Homogenized out-of-plane shear response three-scale fiber-reinforced composites

In the present work we embrace a three scales asymptotic homogenization approach to investigate the effective behavior of hierarchical linear elastic composites reinforced by cylindrical, uniaxially aligned fibers and possessing a periodic structure at each hierarchical level of organization. We present our novel results assuming isotropy of the constituents and focusing on the effective out-of-plane shear modulus, which is computed exploiting the solution of the arising anti-plane problems. The latter are solved semi-analytically by means of complex variables and successfully benchmarked against the results obtained by finite elements. Our findings can pave the way for multiscale modeling of complex hierarchical materials (such as bone and tendons) at a negligible computational cost

Three scales asymptotic homogenization and its application to layered hierarchical hard tissues

In the present work a novel multiple scales asymptotic homogenization approach is proposed to study the effective properties of hierarchical composites with periodic structure at different length scales. The method is exemplified by solving a linear elastic problem for a composite material with layered hierarchical structure. We recover classical results of two-scale and reiterated homogenization as particular cases of our formulation. The analytical effective coefficients for two phase layered composites with two structural levels of hierarchy are also derived. The method is finally applied to investigate the effective mechanical properties of a single osteon, revealing its practical applicability in the context of biomechanical and engineering applications

The influence of anisotropic growth and geometry on the stress of solid tumors

Solid stresses can affect tumor patho-physiology in at least two ways: directly, by compressing cancer and stromal cells, and indirectly, by deforming blood and lymphatic vessels. In this work, we model the tumor mass as a growing hyperelastic material. We enforce a multiplicative decomposition of the deformation gradient to study the role of anisotropic tumor growth on the evolution and spatial distribution of stresses. Specifically, we exploit radial symmetry and analyze the response of circumferential and radial stresses to (a) degree of anisotropy, (b) geometry of the tumor mass (cylindrical versus spherical shape), and (c) different tumor types (in terms of mechanical properties). According to our results, both radial and circumferential stresses are compressive in the tumor inner regions, whereas circumferential stresses are tensile at the periphery. Furthermore, we show that the growth rate is inversely correlated with the stresses’ magnitudes. These qualitative trends are consistent with experimental results. Our findings therefore elucidate the role of anisotropic growth on the tumor stress state. The potential of stress-alleviation strategies working together with anticancer therapies can result in better treatments

Acerca de la homogeneización y propiedades efectivas de la ecuación del calor

This is a work of scientific circulation intended to introduce the homogenization process from the heat equation. An example is studied for a medium made of two conducting materials, matrix and fibers. The fibers are periodically distributed and embedded within the matrix. The composite is isotropic on the macroscopic scale and perfect inter-facial contact conditions are considered. The problem is studied in the context of periodic homogenization. The effective conductivity tensor is calculated as a result of the application of the asymptotic homogenization method. The solution of the problem on the periodic cell is based on well-known tools of Complex Variable Theory. Some limit cases are also presented.Este es un trabajo de divulgación científica, dedicado a recorrer el problema de la conductividad térmica efectiva de un material heterogéneo bifásico tipo matriz inclusión con microestructura periódica. El material compuesto es macroscópicamente isótropo y presenta contacto perfecto en las fases. El problema se estudia en el contexto de la homogeneización periódica. Las propiedades efectivas se determinan como resultado del Método de Homogeneización Asintótica (MHA). Se utilizan conocidas herramientas de la teoría de variable compleja para la resolución del problema sobre la celda periódica. Se presentan los casos límites

Cotas variacionales para coeficientes efectivos en compuestos con contacto imperfecto

The problem of effective thermal conductivity for a matrix-fiber composite with a periodic micro-structure is studied. This composite is globally isotropic with an inter-facial surface resistance between phases. Variational principles and bounds are introduced, describing the effective conductivity tensor as a result of the application of the asymptotic homogenization method. These bounds depend on the concentration of each phase as well as on the geometry of the medium the micro-structure, and the imperfection parameter. Some comparisons with other theoretical results are also providedSe estudia el problema de la conductividad térmica efectiva de un material heterogéneo bifásico tipo matriz-inclusión con microestructura periódica. Este material compuesto es macroscópicamente isótropo y presenta una barrera de resistencia térmica tipo resorte en las superficies de contacto de las fases. Se formulan principios variacionales y cotas para el tensor efectivo de la conductividad térmica, resultado de la aplicación del método de homogeneización asintótica. Las cotas dependen de la concentración de volumen de las fases, de la geometría de la inclusión y de la constante de imperfección que caracteriza la barrera de resistencia térmica. Se muestran comparaciones con resultados derivados de otras teorías

Behavior Of Laminated Shell Composite With Imperfect Contact Between The Layers

The paper focuses on the calculation of the effective elastic properties of a laminated composite shell with imperfect contact between the layers. To achieve this goal, first the two-scale asymptotic homogenization method (AHM) is applied to derive the solutions for the local problems and to obtain the effective elastic properties of a two-layer spherical shell with imperfect contact between the layers. The results are compared with the numerical solution obtained by finite elements method (FEM). The limit case of a laminate shell composite with perfect contact at the interface is recovered. Second, the elastic properties of a spherical heterogeneous structure with isotropic periodic microstructure and imperfect contact is analyzed with the spherical assemblage model (SAM). The homogenized equilibrium equation for a spherical composite is solved using AHM and the results are compared with the exact analytical solution obtained with SAM

Effective Coefficients And Local Fields Of Periodic Fibrous Piezocomposites With 622 Hexagonal Constituents

The asymptotic homogenization method is applied to a family of boundary value problems for linear piezoelectric heterogeneous media with periodic and rapidly oscillating coefficients.We consider a two-phase fibrous composite consisting of identical circular cylinders perfectly bonded in a matrix. Both constituents are piezoelectric 622 hexagonal crystal and the periodic distribution of the fibers follows a rectangular array. Closed-form expressions are obtained for the effective coefficients, based on the solution of local problems using potential methods of a complex variable. An analytical procedure to study the spatial heterogeneity of the strain and electric fields is described. Analytical expressions for the computation of these fields are given for specific local problems. Examples are presented for fiber-reinforced and porous matrix including comparisons with fast Fourier transform (FFT) numerical results

Combinação do ADMM com Homogeneização Matemática na Modelagem da Dispersão de Poluentes na Atmosfera

Resumo O método multicamadas de advecção-difusão (ADMM) produz soluções semianalíticas precisas dos problemas de valores de contorno/iniciais para equações de advecção-difusão com coeficientes variáveis que modelam a dispersão de poluentes na atmosfera, e apresenta o menor custo computacional quando comparado com outros métodos baseados em transformadas integrais. Contudo, em situações operativas tais como desastres naturais/industriais que resultam na fuga de poluentes na atmosfera, é necessário aferir rapidamente e com exatidão a distribuição da concentração dos poluentes no nível do solo para minimizar o impacto na saúde e na economia. Aqui, para acelerar a disponibilidade de resultados com mínima perda de precisão, o ADMM é combinado com homogeneização matemática, cujo emprego na modelagem de dispersão de poluentes parece ser novidade. A abordagem proposta é comparada com a aplicação direta do ADMM e às observações do experimento de Hanford para avaliar a exatidão das estimativas, assim como sua eficiência computacional, considerando condições atmosféricas estáveis e a influência da velocidade de deposição. Os resultados mostram que a combinação do ADMM com a homogeneização matemática apresenta uma redução significativa no custo computacional com pouca perda de precisão

Assessment Of Models And Methods For Pressurized Spherical Composites

The elastic properties of a spherical heterogeneous structure with isotropic periodic components is analyzed and a methodology is developed using the two-scale asymptotic homogenization method (AHM) and spherical assemblage model (SAM). The effective coefficients are obtained via AHM for two different composites: (a) composite with perfect contact between two layers distributed periodically along the radial axis; and (b) considering a thin elastic interphase between the layers (intermediate layer) distributed periodically along the radial axis under perfect contact. As a result, the derived overall properties via AHM for homogeneous spherical structure have transversely isotropic behavior. Consequently, the homogenized problem is solved. Using SAM, the analytical exact solutions for appropriate boundary value problems are provided for different number of layers for the cases (a) and (b) in the spherical composite. The numerical results for the displacements, radial and circumferential stresses for both methods are compared considering a spherical composite material loaded by an inside pressure with the two cases of contact conditions between the layers (a) and (b)