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Research on two dimensional (2D) materials, such as graphene and MoS2, now involves thousands of researchers worldwide cutting across physics, chemistry, engineering and biology. Due to the extraordinary properties of 2D materials, research extends from fundamental science to novel applications of 2D materials. From an engineering point of view, understanding the material properties of 2D materials under various conditions is crucial for tailoring the electrical and mechanical properties of 2D-material-based devices at the nanoscale.Even at the nanoscale, molecular systems typically consist of a vast number of atoms. Molecular dynamics (MD) simulations enable us to understand the properties of assemblies of molecules in terms of their structure and the microscopic interactions between them. From a continuum approach, mechanical properties and thermal properties, such as strain, stress, and heat capacity, are well defined and experimentally measurable. In MD simulations, material systems are considered to be discrete, and only interatomic potential, interatomic forces, and atom positions are directly obtainable. Besides, most of the fracture mechanics concepts, such as stress intensity factors, are not applicable since there is no singularity in MD simulations. However, energy release rate still remains to be a feasible and crucial physical quantity to characterize the fracture mechanical property of materials at the nanoscale. Therefore, equivalent definition of a physical quantity both in atomic scale and macroscopic scale is necessary in order to understand molecular and continuum scale phenomena concurrently.This work introduces atomistic simulation methodologies, based on interatomic potential and interatomic forces, as a tool to unveil the mechanical properties, thermal properties and fracture mechanical properties of 2D materials at the nanoscale. Among many 2D materials, graphene and MoS2 have attracted intense interest. Therefore, we applied our methodologies to graphene and MoS2 as examples. Young’s modulus, Poison’s ratio, heat conductivity, heat capacity, and energy release rate at the nanoscale are studied. These findings lend compelling insights into the atomistic mechanisms of graphene and MoS2, and provide useful guidelines for the design of 2D-material-based nanodevices.

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