Computational homogenization of material surfaces: From atomistic simulations to continuum models

• Published in: Computational materials science Vol. 175; p. 109431
• Main Authors: Sievers, Christian, Mosler, Jörn, Brendel, Lothar, Kurzeja, Patrick
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.2020
• Subjects: Atomistic modeling; Continuum modeling; Energy equivalence; Homogenization; Material surface; Homogenization; Energy equivalence; Material surface; Atomistic modeling; Continuum modeling
• ISSN: 0927-0256; 1879-0801
• DOI: 10.1016/j.commatsci.2019.109431

[Display omitted] •A Ritz-type homogenization is employed to derive continuum surface properties.•The continuum model is matched with an atomistic model by energy equivalence.•Finite-element (FEAP) and molecular simulations (LAMMPS) are implemented.•Application is illustrated in the linear elastic range of copper surfaces.•Dependence on strain, thickness and bulk approximation is reported and discussed. The objective of this work is a numerical multiscale framework that determines mechanical continuum properties of material surfaces based on molecular statics. The key idea is the coupling of representative volume elements in the atomistic and in the continuum model by the principle of energy equivalence. This allows a thermodynamically consistent implementation of various material models and boundary conditions, e.g., to capture size effects in nano scale materials. For the present example of copper, we observe a very good match with literature data. Only the results for the surface stiffness still deviate in the same range as existing data sources do. The presented results concurrently indicate a drastic strain sensitivity. We further eliminate a methodological bulk to surface error propagation by an appropriate strain limit and thickness extrapolation. The latter is calculated by always allowing for fully developed surface regions. Additionally, our method reveals a strain dependence of higher order that is caused by the anharmonic potential and not captured by standard bulk models. The presented multiscale framework finally serves two purposes: validating the reasonableness of a material surface model and determining its parameters.