Semi-analytical atomic-level uncertainty quantification for the elastic properties of 2D materials

Abstract

Abstract Inherent stochasticity in the nanostructural geometry and molecular mechanics properties of lattice-like two-dimensional (2D) materials can significantly deviate the predicted elastic properties that are widely reported in a deterministic framework. Such uncertainties can be attributed to inevitable fabrication uncertainties and random error in parameterizing the atomic-level constants depending on the accuracy of highly complicated nanoscale experiments. Generalized high-fidelity analytical models are developed in this article to quantify the influence of these source-uncertainties on the basis of first- and second-order perturbation theories coupled with nanoscale continuum mechanics. The proposed stochastic mechanics–based analytical framework is further validated using the baseline Monte Carlo simulation–assisted probabilistic approach. To provide comprehensive numerical insights, four different 2D materials with uniform and non-uniform atomic distributions are considered covering the monoplanar as well as multiplanar nanostructural configurations (graphene, hexagonal boron nitride, stanene and molybdenum disulfide). The perturbation-based approach is further extended to quantify the relative sensitivity of different nanostructural and molecular mechanics parameters on the elastic moduli of 2D materials. The proposed analytical approach leads to a significant level of computational efficiency by alleviating the necessity of carrying out thousands of molecular dynamics simulations to obtain deep computational insights concerning uncertainty quantification and sensitivity analysis, which would assume a crucial role to ensure robust analysis and design of technologically demanding multifunctional devices and systems across the length-scales.