturbation method. (July 2017)

• Record Type: Journal Article
• Authors: Shin, Hyunseong; Chang, Seongmin; Jeong, Joonho; Cho, Maenghyo
• Is Part Of: Probabilistic engineering mechanics. Volume 49(2017:Jul.)
• Page Start: 1
• Page End: 12
• Publication Date: 2017-07
• Subjects: Stochastic multiscale analysis -- Monte-Carlo simulation -- Homogenization -- Surface effect -- Structural perturbation method; Engineering -- Statistical methods -- Periodicals; Mechanics, Applied -- Statistical methods -- Periodicals; Probabilities -- Periodicals; Ingénierie -- Méthodes statistiques -- Périodiques; Mécanique appliquée -- Méthodes statistiques -- Périodiques; Probabilités -- Périodiques; 620.100727
• DOI: 10.1016/j.probengmech.2017.08.001
• Languages: English
• ISSNs: 0266-8920

Abstract

Abstract: The aim of this paper is to investigate the statistical response of the homogenized mechanical behavior of nano-thickness thin films with circular holes. For this purpose, a stochastic multiscale framework is proposed. The proposed framework involves molecular dynamics simulation, surface modeling, asymptotic homogenization, moving-mesh technique, Monte-Carlo simulation, and a reduced computational scheme. The surface effect of thin-film material is predicted by the molecular dynamics (MD) approach. The volume fraction and location of each circular hole are considered as geometric uncertainties of a model. In order to investigate the statistical response of the homogenized mechanical behavior, Monte-Carlo simulation is performed to show the probability density distribution of the homogenized elastic modulus against geometric uncertainties. The reduced computational schematic based on the static reduction method and the structural perturbation method is proposed in order to overcome the issues of a cumbersome remeshing procedure and computational inefficiency of Monte-Carlo simulations involving a high number of repetitive trials. A guideline to minimize the coefficient of variation (CV) of the mechanical properties is suggested based on the parametric study. Highlights: We proposed the statistical multiscale analysis method of nano-thickness thin film structures. The effect of nano-scale geometric uncertainties such as volume fraction and distribution of circular holes on homogenized material properties of nanofilm is investigated. The proposed framework involves molecular dynamics simulation, surface modeling, asymptotic homogenization, moving-mesh technique, Monte-Carlo simulation, and a reduced computational scheme with structural perturbation method and static reduction method. Moving mesh is employed to negate the need for cumbersome repeated remeshing procedures. We assured numerical efficiency and accuracy of statistical analysis.