CARACTERIZACIÓN MICROMECÁNICA DE COMPOSITOS MAGNETO-ELECTRO-ELÁSTICOS.

El presente trabajo de tesis está dedicado al cálculo de las propiedades efectivas antiplanas de compositos fibrosos magneto-electro-elásticos bifásicos (fibra/matriz) y trifásicos (fibra/interfase/matriz), con estructura periódica y cuyos elementos representativos del volumen son bidimensionales o tridimensionales. Se implementaron modelos micromecánicos analíticos y semi-analíticos (SAFEM) diferentes, basados en el método de homogeneización asintótica y en el método de los elementos finitos. En particular, se analiza la influencia del efecto de la interfaz entre las fibras y la matriz; del volumen de fracción de los refuerzos; de la distribución de los refuerzos en la matriz y de la selección de los materiales constituyentes en las propiedades efectivas antiplanas de compositos fibrosos magneto-electro-elásticos. Para el análisis del efecto de la interacción entre las fibras y la matriz se formularon dos modelos analíticos: el modelo de imperfección (MHA – Imp) aplicado para la descripción de compositos bifásicos con interfaz imperfecta entre los constituyentes y el modelo de interfase (MHA – 3F) aplicado para la descripción de compositos trifásicos con una interfase existente entre las fibras y la matriz. En ambos modelos se consideraron elementos representativos del volumen en forma de paralelogramos. En el modelo MHA – Imp, las imperfecciones mecánica, eléctrica y magnética en la interfaz son modeladas como una idealización por medio de la existencia de un resorte, un capacitor y un inductor respectivamente. Las formulaciones analíticas derivadas para los problemas locales antiplanos y de las propiedades efectivas asociadas, derivados por MHA – Imp, MHA – 3F y SAFEM son explícitamente descritas, por lo cual, se pueden usar de forma eficiente para verificar la implementación de métodos experimentales, numéricos y modelos analíticos. La eficiencia de los modelos presentados MHA – Imp, MHA  3F y SAFEM y la validación de los resultados obtenidos se demuestra mediante comparaciones con resultados obtenidos por otros modelos teóricos reportados en la literatura. Las fórmulas desarrolladas son, además, válidas para el análisis de las propiedades efectivas antiplanas de compositos fibrosos periódicos, bifásicos y trifásicos piezoeléctricos y elásticos con ERV bidimensional o tridimensional

Elliptic functions and lattice sums for effective properties of heterogeneous materials

Effective properties of fiber-reinforced composites can be estimated by applying the asymptotic homogenization method. Analytical solutions are possible for infinite long circular fibers based on the elliptic quasi-periodic Weierstrass Zeta function. This process leads to numerical convergences issues related to lattice sums calculations. The lattice sums original series converge slowly, which make the calculation difficult. This problem needs to be addressed because effective properties are highly sensitive to these values. Therefore, a systematic review and analysis for the lattice sums are a necessity. In the present work, the Eisenstein–Rayleigh lattices sums are reviewed and numerically implemented for fiber-reinforced composites with parallelogram unit periodic cell whose fibers are centered, or not, at the coordinate origin. Numerical values are reported and compared with available data in the literature obtaining good agreements. In this work, new Eisenstein–Rayleigh lattice sums are obtained that are easy to implement and a set of tables with numerical values are given

The effectiveness of published continuum constitutive laws to predict stress-assisted densification of powder compacts

Commonly used constitutive laws for crystalline and viscous materials have been compared to predict the densification behavior under hot-pressing and sinter-forging. Experimental results, from literature for one loading condition, have been used to extract the constitutive laws for amorphous and crystalline materials and, these in-turn, have been used to predict behavior under a different set of loading conditions. Ideally, the constitutive parameters obtained from one set of loading conditions and thermal history should apply to a different set of conditions. However, there is a lack of systematic experimental studies in which this can be checked. In this paper, we use constitutive parameters obtained from one set of conditions to predict the densification response under a different set of loading conditions. For both sintering of amorphous and crystalline materials, we use two different constitutive parameters and compare the predictions of these for the case where experimental results are not available. In addition, the effect of temperature on densification behavior for stress-assisted sintering has been investigated. It is shown that the two commonly used constitutive models for viscous sintering (Scherer and Skorohod–Olevsky) predict similar behavior for amorphous materials. However, for crystalline materials, the predictions of the Riedel–Svoboda and the Kuhn–Sofronis–McMeeking (KSM) models are different. Finally, it is shown that the dependence of the normalized densification on temperature, under constant heating rate conditions, with parameters obtained from isothermal experiments, is a good test for the models

Effective Complex Properties for Three-Phase Elastic Fiber-Reinforced Composites with Different Unit Cells

The development of micromechanical models to predict the effective properties of multi-phase composites is important for the design and optimization of new materials, as well as to improve our understanding about the structure–properties relationship. In this work, the two-scale asymptotic homogenization method (AHM) is implemented to calculate the out-of-plane effective complex-value properties of periodic three-phase elastic fiber-reinforced composites (FRCs) with parallelogram unit cells. Matrix and inclusions materials have complex-valued properties. Closed analytical expressions for the local problems and the out-of-plane shear effective coefficients are given. The solution of the homogenized local problems is found using potential theory. Numerical results are reported and comparisons with data reported in the literature are shown. Good agreements are obtained. In addition, the effects of fiber volume fractions and spatial fiber distribution on the complex effective elastic properties are analyzed. An analysis of the shear effective properties enhancement is also studied for three-phase FRCs

Effective properties of centro-symmetric micropolar composites with non-uniform imperfect contact conditions

In this work, the homogenization theory is addressed within the framework of three-dimensional linear micropolar composite materials with centro-symmetric constituents and non-uniform imperfect interface conditions. The imperfect contact conditions are modeled like a generalization of the spring model, where tractions and coupled stresses are continuous, but displacements and microrotations are discontinuous across the interface. The jumps in displacement and microrotation components are proportional to the interface traction and coupled stress components in terms of a partition of different spring-factor-type interface parameters, respectively. The two-scale asymptotic homogenization method (AHM) is developed, through series expansions for displacements and micro-rotations, to find the analytical statement of the local problems on the periodic cell and the corresponding effective coefficients. In particular, centro-symmetric multi-laminated micropolar composites with non-uniform imperfect contact conditions are studied, and their corresponding effective properties are explicitly declared. Numerical results show the effects of the interface partition lengths, the non-uniform imperfection values, and the constituent’s fraction volumes on the effective properties of centro-symmetric bi-laminated composite with isotropic constituent materials. We also analyze and discuss the effective behaviors illustrated in the results. In general, the effective properties are always affected by a non-uniform imperfect interface, and they are bounded between those achieved when the contact conditions are perfect and imperfect uniform. The reported formulas and data may be helpful as benchmarks for checking other experimental and numerical results

Interphase effect on the effective magneto-electro-elastic properties for three-phase fib er-reinforce d composites by a semi-analytical approach

A semi-analytical approach is proposed to determine the effective magneto-electro-elastic moduli of a fiber-reinforced composite. We especially focus on predicting the effective properties of three-phase periodic composite reinforced with unidirectional, infinitely long and concentric cylindrical fibers with square transversal distribution. The semi-analytical method is developed combining asymptotic homogenization and finite element meth- ods. Asymptotic homogenization method allows the statements of local problems that are solved by finite element method and the associated effective coefficients. Finite element method is implemented via the principle of minimum potential energy. The effect of inter- phase thickness and the fiber material properties on effective moduli is analyzed. Numer- ical computations were performed, and an exact agreement is obtained by comparing the semi-analytical approach with asymptotic homogenization method linked to the theory of potential functions of a complex variable

Semi-analytic finite element method applied to short-fiber-reinforced piezoelectric composites

In this work, a 3D semi-analytical finite element method (SAFEM) is developed to calculate the effective properties of piezoelectric fiber-reinforced composites (PFRC). Here, the calculations are implemented in one-eighth of the unit cell to simplify the method. The prediction of the effective properties for periodic PFRC made of piezoceramic unidirectional fibers (PZT) with square and hexagonal space arrangements in a soft non-piezoelectric matrix (polymer) is reported as a way to validate the 3D approach. The limit case, when short fibers become long ones, allows us to compare with results reported in the literature. For the analysis of effective properties as a function of fiber relative length, two cases are considered: (i) constant volume fraction and (ii) constant fiber radius. The constant volume fraction case is of special interest because according to the Voigt–Reuss–Hill approximation, the effective properties should remain constant. Then, in order to analyze this case, mechanical and electric fields are also shown. The obtained results show a physically congruent behavior. Good coincidences are obtained by comparing with asymptotic homogenization and the representative volume element methods. The 3D SAFEM is also implemented to study the bone piezoelectric behavior with attention to the role of the mineralized phase on the effective d∗333 piezoelectric coefficient