A New Solution Method for Homogenization of Effective Properties of Electromagnetic Honeycombs

In this paper, an analytical model and its new numerical solution using the homogenization method are developed to determine the effective electromagnetic characteristics of honeycombs. Based on the proposed solution method, the electromagnetic properties are obtained by employing the multi-scale homogenization theory and periodical electric (magnetic) potential boundary conditions. Further, the effect of geometry of honeycomb’s unit cell on effective electromagnetic properties is investigated with the use of the proposed method. The numerical results are compared with analytic results using the Smith-Scarpa’s semi-empirical formula.

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Multi-Scale Homogenization of Transversal Waves in Periodic Composite Beams

International Journal of Applied Mechanics ◽

10.1142/s1758825117500399 ◽

2017 ◽

Vol 09 (03) ◽

pp. 1750039 ◽

Cited By ~ 7

Author(s):

Xiangkun Sun ◽

Changwei Zhou ◽

Mohamed Ichchou ◽

Jean-Pierre Lainé ◽

Abdel-Malek Zine

Keyword(s):

Homogenization Method ◽

Homogenization Theory ◽

Flexural Wave ◽

Frequency Range ◽

Mean Values ◽

Multi Scale ◽

Finite Case ◽

Periodic Composite ◽

Asymptotic Homogenization Method ◽

Infinite Case

This paper deals with the deduction of new homogenized models for the flexural wave in bi-periodic beams. According to the homogenization theory, the long-wave assumption is used and the valid frequency range of homogenized models is limited to the first Bragg band gap. However, the classical homogenization method, whose idea is taking the component’s mean values as effective material properties, has limitations in mimicking the dispersive behavior and the real valid frequency range is far less than the limit. Thus, enriched homogenized models, derived by the multi-scale asymptotic homogenization method, are proposed to provide more accurate homogenization models with larger real valid frequency range. The new homogenized models are validated by investigating the dispersion relation in the infinite case and the frequency response function in the finite case. Wave finite element method (WFEM) are used to provide associated references. A parametric study is carried out in the infinite case while two different boundary conditions are considered in the finite case.

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COMPARING MORI-TANAKA METHOD AND FIRST-ORDER HOMOGENIZATION SCHEME IN THE VISCOELASTIC MODELING OF UNIDIRECTIONAL FIBROUS COMPOSITES

Acta Polytechnica CTU Proceedings ◽

10.14311/app.2020.26.0133 ◽

2020 ◽

Vol 26 ◽

pp. 133-138

Author(s):

Soňa Valentová ◽

Michal Šejnoha ◽

Jan Vorel

Keyword(s):

Viscoelastic Behavior ◽

Transversely Isotropic ◽

Homogenization Method ◽

Textile Composites ◽

Homogenization Theory ◽

Elastic Response ◽

Fibrous Composites ◽

Two Phase ◽

Multi Scale ◽

Viscoelastic Modeling

A comparative study of the viscous response of polymer matrix based fibrous composites predicted by the Mori-Tanaka method and finite element simulations based on the 1st order homogenization theory is presented. Aligned basalt and carbon fibers embedded into a polymeric matrix are considered to represent a quasi isotropic and transversely isotropic two-phase systems. While differences in the prediction of the macroscopic elastic response are attributed merely to the properties of the fiber phase, the viscoelastic behavior is largely affected by the selected homogenization method. A stiffer response predicted by the Mori-Tanaka method for both creep and relaxation tests is observed for both material systems and supports similar finding found in the literature. Thus suitable modifications of the original formulation of such two-point averaging schemes are needed for them to be applicable in the multi-scale modeling of generally anisotropic yarns in plane weave textile composites.

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On the Effective Mechanical Properties of Fluid-Saturated Composites: A Homogenization Approach

Materials Science Forum ◽

10.4028/www.scientific.net/msf.654-656.2273 ◽

2010 ◽

Vol 654-656 ◽

pp. 2273-2276

Author(s):

Lian Hua Ma ◽

Bernard F. Rolfe ◽

Qing Sheng Yang ◽

Chun Hui Yang

Keyword(s):

Mechanical Properties ◽

Effective Properties ◽

Micromechanical Model ◽

Fluid Pressure ◽

Fluid Phase ◽

Homogenization Theory ◽

Small Scale ◽

Multi Scale ◽

Homogenization Approach ◽

Effective Mechanical Properties

Composites containing saturated fluid are widely distributed in nature, such as saturated rocks, colloidal materials and biological cells. In the study to determine effective mechanical properties of fluid-saturated composites, a micromechanical model and a multi-scale homogenization-based model are developed. In the micromechanical model the internal fluid pressure is generated by applying eigenstrains in the domain of the fluid phase and the explicit expressions of effective bulk modulus and shear modulus are obtained. Meanwhile a multi-scale homogenization theory is employed to develop the homogenization-based model on determination of effective properties at the small scale in a unit cell level. Applying the two proposed approaches, the effects of the internal pressure of hydrostatic fluid on effective properties are further investigated.

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Multi-scale failure analysis of plain-woven composites

The Journal of Strain Analysis for Engineering Design ◽

10.1177/0309324712448301 ◽

2012 ◽

Vol 47 (6) ◽

pp. 379-388 ◽

Cited By ~ 14

Author(s):

Omar Bacarreza ◽

MH Aliabadi ◽

Alfonso Apicella

Keyword(s):

Damage Mechanics ◽

Effective Properties ◽

Progressive Failure ◽

Continuum Damage Mechanics ◽

Internal Variable ◽

Homogenization Method ◽

Woven Composites ◽

Computationally Efficient ◽

Efficient Manner ◽

Multi Scale

A numerical model capable of dealing with progressive degradation of plain woven composites in a computationally efficient manner is presented in this article. A semi-analytical homogenization method is used to derive effective properties of the composite from the material properties of the constituents. The progressive failure is described using nonlocal continuum damage mechanics where the driving internal variable for the damage is the nonlocal strain. The model was implemented into Abaqus/Explicit, where the failure of a longitudinal tension and an open hole tension specimens were simulated in a multi-scale manner and verified experimentally.

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The Design of Functional Gradient Materials with Inverse Homogenization Method

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.32.245 ◽

2008 ◽

Vol 32 ◽

pp. 245-250 ◽

Cited By ~ 1

Author(s):

Shi Wei Zhou ◽

Qing Li

Keyword(s):

Effective Properties ◽

Design Procedure ◽

Homogenization Method ◽

Homogenization Theory ◽

Layer By Layer ◽

Inverse Homogenization ◽

Gradient Materials ◽

Functional Gradient ◽

Effective Elasticity ◽

Elasticity Tensors

This study systemically presents an inverse homogenization method in the design of functional gradient materials, which gained substantial attention recently due to their layer-by-layer defined physical properties. Each layer of these materials is unilaterally constructed by periodically extended microstructural elements (namely base cells), whose effective properties can be decided by the homogenization theory in accordance with the material distribution within the base cell. The design objective is to minimize the summation of the least squares of the difference between corresponded entries in target and effective elasticity tensors. The method of moving asymptote drives the minimization of this positive objective function, which forces the effective values approach to the targets as closely as possible. The sensitivity of the effective elasticity tensors with respect to the design variables is derived from the adjoint variable method and it guides the minimization algorithm efficiently. To guarantee the connectivity between adjacent layers, non-design domains occupied by solid materials acting as connective bars are fixed in the design of base cells. Furthermore, nonlinear diffusion technique is introduced to avoid checkerboard patterns and blur boundaries in the microstructures. A series of two-dimensional examples targeted for the elasticity tensors with same extreme Poisson ratios but different densities in each layer are illustrated to highlight the computational material design procedure.

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