Depolarization volume and correlation length in the homogenization of anisotropic dielectric composites

In conventional approaches to the homogenization of random particulate composites, both the distribution and size of the component phase particles are often inadequately taken into account. Commonly, the spatial distributions are characterized by volume fraction alone, while the electromagnetic response of each component particle is represented as a vanishingly small depolarization volume. The strong-permittivity-fluctuation theory (SPFT) provides an alternative approach to homogenization wherein a comprehensive description of distributional statistics of the component phases is accommodated. The bilocally-approximated SPFT is presented here for the anisotropic homogenized composite which arises from component phases comprising ellipsoidal particles. The distribution of the component phases is characterized by a two-point correlation function and its associated correlation length. Each component phase particle is represented as an ellipsoidal depolarization region of nonzero volume. The effects of depolarization volume and correlation length are investigated through considering representative numerical examples. It is demonstrated that both the spatial extent of the component phase particles and their spatial distributions are important factors in estimating coherent scattering losses of the macroscopic field.Comment: Typographical error in eqn. 16 in WRM version is corrected in arxiv versio

On the propagation of Voigt waves in energetically active materials

If a dissipative anisotropic dielectric material, characterized by the permittivity matrix $\underline{\underline{\epsilon}}$, supports Voigt-wave propagation, then so too does the analogous active material characterized by the permittivity matrix $\underline{\underline{{\tilde{\epsilon}}}}$, where $\underline{\underline{{\tilde{\epsilon}}}}$ is the hermitian conjugate of $\underline{\underline{\epsilon}}$. Consequently, a dissipative material that supports Voigt-wave propagation can give rise to a material that supports the propagation of Voigt waves with attendant linear gain in amplitude with propagation distance, by infiltration with an active dye

Multiple scattering theory for heterogeneous elastic continua with strong property fluctuation: theoretical fundamentals and applications

In this work, the author developed a multiple scattering model for heterogeneous elastic continua with strong property fluctuation and obtained the exact solution to the dispersion equation derived from the Dyson equation under the first-order smoothing approximation. The model establishes accurate quantitative relation between the microstructural properties and the coherent wave propagation parameters and can be used for characterization or inversion of microstructures. As applications of the new model, dispersion and attenuation curves for coherent waves in the Earth lithosphere, the porous and two-phase alloys, and human cortical bone are calculated. Detailed analysis shows the model can capture the major dispersion and attenuation characteristics, such as the longitudinal and transverse wave Q-factors and their ratios, existence of two propagation modes, anomalous negative dispersion, nonlinear attenuation-frequency relation, and even the disappearance of coherent waves. Additionally, it helps gain new insights into a series of longstanding problems, such as the dominant mechanism of seismic attenuation and the existence of the Mohorovicic discontinuity. This work provides a general and accurate theoretical framework for quantitative characterization of microstructures in a broad spectrum of heterogeneous materials and it is anticipated to have vital applications in seismology, ultrasonic nondestructive evaluation and biomedical ultrasound.Comment: 70 pages, 42 figure

Problems In Nonlinear Homogenization: Bounds, Estimates, Macroscopic Instabilities, And Post-Bifurcation Response

Due to the ever-growing interest in composite materials designed with complex microstructures and capable of possessing exotic properties, it has become increasingly important to be able to accurately capture the interplay between the macroscopic response and the underlying microstructure, as the former is greatly influenced by the latter. Of the different approaches available, this thesis is concerned with the use of nonlinear homogenization to study the effective response of composites. We look to illustrate the effect that constitutive assumptions have on the methods by which such estimates can be obtained, and on the actual effective, or homogenized, response of the material. For materials whose constitutive response is governed by convex functions, we show how the convexity itself can be utilized to obtain rigorous bounds and improved estimates. We prove the optimality of variational linear comparison bounds over the class of nonlinear anisotropic composites with linearly isotropic response and introduce a new symmetric fully optimized second-order method which is able to generate estimates for the effective response of nonlinear composites. On the other hand, convexity is often inconsistent with certain physical requirements (e.g. objectivity). Such is the case of hyperelasticity, where the lack of convexity of the stored-energy functions has long been known to lead to the development of instabilities. We present a framework for studying the post-bifurcation response of such systems and apply it to a specific class of reinforced hyperelastic composites under general three-dimensional loading conditions. We also consider the class of magneto-elastic composites, which consist of hyperelastic materials that are also magnetically susceptible. Unlike in the case of hyperelasticity, there lacks a complete mathematical framework for obtaining the effective response of such materials, and researchers have only begun to investigate the potential for instabilities in these materials. We therefore generalize the same methodology used successfully in the purely mechanical context to study the post-bifurcation behavior of magneto-elastic composites. This in part requires a rigorous generalization of the theoretical aspects that underlie the method. We then calculate the post-bifurcation response of a magneto-elastic material under general plane-strain loading conditions with a magnetic field applied in the plane of deformation

Development of green composites based on epoxidized vegetable oils (EVOs) with hybrid reinforcements: natural and inorganic fibers

The main aim of this work id to provide integral methods to predict and characterize the properties of composite structures based on hybrid polymers and reinforcements, that could lead to useful results from an industrial point of view. This is addressed, if possible, by theoretical predictions of the effective properties by using the available experimental data. The first part is focused on the scientific achievements of the author that allowed a quantitative characterization of the main effective properties of several composite architectures from hybrid polymers and reinforcements, based on bio matrices, tailor-made matrices and different theoretical and simulation methods using computer software to allow good comparison. The second part defines the future research lines to continue this initial investigation. The main objectives are clearly defined to give the reader a sound background with the appropriate concepts that are specifically discussed in the following chapters. As a main objective, this research work makes a first attempt to provide a systematic analysis and prediction of composite hybrid structures.El objetivo general del trabajo es proporcionar medios integrales para predecir y caracterizar las propiedades de las estructuras de compuestos basados en polímeros y refuerzos híbridos, principales que pueden producir resultados de utilidad práctica simultáneamente. Esto se logra comparando, siempre que sea posible, las predicciones teóricas de las propiedades efectivas con los datos experimentales disponibles. Una primera parte se ocupa de los logros científicos del autor que permitieron caracterizar cuantitativamente las principales propiedades efectivas de las arquitecturas de compuestos basados en polímeros y refuerzos híbridos, basados en matrices bio, auto-desarrollados y diferentes métodos teóricos y de simulación por ordenador utilizados para la comparación. La segunda parte identifica las orientaciones futuras para la evolución y desarrollo de la ciencia y la investigación. Los objetivos generales fueron subrayados y concisos para dar al lector una visión previa de los conceptos que serán discutidos específicamente en los siguientes capítulos. Indirectamente, apuntan hacia uno de los objetivos principales de este trabajo, a saber, proporcionar una dirección para el análisis sistemático de materiales compuestos a base de refuerzos híbridos.L'objectiu general d'aquest treball es proporcionar els mitjos integrals per tal de predir i caracteritzar les propietats d'estructures de compòsits basats en polímers i reforçaments híbrids, que poden produir resultats amb utilitat pràctica simultàniament. Aquest objectiu s'aconsegueix comparant, sempre que és possible, les prediccions teòriques de les propietats efectives amb les dades experimentals disponibles. Una primera part es centra en els temes científics en què ha treballat l'autor que han permès caracteritzar quantitativament les principals propietats efectives de les arquitectures de compòsits basades en polímers i reforçaments híbrids, derivats de matrius bio, auto-desenvolupats i diferents mètodes teòrics i de simulació informàtica per a una correcta comparació. La segona part identifica les orientacions futures per tal d'establir l'evolució i desenvolupament de la ciència i investigació lligada a la temàtica de la tesi. Els objectius generals han sigut clarament definits per tal de donar-li al lector una visió prèvia i sòlida dels conceptes que es discuteixen en capítols venidors. Indirectament, apunten cap a un dels objectius principals d'aquest treball, a saber, proporcionar una direcció per a l'anàlisi sistemàtica de materials compòsits a base de polímers i reforçaments híbrids.Motoc, D. (2017). Development of green composites based on epoxidized vegetable oils (EVOs) with hybrid reinforcements: natural and inorganic fibers [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/90399TESI

Thermoelastic Properties of Particle Reinforced Composites at the Micro and Macro Scales

Particle reinforced composites are widely used in tires, heat exchangers, thermal barrier coatings and many other applications, as they have good strength to weight ratio, excellent thermal insulation, ease of manufacturing and flexibility in design. During their service life, these composites are often subjected to harsh environments, which can degrade the thermo-mechanical properties of the constituents in the composites, affecting performance and lifetime of the composites. This study investigates performance of particle reinforced composites subjected to coupled heat conduction and thermo-elastic deformation at the macro and micro levels. A micromechanical model is used to determine the effective thermal and mechanical properties of the homogenized composite by incorporating microscopic characteristics of the composites. The constituent?s thermal conductivities of the composite are assumed to be functions of temperature and the elastic moduli to be functions of temperature and stress fields. The effective properties obtained from the micromechanical model represent average (macroscopic) properties. The effective heat conduction and thermo-elastic responses in the homogenized composites are compared with the responses of the composite with particles randomly distributed in the matrix (heterogeneous materials) which represent microscopic responses. For this purpose, two sets of finite element (FE) models are generated for composites with particle volume contents 12.5, 25, and 50%. The first FE model represents a homogenized composite panel and the effective responses from the micromechanical model are used as input for the material properties. The second FE model mimics composite microstructure with discontinuous particles randomly dispersed in a homogeneous matrix. Parametric studies on effects of conductivity ratio between particle and matrix, degree of nonlinearity, and volume fraction on the temperature distribution and steady state times have been studied. For lower volume fractions the temperature profiles of homogenized and heterogeneous composite models are in good agreement with each other. But for higher volume fractions, the detailed model showed a wavy profile whereas the effective model showed no signs of it. When the nonlinearity in thermal conductivity of the particle and matrix constituents is increased, the steady state time significantly deviates from the ones with constant constituent properties. When the volume fraction of particles in the composite increases, the steady state is reached in less time, since the thermal conductivity of particles are taken larger than that of the matrix. Effects of coefficient of thermal expansion (CTE) ratio of particle and matrix, temperature change, and volume fraction on the discontinuity of stress and strain fields at the interphase of matrix and particle have been studied. The stresses developed were more for higher CTE ratios and the magnitude of discontinuity also follows the same trend. As the volume fraction increases, the stresses developed and the magnitude of discontinuity also increase. Finally, sequentially coupled heat conduction and deformation analyses are performed on thermal barrier coating (TBC) systems to demonstrate the applicability of the micromechanical model in predicting overall thermo-elastic responses of the TBC

Peridynamics review

Peridynamics (PD) is a novel continuum mechanics theory established by Stewart Silling in 2000 [1]. The roots of PD can be traced back to the early works of Gabrio Piola according to dell'Isola et al. [2]. PD has been attractive to researchers as it is a nonlocal formulation in an integral form; unlike the local differential form of classical continuum mechanics. Although the method is still in its infancy, the literature on PD is fairly rich and extensive. The prolific growth in PD applications has led to a tremendous number of contributions in various disciplines. This manuscript aims to provide a concise description of the peridynamic theory together with a review of its major applications and related studies in different fields to date. Moreover, we succinctly highlight some lines of research that are yet to be investigated