In this thesis we investigate theoretically various types of sculptured thin film (STF) envisioned as platforms for optical sensing. A STF consists of an array of parallel nanowires which can be grown on a substrate using vapour deposition techniques. Typically, each nanowire has a diameter in the range from ~ 10-300 nmwhile the film thickness is ~<1μm. Through careful control of the fabrication process, both the optical properties and the porosity of the STF can be tailored to order. These abilities make STFs promising for optical sensing applications, wherein it is envisaged that the material to be sensed infiltrates the void region in between the parallel nanowires and hence changes the optical properties of the STF. Various homogenization formalisms can be used to estimate the constitutive parameters of the infiltrated STFs. In this thesis two different homogenization formalisms were used: the Bruggeman formalism (extended and non–extended versions) and the strong-permittivityfluctuation theory (SPFT). These were used in investigations of the following optical–sensing scenarios: (i) Electromagnetic radiation emitted by a dipole source inside an infiltrated chiral STF. The effects of using the extended Bruggeman homogenization formalism, which takes into account the nonzero size of the component particles,were studied. (ii) Surface–plasmon– polariton waves on ametal–coated, infiltrated columnar thin film. The influences of using the extended SPFT formalism, which takes into account the nonzero size of the component particles and their statistical distributions, were explored. (iii) A metal-coated infiltrated chiral STF which supports both surface-plasmon-polariton waves and the circular Bragg phenomenon. The possibility of using in parallel both surface-plasmon-polariton waves and the circular Bragg phenomenon was investigated using the non–extended Bruggeman formalism. Our numerical studies revealed that the design performance parameters of the infiltrated STF are bode well for these optical–sensing scenarios. The use of inverse Bruggeman formalism was also investigated: this was found to be problematic in certain constitutive parameter regimes, but not those for optical–sensing scenarios considered in this thesis.

Ce travail vise à étudier un matériau biphasé métallique matrice/inclusion. Une méthode simple est proposée pour évaluer les propriétés élastiques d'une phase si les propriétés de l'autre phase sont connues. La méthode est basée à la fois sur un modèle d'homogénéisation inverse et sur les mesures de champs mécaniques par corrélation d'images numériques 2D. L'originalité de la méthode repose sur l'échelle étudiée, à savoir l'échelle de la microstructure du matériau : la taille caractéristique des inclusions est d'environ quelques dizaines de microns. L'évaluation est réalisée sur des essais de traction uniaxiale standards associés à un microscope longue distance. Cela permet d'observer la surface de l'échantillon à l'échelle de la microstructure au cours de la sollicitation mécanique. Tout d'abord, la précision de la méthode est examinée à partir de champs mécaniques 'parfaits' provenant des simulations numériques pour quatre microstructures : inclusions simples élastiques ou poreux ayant une forme sphérique ou cylindrique. Deuxièmement, cette précision est examinée sur les vrais champs mécaniques provenant des deux microstructures simples : une matrice métallique élasto-plastique contenant un ou quatre micro-trous cylindriques arrangés en un motif carré. Troisièmement, la méthode est utilisée pour évaluer les propriétés élastiques des inclusions de forme arbitraire dans un échantillon Zircaloy-4 oxydé présentant le gainage du combustible d'un réacteur à eau sous pression après un accident de perte de réfrigérant primaire (APRP). Dans toute cette étude, les phases sont supposées avoir des propriétés isotropes. / This work is focused on a matrix/inclusion metal composite. A simple method is proposed to evaluate the elastic properties of one phase while the properties of the other phase are assumed to be known. The method is based on both an inverse homogenization scheme and mechanical field's measurements by 2D digital image correlation. The originality of the approach rests on the scale studied, i.e. the microstructure scale of material: the characteristic size of the inclusions is about few tens of microns. The evaluation is performed on standard uniaxial tensile tests associated with a long-distance microscope. It allows observation of the surface of a specimen on the microstructure scale during the mechanical stress. First, the accuracy of the method is estimated on ‘perfect' mechanical fields coming from numerical simulations for four microstructures: elastic or porous single inclusions having either spherical or cylindrical shape. Second, this accuracy is estimated on real mechanical field for two simple microstructures: an elasto-plastic metallic matrix containing a single cylindrical micro void or four cylindrical micro voids arranged in a square pattern. Third, the method is used to evaluate elastic properties of inclusions with arbitrary shape in an oxidized Zircaloy-4 sample of the fuel cladding of a pressurized water reactor after an accident loss of coolant accident (LOCA). In all this study, the phases are assumed to have isotropic properties.

This thesis explores using multi-scale topology optimization (TO) by utilizing inverse homogenization to automate the adjustment of each unit-cell's geometry and placement in a lattice structure within a pressure vessel (the design domain) to achieve desired structural properties. The aim is to find the optimal material distribution within the design domain as well as desired material properties at each discretized element and use machine learning (ML) to map microstructures with corresponding prescribed effective properties. Effective properties are obtained through homogenization, where microscopic properties are upscaled to macroscopic ones. The symmetry group of a unit-cell's elasticity tensor can be utilized for stiffness directional tunability, i.e., to tune the cell's performance in different load directions.  A few geometrical variations of a chosen unit-cell were homogenized to build an effective anisotropic elastic material model by obtaining their effective elasticity. The symmetry group and the stiffness directionality of the cells’ effective elasticity tensors were identified. This was done using both the pattern of the matrix representation of the effective elasticity tensor and the roots of the monoclinic distance function. A cell library of symmetry-preserving variations with a corresponding material property space was created, displaying the achievable properties within the library. Two ML models were implemented to map material properties to appropriate cells. A TO algorithm was also implemented to produce an optimal material distribution within a design domain of a pressure vessel in 2D to maximize stiffness. However, the TO algorithm to obtain desired material properties for each element in the domain was not realized within the time frame of this thesis.  The cells were successfully homogenized. The effective elasticity tensor of the chosen cell was found to belong to the cubic symmetry group in its natural coordinate system. The results suggest that the symmetry group of an elasticity tensor retrieved through numerical experiments can be identified using the monoclinic distance function. If near-zero minima are present, they can be utilized to find the natural coordinate system. The cubic symmetry allowed the cell library's material property space to be spanned by only three elastic constants, derived from the elasticity matrix. The orthotropic symmetry group can enable a greater directional tunability and design flexibility than the cubic one. However, materials exhibiting cubic symmetry can be described by fewer material properties, limiting the property space, which could make the multi-scale TO less complex. The ML models successfully predicted the cell parameters for given elastic constants with satisfactory results. The TO algorithm was successfully implemented. Two different boundary condition cases were used – fixing the domain’s corner nodes and fixing the middle element’s nodes. The latter was found to produce more sensible results. The formation of a cylindrical outer shape could be distinguished in the produced material design, which was deemed reasonable since cylindrical pressure vessels are consistent with engineering practice due to their inherent ability to evenly distribute load. The TO algorithm must be extended to include the elastic constants as design variables to enable the multi-scale TO.