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Wang, Xiaojia. "Study of the radiative properties of aligned carbon nanotubes and silver nanorods". Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/42871.
Pełny tekst źródłaGuerra, Timothée. "Interaction lumière-matière dans des suspensions de nanoparticules : homogénéisation et conception de nouvelles propriétés optiques". Electronic Thesis or Diss., Orléans, 2024. http://www.theses.fr/2024ORLE1005.
Pełny tekst źródłaDisordered media composed of nanoparticles are of great importance in many applications, particularly those related to energy efficiency such as radiative cooling. Understanding the light-matter interaction is therefore essential, but highly complex. Indeed, these studies often involve solving Maxwell's equations in systems made up of thousands of particles, to take account of scattering and interference phenomena. In order to reduce the ensuing numerical burden, this thesis focuses on 2D systems, with some discussion of 3D systems. In this context, the first part of this manuscript focuses on the concept of homogenization for particle systems that are small relative to the radiation wavelength and may exhibit resonances. This study highlights exotic behaviours that allow us to discuss, among other things, the link between homogenization and coherent and incoherent parts of the scattered field.The second part is dedicated to optimizing the absorption of radiation in subwavelength plates made of nanoparticles. It is shown that the use of resonant particles only results in absorption up to 70%. However, combining them with purely scattering particles results in near-perfect absorption (∼95%), through an effect similar to critical coupling. Finally, a detailed study of the mechanisms governing absorption gain in 2D has enabled them to be reproduced in 3D systems
Burnett, P. D. S. "Radiative properties of confined plasmas". Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275600.
Pełny tekst źródłaFrancis, Peter N. "Infrared radiative properties of clouds". Thesis, University of Oxford, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302829.
Pełny tekst źródłaGarrett, Timothy J. "Radiative properties of arctic clouds /". Thesis, Connect to this title online; UW restricted, 2000. http://hdl.handle.net/1773/10090.
Pełny tekst źródłaJiang, Jingyi. "Retrieving leaf and canopy characteristics from their radiative properties using physically based models : from laboratory to satellite observations Estimation of leaf traits from reflectance measurements: comparison between methods based on vegetation indices and several versions of the PROSPECT model a model of leaf optical properties accounting for the differences between upper and lower faces Speeding up 3D radiative transfer simulations: a physically based approximation of canopy reflectance dependency on wavelength, leaf biochemical composition and soil reflectance Effective GAI for crops is best estimated from reflectance observations as compared to GAI and LAI Optimal learning for GAI and chlorophyll estimation from 1D and 3D radiative transfer model inversion: the case of wheat and maize crops observed by Sentinel2". Thesis, Avignon, 2019. http://www.theses.fr/2019AVIG0708.
Pełny tekst źródłaMeasuring leaf and canopy characteristics from remote sensing acquisitions is an effective and non destructive way to monitor crops both for decision making within the smart agriculture practices or for phenotyping under field conditions to improve the selection efficiency. With the advancement of computer computing power and the increasing availability of high spatial resolution images, retrieval methods can now benefit from more accurate simulations of the Radiative Transfer (RT) models within the vegetation. The objective of this work is to propose and evaluate efficient ways to retrieve leaf and canopy characteristics from close and remote sensing observations by using RT models based on a realistic description of the leaf and canopy structures. At the leaf level, we first evaluated the ability of the different versions of the PROSPECT model to estimate biochemical variables like chlorophyll (Cab), water and dry matter content. We then proposed the FASPECT model to describe the optical properties differences between the upper and lower leaf faces by considering a four-layer system. After calibrating the specific absorption coefficients of the main absorbing material, we validated FASPECT against eight measured ground datasets. We showed that FASPECT simulates accurately the reflectance and transmittance spectra of the two faces and overperforms PROSPECT for the upper face measurements. Moreover, in the inverse mode, the dry matter content estimation is significantly improved with FASPECT as compared to PROSPECT. At the canopy level, we used the physically based and unbiased rendering engine, LuxCoreRender to compute the radiative transfer from a realistic 3D description of the crop structure. We checked its good performances by comparison with the state of the art 3D RT models using the RAMI online model checker. Then, we designed a speed-up method to simulate canopy reflectance from a limited number of soil and leaf optical properties. Based on crop specific databases simulated from LuxCoreRender for wheat and maize and crop generic databases simulated from a 1D RT model, we trained some machine learning inversion algorithms to retrieve canopy state variables like Green Area Index GAI, Cab and Canopy Chlorophyll Content (CCC). Results on both simulations and in situ data combined with SENTINEL2 images showed that crop specific algorithms outperform the generic one for the three variables, especially when the canopy structure breaks the 1D turbid medium assumption such as in maize where rows are dominant during a significant part of the growing season
Assi, Benoît [Verfasser]. "Electroweak Radiative Corrections and Effective Field Theories / Benoît Assi". Hamburg : Staats- und Universitätsbibliothek Hamburg Carl von Ossietzky, 2021. http://d-nb.info/1240835590/34.
Pełny tekst źródłaBecker, H. "Controlling the radiative properties of conjugated polymers". Thesis, University of Cambridge, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.596510.
Pełny tekst źródłaLiu, Xianglei. "Tailoring thermal radiative properties and enhancing near-field radiative heat flux with electromagnetic metamaterials". Diss., Georgia Institute of Technology, 2016. http://hdl.handle.net/1853/54960.
Pełny tekst źródłaBourgeois, C. Saskia. "The radiative properties of snow at Summit, Greenland /". Zürich : ETH, 2006. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=16758.
Pełny tekst źródłaMavrogordatos, Themistoklis. "Emission properties of radiative chiral nematic liquid crystals". Thesis, University of Cambridge, 2015. https://www.repository.cam.ac.uk/handle/1810/247156.
Pełny tekst źródłaBantges, Richard John. "Cirrus cloud radiative properties in the thermal infrared". Thesis, Imperial College London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.344152.
Pełny tekst źródłaCunsolo, Salvatore. "Radiative properties computational modeling of porous cellular materials". Thesis, Lyon, 2018. http://www.theses.fr/2018LYSEI005/document.
Pełny tekst źródłaCellular media such as plastic, ceramic and metal foams present specific characteristics that make them interesting for a number of applications related to thermal engineering. Their ability to minimize natural convection makes them ideal candidates for insulation applications, while the high specific surface and permeability to fluid of open cell foams makes them interesting heat transfer enhancers. In addition, their permeability to light makes them an ideal candidate for thermal radiation based applications, such as porous burners or solar energy collectors. In many of these application, thermal radiation heat transfer can have a significant influence on the heat transfer process. Both accurate radiation models and accurate morphological models of the structure of the foam are required. This work provides an original contribution on both these accounts. A discussion of the literature on numerical methods for radiation heat transfer in cellular media is presented, with focus on Monte Carlo methods. Homogeneous Phase (HPA) and Multi Phase (MPA) methods are discussed. Further efforts are required to accurately model and digitally replicate of foam morphologies. Our goal is to digitally generate three commonly occurring types of foam structures, covering a large range of real materials: high-porosity open cell foams, high-porosity closed cell foams, low-porosity open-cell structures. For high-porosity open cell foams, the automated parametric digital generation technique was validated against a dataset consisting of raw morphological data obtained by tomographic analysis. The generation capabilities were then applied to parametrically investigate the influence of morphological parameters on the radiative properties (namely, the extinction coefficient) of an opaque open-cell foam. Highly accurate analytical relationships were subsequently deduced and validated by comparison with results obtained from tomography samples. Modeling radiation in foams with a semi-transparent solid phase is substantially more complex. A Direct Monte-Carlo Homogenization reference technique is proposed, that allows to simulate radiation within arbitrary cavities and calculate macroscopic radiative quantities based on a Representative Elementary Volume (REV) of cellular material. The technique is validated against full scale Monte Carlo simulations. Improvements of the existing Homogeneous Phase and Multi Phase approach are proposed, through extensive use of inverse methods and the addition of one equation to take into account specific phenomena taking place in the semi-transparent solid phase. The resulting Improved Homogenized Approaches are extensively tested by comparing them with Direct Monte Carlo Homogenization simulations and existing homogenized models, on a varied set of morphologies making full use of the previously developed digital generation techniques. The improved models consistently outperform existing homogenized models
Rogne, Henrik. "Thermal radiative properties of Si, GaAs, and InP". Thesis, University of Cambridge, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627277.
Pełny tekst źródłaXu, Jin. "Direct aerosol radiative forcing based on measurements of aerosol radiative, chemical and physical properties in China". Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/20173.
Pełny tekst źródłaNouri, Nima. "Radiative Conductivity Analysis Of Low-Density Fibrous Materials". UKnowledge, 2015. https://uknowledge.uky.edu/me_etds/66.
Pełny tekst źródłaSun, Wenbo. "An investigation of infrared radiative properties of cirrus clouds". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq24928.pdf.
Pełny tekst źródłaChalmers, Nicky. "Using retrieved cloud properties to investigate their radiative impact". Thesis, University of Reading, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.553137.
Pełny tekst źródłaBrent, Kevin M. "Optimization of Fire Blanket Performance by Varying Radiative Properties". Case Western Reserve University School of Graduate Studies / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=case1313767793.
Pełny tekst źródłaSweet, Julian. "RADIATIVE COUPLING AND DECAY PROPERTIES OF QUANTUM CONFINED SEMICONDUCTORS". Diss., The University of Arizona, 2009. http://hdl.handle.net/10150/194915.
Pełny tekst źródłaDe, Silva A. A. "Measurement of some radiative properties of solar absorber materials". Thesis, Open University, 1986. http://oro.open.ac.uk/56922/.
Pełny tekst źródłaAllen, Clare. "The influence of multi-dimensional radiative transfer on the evolution and radiative properties of tropical convective clouds". Thesis, University of Leeds, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.490579.
Pełny tekst źródłaRing, Harvey Brents III. "Radiative ignition of a wall jet". Thesis, Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/18937.
Pełny tekst źródłaCharron, Luc G. "Radiative properties of molybdenum sulfide and other transition metal dichalcogenides". Thesis, University of Ottawa (Canada), 2004. http://hdl.handle.net/10393/26599.
Pełny tekst źródłaRidley, David A. "Aerosol Radiative Properties Analysed using Global Models of Aerosol Microphysics". Thesis, University of Leeds, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.494262.
Pełny tekst źródłaCRISCUOLI, SERENA. "Radiative properties of complex magnetic elements in the solar photosphere". Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2008. http://hdl.handle.net/2108/599.
Pełny tekst źródłaGhaemi, Hamid. "The effective properties of composite material". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0020/MQ58036.pdf.
Pełny tekst źródłaChopra, Prateek. "Effective mechanical properties of lattice materials". Thesis, University of British Columbia, 2011. http://hdl.handle.net/2429/39436.
Pełny tekst źródłaLehmann, Brian (Brian Todd). "Numerical properties of pseudo-effective divisors". Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/60194.
Pełny tekst źródłaCataloged from PDF version of thesis.
Includes bibliographical references (p. 69-71).
Suppose that X is a smooth variety and L is an effective divisor. One of the main goals of bi rational geometry is to understand the asymptotic behavior of the linear series... as m increases. The two most important features of the asymptotic behavior - the litaka dimension and the litaka fibration - are subtle and difficult to work with. In this thesis we will construct approximations to these objects that depend only on the numerical class of L. The main interest in such results arises from the Abundance Conjecture which predicts that the Iitaka fibration for Kx is determined by its numerical properties. In the second chapter we study a numerical approximation to the Iitaka dimension of L. For a nef divisor L, this quantity is a classical invariant known as the numerical dimension. There have been several proposed extensions of the numerical dimension to pseudo-effective divisors in [Nak04] and [BDPP04]. We show that these proposed definitions coincide and agree with many other natural notions. Just as in the nef case, the numerical dimension v(L) of a pseudo-effective divisor L should measure the maximum dimension of a subvariety ... such that the "positive restriction" of L is big along W. In the third chapter, we analyze how the properties of the Iitaka fibration OL for L are related to the numerical properties of L. Although the numerical dimension detects the existence of "virtual sections", it does not have a direct relationship with the Iitaka fibration. However, we do construct a rational map that only depends on the numerical class of L and approximates the Jitaka fibration. This rational map is the maximal possible fibration for which a general fiber F satisfies v(LIF) = 0. Thus, this chapter recovers and extends the work of [Eck05] from an algebraic viewpoint. Finally, we use the pseudo-effective reduction map to study the Abundance Conjecture.
by Brian Lehmann.
Ph.D.
Lee, Hyunjin. "Radiative properties of silicon wafers with microroughness and thin-film coatings". Diss., Available online, Georgia Institute of Technology, 2006, 2006. http://etd.gatech.edu/theses/available/etd-07092006-181152/.
Pełny tekst źródłaZhang, Zhuomin, Committee Chair ; Joshi, Yogendra, Committee Member ; Lee, Kok-Meng, Committee Member ; Gallivan, Martha, Committee Member ; Zhao, Yiping, Committee Member.
Gilbert, Dean. "Observations and calculations of radiative properties of clouds observed during RACE". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0003/MQ44171.pdf.
Pełny tekst źródłaIvanov, Vladyslav Victorovych. "Cold atoms modified radiative properties and evaporative cooling from optical traps /". [S.l. : Amsterdam : s.n.] ; Universiteit van Amsterdam [Host], 2007. http://dare.uva.nl/document/47332.
Pełny tekst źródłaTaylor, Jonathan P. "The remote retrieval of stratiform water cloud radiative and microphysical properties". Thesis, University of Reading, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357173.
Pełny tekst źródłaAasum, Yngve. "Effective properties of reservoir simulator grid blocks /". Access abstract and link to full text, 1992. http://0-wwwlib.umi.com.library.utulsa.edu/dissertations/fullcit/9300177.
Pełny tekst źródłaOkyay, Gizem. "Impact of the morphology of soot aggregates on their radiative properties and the subsequent radiative heat transfer through sooty gaseous mixtures". Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLC031/document.
Pełny tekst źródłaSoot and its characterization are of interest to researchers from various domains such as combustion diagnostics, numerical combustion, atmospheric optics, environmental and health applications. In this study, the main interest is on the radiative properties of soot aggregates issued directly from combustion flames in order to determine the effect of the presence of soot on the radiative heat transfer in the simulation of high temperature industrial applications involving gas combustion. Current studies modeling the radiative heat transfer through sooty gaseous media consider only the absorption as the main phenomenon of material-radiation interaction. Generalized correlations are used to determine the radiative properties of soot: these radiative properties are either computed over numerically generated aggregate morphologies or simply as a function of the soot average size, the fractal dimension and the volume fraction. However, the material-radiation interaction is susceptible to be more complex and morphology dependent at the aggregate level because of multiple scattering when the size of the object reaches the order of magnitude of the incident radiation wavelengths.In our work, we investigate the possibility to establish a computational methodology and workflow, starting from the definition of a realistic soot morphology up to the computation of the radiative heat transfer. To that end, observations of soot issued from propane/air, methane/air and methane/oxygen flames are performed using Scanning Electron Microscopy (SEM). SEM tomography is applied for the first time on soot issued from a propane/air flame, combined with Transmission Electron Microscopy (TEM) observations. 2D and 3D fractal analysis techniques are used to investigate the fractal properties of virtual (numerically generated) soot clusters and also of the tomography reconstructed objects. The radiative properties of soot are then computed using our in-house developed DDA (Discrete Dipole Approximation) code. Special attention is paid to the DDA modeling of soot because of the high complex extinction index of the material, and to the directional integration numerical methods because direction-averaged radiative properties are required for the subsequent radiative heat transfer simulations. The morphology and the radiative properties of the realistic morphology are compared to the ones of representative soot aggregates numerically generated by a DLCCA (Diffusion Limited Cluster-Cluster Aggregation) algorithm. The similarities and discrepancies on the radiative properties are investigated, and the differences between representative virtual aggregates on the one hand and the tomography reconstructed object on the other hand in terms of radiative properties are highlighted. Finally the effect of the presence and of the morphology of soot on the radiative heat transfer within a sooty gaseous mixture in a 1D isothermal parallel plate configuration is investigated by the resolution of the radiative transfer equation using DOM (Discrete Ordinates Method)
Lee, Yong-Keun. "Study of cloud properties from single-scattering, radiative forcing, and retrieval perspectives". [College Station, Tex. : Texas A&M University, 2006. http://hdl.handle.net/1969.1/ETD-TAMU-1734.
Pełny tekst źródłaFu, Ceji. "Radiative Properties of Emerging Materials and Radiation Heat Transfer at the Nanoscale". Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/4941.
Pełny tekst źródłaAbel, Steven John. "The radiative properties and direct effect of Southern African biomass burning aerosols". Thesis, University of Reading, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.417397.
Pełny tekst źródłaWang, Xuan Ph D. Massachusetts Institute of Technology. "Exploring the absorption properties and direct radiative impact of atmospheric carbonaceous aerosols". Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/113493.
Pełny tekst źródłaCataloged from PDF version of thesis.
Includes bibliographical references (pages 125-141).
Atmospheric aerosols are important due to their adverse effects on human health and their direct and indirect radiative effects on climate, which are significant and very uncertain factors contributing to global climate change. In estimating the direct radiative effect (DRE), the absorption from carbonaceous aerosols, including black carbon (BC) and brown carbon (BrC, a component of organic aerosol, OA), are highly uncertain. This thesis addresses this uncertainty by combining models and observations to better constrain the optical properties and radiative impact of carbonaceous aerosols. First, a global model simulation (GEOS-Chem) of BC is expanded to separately treat both the aging and physical properties of BC from different sources. By combining model and observations, the global BC lifetime is found to be overestimated in previous investigations, leading to higher estimates of its warming potential. The DRE of BC is estimated to be less than one quarter of the previously reported value. Second, a new method is developed to derive BrC absorption from measurements and used to identify BrC from total absorption observations. The absorption efficiency of BrC is found to be positively correlated with the emitted BC/OA mass ratio, which is related to combustion conditions. In addition, measured BrC absorption from biomass burning plumes is found to decrease with photochemical aging with a lifetime of one day. Third, a global model simulation of BrC is developed and tested against BrC absorption measurements from aircraft campaigns in the continental United States. The BrC absorption properties from biomass burning estimated based on laboratory measurements are found to overestimate the direct measurements of ambient BrC absorption. In addition, applying a photochemical aging scheme for BrC improves the model skill. The simulation suggests that the DRE of BrC has been overestimated previously due to the lack of observational constraints from direct measurements and omission of the effects of photochemical aging. Finally, the influence of mixing state on the global absorption of carbonaceous aerosols is estimated through simplified model experiments. This thesis suggests that policies for reducing emissions of carbonaceous aerosols may have a limited impact on mitigating global climate warming.
by Xuan Wang.
Ph. D. in Environmental Chemistry
Takeuti, Douglas de Freitas. "Thermal radiative properties of ion-implanted silicon and titanium and cobalt silicides". Thesis, University of Cambridge, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627343.
Pełny tekst źródłaReid, Jeffrey Spencer. "Emission, evolution, and radiative properties of particles from biomass burning in Brazil /". Thesis, Connect to this title online; UW restricted, 1998. http://hdl.handle.net/1773/10099.
Pełny tekst źródłaToullier, Thibaud. "Simultaneous characterization of objects temperature and radiative properties through multispectral infrared thermography". Thesis, Rennes 1, 2019. http://www.theses.fr/2019REN1S038/document.
Pełny tekst źródłaThe latest technological improvements in low-cost infrared cameras have brought new opportunities for long-term infrastructures monitoring. The accurate measurement of surfaces' temperatures is facing the lack of knowledge of radiatives properties of the scene. By using multi-sensors instrumentation, the measurement model can be refined to get a better estimate of the temperature. To overcome a lack of sensors instrumentation, it is shown that online and free available climatic data can be used. Then, Bayesian methods to estimate simultaneously the emissivity and temperature have been developed and compared to literature's methods. A radiative exchange simulator of 3D scenes have been developed to compare those different methods on numerical data. This software uses the hardware acceleration as well as a GPGPU approach to reduce the computation time. As a consequence, obtained numerical results emphasized an advanced use of multi-spectral infrared thermography for the monitoring of structures. This simultaneous estimation enables to have an estimate of the temperature by infrared thermography with a known uncertainty
Bulgin, Claire Elizabeth. "Improved understanding of aerosol processes using satellite observations of aerosol optical properties". Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/4906.
Pełny tekst źródłaSchubert, Richard [Verfasser]. "On the effective properties of suspensions / Richard Schubert". Bonn : Universitäts- und Landesbibliothek Bonn, 2019. http://d-nb.info/118185590X/34.
Pełny tekst źródłaJohnston, Desmond Alexander. "Gauge properties and convexity of the effective potential". Thesis, Imperial College London, 1986. http://hdl.handle.net/10044/1/38054.
Pełny tekst źródłaZhu, Junlin. "Effective properties for flow in heterogeneous porous media". Diss., Virginia Tech, 1990. http://hdl.handle.net/10919/39416.
Pełny tekst źródłaPoladian, Leon. "Effective transport and optical properties of composite materials". Phd thesis, Department of Theoretical Physics, 1990. http://hdl.handle.net/2123/11724.
Pełny tekst źródłaDauchet, Jérémi. "Analyse radiative des photobioréacteurs". Phd thesis, Université Blaise Pascal - Clermont-Ferrand II, 2012. http://tel.archives-ouvertes.fr/tel-00914315.
Pełny tekst źródłaZheng, Xiaoyu Forest M. Gregory. "On the effective properties of nematic polymer nano-composites". Chapel Hill, N.C. : University of North Carolina at Chapel Hill, 2006. http://dc.lib.unc.edu/u?/etd,248.
Pełny tekst źródłaTitle from electronic title page (viewed Oct. 10, 2007). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics." Discipline: Mathematics; Department/School: Mathematics.
Dimas, Leon Sokratis Scheie. "Effective mechanical Properties of material models with random heterogeneities". Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/103706.
Pełny tekst źródłaCataloged from PDF version of thesis.
Includes bibliographical references (pages 191-198).
In this thesis we obtain analytical approximations to the probability distribution of the elastic tensor and fracture strengths of material models with random heterogeneities. We start by investigating the effective elastic properties of one-, two-, and three-dimensional rectangular blocks whose Young's modulus varies spatially as a lognormal random field. We decompose the spatial fluctuations of the Young's log-modulus F = In E into first- and higher-order terms and find the joint distribution of the effective elastic tensor by multiplicatively combining the term-specific effects. Through parametric analysis of the analytical solutions, we gain insight into the effective elastic properties of this class of heterogeneous materials. Building on this analysis we find analytical approximations to the probability distribution of fracture properties of one-dimensional rods and thin two-dimensional plates for systems in which: only the Young's modulus varies spatially as an isotropic lognormal field and more generally, both the Young's modulus and the local material strength vary spatially as possibly correlated lognormal fields. The properties considered are the elongation, strength, and toughness modulus at fracture initiation and at ultimate failure. For all quantities at fracture initiation our approach is analytical in I D and semi-analytical in 2D. For ultimate failure, we quantify the random effects of fracture propagation and crack arrest by fitting regression models to simulation data and combine the regressions with the distributions at fracture initiation. Through parametric analysis, we gain insight into the strengthening/weakening roles of the Euclidean dimension, size of the specimen, and the correlation, variance and correlation function of the random fields. Finally, we extend the approach to investigate the elasticity of non-lognormal random heterogeneous materials. First we investigate the elastic bulk stiffness of two-dimensional checkerboard specimens in which square tiles are randomly assigned to one of two component phases. This is a model system for multi-phase polycrystalline materials such as granitic rocks and many ceramics. We study how the bulk stiffness is affected by different characteristics of the specimen and obtain analytical approximations to the probability distribution of the effective stiffness. In particular we examine the role of percolation of the soft and stiff phases. In small specimens, we find that the onset of percolation causes significant discontinuities in the effective modulus, whereas in large specimens the influence of percolation is smaller and gradual. Secondly we study the effective stiffness of multi-phase composite systems in which the Young's modulus varies as a filtered Poisson point process and find that the homogenization approach initially developed for lognormal systems produces accurate results also for this class of non-lognormal systems.
by Leon Sokratis Scheie Dimas.
Ph. D.