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.

2021 ◽  
Author(s):  
◽  
Kim-Quang Hoang
Keyword(s):  
Solid Mechanics ◽  
Interatomic Potential ◽  
Single Layer ◽  
Atomic Structures ◽  
Multi Scale ◽  
Modelling Framework ◽  
Molecular Force ◽  
Microscopic Models ◽  
Acoustic Tensor ◽  
Element Type

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.

scholarly journals Multi-Scale Analyses and Modeling of Metallic Nano-Layers

Materials ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 450
Author(s):  
Zara Moleinia ◽  
David Bahr
Keyword(s):  
Experimental Data ◽  
Constitutive Model ◽  
Crystal Plasticity ◽  
Single Layer ◽  
Adaptive Boosting ◽  
Multi Scale ◽  
Nano Scale ◽  
Boosting Technique ◽  
Constitutive Parameters ◽  
Computational Processes

The current work centers on multi-scale approaches to simulate and predict metallic nano-layers’ thermomechanical responses in crystal plasticity large deformation finite element platforms. The study is divided into two major scales: nano- and homogenized levels where Cu/Nb nano-layers are designated as case studies. At the nano-scale, a size-dependent constitutive model based on entropic kinetics is developed. A deep-learning adaptive boosting technique named single layer calibration is established to acquire associated constitutive parameters through a single process applicable to a broad range of setups entirely different from those of the calibration. The model is validated through experimental data with solid agreement followed by the behavioral predictions of multiple cases regarding size, loading pattern, layer type, and geometrical combination effects for which the performances are discussed. At the homogenized scale, founded on statistical analyses of microcanonical ensembles, a homogenized crystal plasticity-based constitutive model is developed with the aim of expediting while retaining the accuracy of computational processes. Accordingly, effective constitutive functionals are realized where the associated constants are obtained via metaheuristic genetic algorithms. The model is favorably verified with nano-scale data while accelerating the computational processes by several orders of magnitude. Ultimately, a temperature-dependent homogenized constitutive model is developed where the effective constitutive functionals along with the associated constants are determined. The model is validated by experimental data with which multiple demonstrations of temperature effects are assessed and analyzed.

scholarly journals Multi-scale Method for the Crack Problem in Microstructural Materials

2010 ◽  
Vol 10 (1) ◽  
pp. 69-86 ◽  
Author(s):  
R. H. W. Hoppe ◽  
S.I. Petrova
Keyword(s):  
Finite Element ◽  
Crack Problem ◽  
Material Model ◽  
Superposition Method ◽  
The Finite Element Method ◽  
Multi Scale ◽  
Microscopic Models ◽  
Modeling Strategy ◽  
Porous Microstructures ◽  
Global And Local

AbstractThe paper deals with the numerical computation of a crack problem posed on microstructural heterogeneous materials containing multiple phases in the microstructure. The failure of such materials is a natural multi-scale effect since cracks typically nucleate in regions of defects on the microscopic scale. The modeling strategy for solving the crack problem concerns simultaneously the macroscopic and microscopic models. Our approach is based on an efficient combination of the homogenization technique and the mesh superposition method (s-version of the finite element method). The homogenized model relies on a double-scale asymptotic expansion of the displacement field. The mesh superposition method uses two independent (global and local) finite element meshes and the concept of superposing the local mesh arbitrarily on the global continuous mesh. The crack is treated by the local mesh and the homogenized material model is considered on the global mesh. Numerical experiments for problems on biomorphic microcellular ceramic templates with porous microstructures of different materials constituents are presented.

Prediction of SCC Initiation in Weld Components by Multi-Scale Analysis Incorporating Crystal Plasticity

2010 ◽  
Author(s):  
Masahito Mochizuki ◽  
Yoshiki Mikami
Keyword(s):  
Residual Stress ◽  
Crystal Orientation ◽  
Microscopic Model ◽  
Macroscopic Model ◽  
Scale Analysis ◽  
Analysis Method ◽  
Multi Scale ◽  
Microscopic Models ◽  
Multi Scale Analysis ◽  
Good Agreement

A multi-scale analysis method of microscopic stress is proposed to predict the occurrence of stress corrosion cracking (SCC) in the welded components in power plants. The method includes a macroscopic model and microscopic models. Calculation of the stress was first performed in the macroscopic model. Subsequent to this calculation, simulation of the microscopic model was conducted to evaluate the microscopic stress on the scale of the grains and microstructure. Then, the nodal temperatures and nodal displacements were transferred from the macroscopic model to the microscopic model as boundary conditions. The proposed multi-scale analysis was used to evaluate the weld residual stress of a bead-on-plate weld model to demonstrate the validity of the method. Good agreement was obtained between the macroscopic and microscopic models in nodal temperature, nodal displacement, and in the residual stress distribution. Following the bead-on-plate model, the multi-scale analysis method was applied to the model of an SCC test specimen of type 600 Nickel-based alloy. Crystal plasticity and inhomogeneous grain shapes were introduced into the microscopic model to consider the effect of crystal orientation. The crystal orientation was measured by electron backscattering pattern (EBSP) technique and applied to the microscopic model. The stress concentration at the grain boundaries was shown by the multi-scale analysis. In the simulated SCC tests, cracks were observed in the grain boundaries. The locations where microscopic stress concentrations occurred in the multi-scale analysis were in good agreement with the locations of cracks observed in the SCC test. The proposed multi-scale analysis method of microscopic stress distribution is thus applicable to the prediction of the locations of stress corrosion cracks.

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