The purpose of this work is the development and application of an RVE-based multiscale modelling framework for the transition from micro-discrete to macro- continuum by means of the Method of Multi-scale Virtual Power (MMVP). In con- tinua, the homogenisation operators (micro-to-macro) are successfully developed and implemented purely within the context of applied and computational solid mechanics. In order to predict mechanical properties and design new composite materials with complex microscopic structures, it is essential to use the discrete microscopic models based on Representative Volume Elements (RVE).In the first part of this thesis, a methodology is developed for the micro-discrete to macro-continuum transition by means of the MMVP. A discrete model of atomic structure is proposed which incorporates interatomic potential energies using well- known potential functions and molecular force field constants. At the micro-scale level, a Finite Element-type procedure is used to describe interatomic forces and a Newton-Raphson/arc-length method is used to solve the corresponding equilibriumproblem.The second part of this work investigates the macroscopic continuum elastic prop- erties and strength of atomic lattices. Macroscopic strength is determined as the onset of material instability at the macroscale. This is predicted by means of the analysis of the acoustic tensor associated with the homogenised constitutive tangent operators that results from the proposed micro-to-macro transition procedure.Numerical examples are presented including the modelling of two common atomic structures: graphene and boron nitride. In addition, the atomic RVE models are considered as a single layer and multiple layers, with and without defects. The ob- tained results are in good agreement with numerical and experimental data reported in the literature. The results demonstrate the capability of the proposed framework to predict the behaviour of macro-continuum with discrete structure at microscalelevel.
Authors:   , Hoang Kim-Quang 
Published: December 2021

The purpose of this work is the development and application of an RVE-based multiscale modelling framework for the transition from micro-discrete to macro- continuum by means of the Method of Multi-scale Virtual Power (MMVP). In continua, the homogenisation operators (micro-to-macro) are successfully developed and implemented purely within the context of applied and computational solid mechanics. In order to predict mechanical properties and design new composite materials with complex microscopic structures, it is essential to use the discrete microscopic models based on Representative Volume Elements (RVE).In the first part of this thesis, a methodology is developed for the micro-discrete to macro-continuum transition by means of the MMVP. A discrete model of atomic structure is proposed which incorporates interatomic potential energies using well- known potential functions and molecular force field constants. At the micro-scale level, a Finite Element-type procedure is used to describe interatomic forces and a Newton-Raphson /arc-length method is used to solve the corresponding equilibrium problem.The second part of this work investigates the macroscopic continuum elastic properties and strength of atomic lattices. Macroscopic strength is determined as the onset of material instability at the macroscale. This is predicted by means of the analysis of the acoustic tensor associated with the homogenised constitutive tangent operators that results from the proposed micro-to-macro transition procedure.Numerical examples are presented including the modelling of two common atomic structures: graphene and boron nitride. In addition, the atomic RVE models are considered as a single layer and multiple layers, with and without defects. The obtained results are in good agreement with numerical and experimental data reported in the literature. The results demonstrate the capability of the proposed framework to predict the behaviour of macro-continuum with discrete structure at microscale level.