Three-dimensional image-based numerical homogenisation using octree meshes

The determination of effective material properties of composites based on a three-dimensional representative volume element (RVE) is considered in this paper. The material variation in the RVE is defined based on the colour intensity in each voxel of an image which can be obtained from imaging techniques such as X-ray computed tomography (XCT) scans. The RVE is converted into a numerical model using hierarchical meshing based on octree decompositions. Each octree cell in the mesh is modelled as a scaled boundary polyhedral element, which only requires a surface discretisation on the polyhedron's boundary. The problem of hanging (incompatible) nodes – typically encountered when using the finite element method in conjunction with octree meshes – is circumvented by employing special transition elements. Two different types of boundary conditions (BCs) are used to obtain the homogenised material properties of various samples. The numerical results confirm that periodic BCs provide a better agreement with previously published results. The reason is attributed to the fact that the model based on the periodic BCs is not over-constrained as is the case for uniform displacement BCs

Advanced numerical method for generation of three-dimensional particles and its application in microstructure-based simulation of fatigue behavior

International audienceThe topology of representative elementary volumes (REV) generated to model materials microstructure is getting more and more complex. This paper presents advanced mesh generation methods used to improve the description of 3D microstructural particles. The goal is to adapt easily the shape of the elements at the interface between the isotropic matrix and embedded inclusions. Two methods are described in this work to generate inclusions: an analytical method based on statistical experimental data and a reconstruction approach, based on tomographic imaging. Sensitivity analyses on meshing parameters are performed to obtain efficient data in order to reconstruct the most representative volume and to perform subsequent accurate numerical computations. As an example of calculations, fatigue tests are chosen to validate the proposed approach

Virtual Element based formulations for computational materials micro-mechanics and homogenization

In this thesis, a computational framework for microstructural modelling of transverse behaviour of heterogeneous materials is presented. The context of this research is part of the broad and active field of Computational Micromechanics, which has emerged as an effective tool both to understand the influence of complex microstructure on the macro-mechanical response of engineering materials and to tailor-design innovative materials for specific applications through a proper modification of their microstructure. While the classical continuum approximation does not account for microstructural details within the material, computational micromechanics allows detailed modelling of a heterogeneous material's internal structural arrangement by treating each constituent as a continuum. Such an approach requires modelling a certain material microstructure by considering most of the microstructure's morphological features. The most common numerical technique used in computational micromechanics analysis is the Finite Element Method (FEM). Its use has been driven by the development of mesh generation programs, which lead to the quasi-automatic discretisation of the artificial microstructure domain and the possibility of implementing appropriate constitutive equations for the different phases and their interfaces. In FEM's applications to computational micromechanics, the phase arrangements are discretised using continuum elements. The mesh is created so that element boundaries and, wherever required, special interface elements are located at all interfaces between material's constituents. This approach can be effective in modelling many microstructures, and it is readily available in commercial codes. However, the need to accurately resolve the kinematic and stress fields related to complex material behaviours may lead to very large models that may need prohibitive processing time despite the increasing modern computers' performance. When rather complex microstructure's morphologies are considered, the quasi-automatic discretisation process stated before might fail to generate high-quality meshes. Time-consuming mesh regularisation techniques, both automatic and operator-driven, may be needed to obtain accurate numeric results. Indeed, the preparation of high-quality meshes is today one of the steps requiring more attention, and time, from the analyst. In this respect, the development of computational techniques to deal with complex and evolving geometries and meshes with accuracy, effectiveness, and robustness attracts relevant interest. The computational framework presented in this thesis is based on the Virtual Element Method (VEM), a recently developed numerical technique that has proven to provide robust numerical results even with highly-distorted mesh. These peculiar features have been exploited to analyse two-dimensional representations of heterogeneous materials' microstructures. Ad-hoc polygonal multi-domain meshing strategies have been developed and tested to exploit the discretisation freedom that VEM allows. To further simplify the preprocessing stage of the analysis and reduce the total computational cost, a novel hybrid formulation for analysing multi-domain problems has been developed by combining the Virtual Element Method with the well-known Boundary Element Method (BEM). The hybrid approach has been used to study both composite material's transverse behaviour in the presence of inclusions with complex geometries and damage and crack propagation in the matrix phase. Numerical results are presented that demonstrate the potential of the developed framework

Thermo-mechanical properties prediction of Ni-reinforced Al2_2O3_3 composites using micro-mechanics based representative volume elements

For effective cutting tool inserts that absorb thermal shock at varying temperature gradients, improved thermal conductivity and toughness are required. In addition, parameters such as the coefficient of thermal expansion must be kept within a reasonable range. This work presents a novel material design framework based on a multi-scale modeling approach that proposes nickel (Ni)-reinforced alumina (Al$_2$O$_3$) composites to tailor the mechanical and thermal properties required for ceramic cutting tools by considering numerous composite parameters. The representative volume elements (RVEs) are generated using the DREAM.3D software program and the output is imported into a commercial finite element software ABAQUS. The RVEs which contain multiple Ni particles with varying porosity and volume fractions are used to predict the effective thermal and mechanical properties using the computational homogenization methods under appropriate boundary conditions (BCs). The RVE framework is validated by the sintering of Al$_2$O$_3$-Ni composites in various compositions. The predicted numerical results agree well with the measured thermal and structural properties. The properties predicted by the numerical model are comparable with those obtained using the rules of mixtures and SwiftComp, as well as the Fast Fourier Transform (FFT) based computational homogenization method. The results show that the ABAQUS, SwiftComp and FFT results are fairly close to each other. The effects of porosity and Ni volume fraction on the mechanical and thermal properties are also investigated. It is observed that the mechanical properties and thermal conductivities decrease with the porosity, while the thermal expansion remains unaffected. The proposed integrated modeling and empirical approach could facilitate the development of unique Al$_2$O$_3$-metal composites with the desired thermal and mechanical properties for ceramic cutting inserts

Micromechanical finite element modeling of long fiber reinforced thermoplastics

Long fiber reinforced thermoplastics are promising candidates for the mass production of lightweight components. In order to predict their microstructure-dependent properties, a novel procedure for the generation of a representative volume element is developed. The approach mimics the pressing process during the fabrication of the material by compression molding. The model is experimentally validated with respect to different mechanical properties, including elasticity, creep and damage

Analytical and numerical modelling of damage and fracture of advanced composites

Tese de Doutoramento. Engenharia Mecânica. Faculdade de Engenharia. Universidade do Porto. 201

Automatic statistical volume element modeling based on the unified topology model

Needs for new particle based heterogeneous materials as led to the development of many Statistical Volume Element (SVE) modeling schemes tailored to specific shapes of particles or meshing procedures. To generalize the numerical analysis of particle filled SVEs, a modeling methodology based on the Unified Topology Model (UTM) is proposed. Using the concept of Boundary Representation (BRep) and a modified Random Sequential Adsorption (RSA) algorithm, the geometry of a Statistical Volume Element (SVE) can be generated automatically with any shape of particles. Using an integration of Computer-Aided Design (CAD) and mesh tools, a mesh size map is constructed with the objective of minimizing the number of mesh elements while preserving quality of the discretization. The SVE is meshed using proven CAD model meshing algorithms for a robust and reliable result. Simulation and post processing are carried out automatically, without any user interaction. To illustrate the potential of this new method, a short glass fiber / epoxy matrix composite is modeled with spherical and elongated cylindrical particles

An X-FEM and Level Set computational approach for image-based modeling. Application to homogenization.

International audienceThe advances in material characterization by means of imaging techniques require powerful computational methods for numerical analysis. The present contribution focuses on highlighting the advantages of coupling the Extended Finite Elements Method (X-FEM) and the level sets method, applied to solve microstructures with complex geometries. The process of obtaining the level set data starting from a digital image of a material structure and its input into an extended finite element framework is presented. The coupled method is validated using reference examples and applied to obtain homogenized properties for heterogeneous structures. Although the computational applications presented here are mainly two dimensional, the method is equally applicable for three dimensional problems

A new approach to rapidly generate random periodic representative volume elements for microstructural assessment of high volume fraction composites

The final publication is available at Elsevier via https://dx.doi.org/10.1016/j.matdes.2018.04.031 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/An algorithm based on event-driven molecular dynamics theory was developed to rapidly generate periodic representative volume elements (RVEs) with nonuniform distributions for both unidirectional fibre-reinforced and spherical particle-reinforced composites. Detailed statistical analyses were conducted for assessing the ability to generate RVEs with nonuniformly dispersed microstructures and either constant or random inclusion sizes for a wide range of volume fractions. The generated microstructures were directly compared with available microstructural optical images of a composite material, showing excellent statistical correlation and providing validation for the developed RVE generation approach. For further validation, finite element analysis was conducted using the generated RVEs in order to evaluate volume averaged elastic constants. The expected isotropic characteristics of the RVEs were correctly calculated, and excellent correlations with experimental data from the literature provided additional support for the algorithm accuracy. The versatile algorithm can rapidly generate RVEs with realistic reinforcement dispersions and high volume fractions up to 80%, which is advantageous compared to other algorithms. The proposed algorithm can be used as a design tool to accurately evaluate and tailor the mechanical properties of distinct composite material systems, and for their microstructural assessment including local damage predictions.University of WaterlooChina Scholarship CouncilOntario Graduate Scholarshi