The Design of Functional Gradient Materials with Inverse Homogenization Method

2008 ◽  
Vol 32 ◽  
pp. 245-250 ◽  
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.

Characterization of Interphase/Interface Parameters of Unidirectional Fibrous Composites by Optimization-Based Inverse Homogenization

2019 ◽  
Vol 11 (08) ◽  
pp. 1950074 ◽  
Author(s):  
Guannan Wang ◽  
Wenqiong Tu ◽  
Qiang Chen
Keyword(s):  
Effective Properties ◽  
Free Particle ◽  
Homogenization Theory ◽  
Fibrous Composites ◽  
Stress Concentrations ◽  
Inverse Homogenization ◽  
Surrounding Matrix ◽  
Interphase Interface ◽  
Micromechanical Models ◽  
Interface Parameters

Optimization-based micromechanical and inverse-homogenization models are developed to inversely calculate the interphase/interface properties of unidirectional periodic fibrous composites from prescribed effective properties or localized stress concentrations. The interphase/interface effects between fibers and the surrounding matrix are described by four different mathematical models that are reviewed in the present work. In order to guarantee the stability of the characterization process, two sophisticated micromechanical models, locally exact homogenization theory and finite-volume direct averaging micromechanics, are introduced in this work and connected to the gradient-free particle swarm optimization to search for the optimal parameters to minimize the cost/objective functions that consider the homogenized or localized responses of unidirectional composites. The accuracy and efficiency of the proposed procedure are tested by substituting the optimized parameters back into the direct micromechanical models and validating against the target functions, where good agreement is always obtained. More importantly, the numerical effects generated by those parameters are also tested on the effective properties and localized stress distributions of fibrous composites.

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

2010 ◽  
Vol 443 ◽  
pp. 551-556
Author(s):  
Lian Hua Ma ◽  
Bernard F. Rolfe ◽  
Qing Sheng Yang ◽  
Chun Hui Yang
Keyword(s):  
Boundary Conditions ◽  
Empirical Formula ◽  
Solution Method ◽  
Effective Properties ◽  
Homogenization Method ◽  
Homogenization Theory ◽  
Electromagnetic Properties ◽  
Multi Scale ◽  
Electromagnetic Characteristics ◽  
Semi Empirical

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.

scholarly journals Multiscale seismic imaging with inverse homogenization

2021 ◽  
Author(s):  
N Hedjazian ◽  
Y Capdeville ◽  
T Bodin
Keyword(s):  
Seismic Imaging ◽  
Effective Properties ◽  
Waveform Inversion ◽  
Homogenization Theory ◽  
Small Scale ◽  
Full Waveform Inversion ◽  
Inverse Homogenization ◽  
Long Wavelength ◽  
Full Waveform ◽  
Scale Models

Summary Seismic imaging techniques such as elastic full waveform inversion (FWI) have their spatial resolution limited by the maximum frequency present in the observed waveforms. Scales smaller than a fraction of the minimum wavelength cannot be resolved, and only a smoothed, effective version of the true underlying medium can be recovered. These finite-frequency effects are revealed by the upscaling or homogenization theory of wave propagation. Homogenization aims at computing larger scale effective properties of a medium containing small-scale heterogeneities. We study how this theory can be used in the context of FWI. The seismic imaging problem is broken down in a two-stage multiscale approach. In the first step, called homogenized full waveform inversion (HFWI), observed waveforms are inverted for a smooth, fully anisotropic effective medium, that does not contain scales smaller than the shortest wavelength present in the wavefield. The solution being an effective medium, it is difficult to directly interpret it. It requires a second step, called downscaling or inverse homogenization, where the smooth image is used as data, and the goal is to recover small-scale parameters. All the information contained in the observed waveforms is extracted in the HFWI step. The solution of the downscaling step is highly non-unique as many small-scale models may share the same long wavelength effective properties. We therefore rely on the introduction of external a priori information, and cast the problem in a Bayesian formulation. The ensemble of potential fine-scale models sharing the same long wavelength effective properties is explored with a Markov chain Monte Carlo algorithm. We illustrate the method with a synthetic cavity detection problem: we search for the position, size and shape of void inclusions in a homogeneous elastic medium, where the size of cavities is smaller than the resolving length of the seismic data. We illustrate the advantages of introducing the homogenization theory at both stages. In HFWI, homogenization acts as a natural regularization helping convergence toward meaningful solution models. Working with fully anisotropic effective media prevents the leakage of anisotropy induced by the fine scales into isotropic macro-parameters estimates. In the downscaling step, the forward theory is the homogenization itself. It is computationally cheap, allowing us to consider geological models with more complexity (e.g. including discontinuities) and use stochastic inversion techniques.

scholarly journals A New Estimate for the Homogenization Method for Second-Order Elliptic Problem with Rapidly Oscillating Periodic Coefficients

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Xiong Liu ◽  
Wenming He
Keyword(s):  
Elliptic Problem ◽  
Homogenization Method ◽  
Second Order ◽  
Homogenization Theory ◽  
High Demand ◽  
Periodic Coefficients ◽  
Order Elliptic Problem ◽  
Multiscale Homogenization

In this paper, we will investigate a multiscale homogenization theory for a second-order elliptic problem with rapidly oscillating periodic coefficients of the form ∂ / ∂ x i a i j x / ε , x ∂ u ε x / ∂ x j = f x . Noticing the fact that the classic homogenization theory presented by Oleinik has a high demand for the smoothness of the homogenization solution u 0 , we present a new estimate for the homogenization method under the weaker smoothness that homogenization solution u 0 satisfies than the classical homogenization theory needs.

Homogenization Techniques and Micromechanics. A Survey and Perspectives

2010 ◽  
Vol 63 (3) ◽  
Author(s):  
Nicolas Charalambakis
Keyword(s):  
Effective Properties ◽  
Nonlinear Problems ◽  
Homogenization Theory ◽  
Computational Techniques ◽  
Complex Structures ◽  
Critical Survey ◽  
Layered Composites ◽  
Properties Of Materials ◽  
Dynamical Properties

In this paper, we present a critical survey on homogenization theory and related techniques applied to micromechanics. The validation of homogenization results, the characterization of composite materials and the optimal design of complex structures are issues of great technological importance and are viewed here as a combination of mathematical and mechanical homogenization. The mathematical tools for modeling sequentially layered composites are explained. The influence of initial and boundary conditions on the effective properties in nonlinear problems is clarified and the notion of stability by homogenization is analyzed. Multiscale micromechanics methods are outlined and the classical as well as the emerging analytical and computational techniques are presented. Computation of effective static and dynamical properties of materials with linear or nonlinear constitutive equations is closely related to the development of generalized theories such as the strain-gradient mechanics. Selected applications of these techniques are outlined. Moreover, the extension of kinetic techniques in homogenization and the related inverse imaging problem are presented.

scholarly journals Alginate Nanoformulation: Influence of Process and Selected Variables

2020 ◽  
Vol 13 (11) ◽  
pp. 335
Author(s):  
Hazem Choukaife ◽  
Abd Almonem Doolaanea ◽  
Mulham Alfatama
Keyword(s):  
Drug Delivery ◽  
Biomedical Applications ◽  
Effective Properties ◽  
Matrix Material ◽  
Cost Effective ◽  
Biological Properties ◽  
Layer By Layer ◽  
Therapeutic Outcomes ◽  
Manufacturing Techniques ◽  
Formulation Parameters

Nanocarriers are defined as structures and devices that are constructed using nanomaterials which add functionality to the encapsulants. Being small in size and having a customized surface, improved solubility and multi-functionality, it is envisaged that nanoparticles will continue to create new biomedical applications owing to their stability, solubility, and bioavailability, as well as controlled release of drugs. The type and physiochemical as well as morphological attributes of nanoparticles influence their interaction with living cells and determine the route of administration, clearance, as well as related toxic effects. Over the past decades, biodegradable polymers such as polysaccharides have drowned a great deal of attention in pharmaceutical industry with respect to designing of drug delivery systems. On this note, biodegradable polymeric nanocarrier is deemed to control the release of the drug, stabilize labile molecules from degradation and site-specific drug targeting, with the main aim of reducing the dosing frequency and prolonging the therapeutic outcomes. Thus, it is essential to select the appropriate biopolymer material, e.g., sodium alginate to formulate nanoparticles for controlled drug delivery. Alginate has attracted considerable interest in pharmaceutical and biomedical applications as a matrix material of nanocarriers due to its inherent biological properties, including good biocompatibility and biodegradability. Various techniques have been adopted to synthesize alginate nanoparticles in order to introduce more rational, coherent, efficient and cost-effective properties. This review highlights the most used and recent manufacturing techniques of alginate-based nanoparticulate delivery system, including emulsification/gelation complexation, layer-by-layer, spray drying, electrospray and electrospinning methods. Besides, the effects of the main processing and formulation parameters on alginate nanoparticles are also summarized.

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