Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 9

Homogenization Related Abstracts

9 Homogenization of a Non-Linear Problem with a Thermal Barrier

Authors: Hassan Samadi, Mustapha El Jarroudi


In this work, we consider the homogenization of a non-linear problem in periodic medium with two periodic connected media exchanging a heat flux throughout their common interface. The interfacial exchange coefficient λ is assumed to tend to zero or to infinity following a rate λ=λ(ε) when the size ε of the basic cell tends to zero. Three homogenized problems are determined according to some critical value depending of λ and ε. Our method is based on Γ-Convergence techniques.

Keywords: Variational Methods, Homogenization, epiconvergence, convergence technique

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8 Numerical Homogenization of Nacre

Authors: M. Arunachalam, M. Pandey


Nacre, a biological material that forms the inner-layer of sea shells can achieve high toughness and strength by way of staggered arrangement of strong tablets with soft and weak organic interface. Under applied loads the tablets slide over the adjacent tablets, thus generating inelastic deformation and toughness on macroscopic scale. A two dimensional finite element based homogenization methodology is adopted for obtaining the effective material properties of Nacre using a representative volume element (RVE) at finite deformations. In this work, the material behaviour for tablet and interface are assumed to be Isotropic elastic and Isotropic elastic-perfectly plastic with strain softening respectively. Numerical experiments such as uniaxial tension test along X, Y directions and simple shear test are performed on the RVE with uniform displacement and periodic constraints applied at the RVE boundaries to obtain the anisotropic homogenized response and maximum local stresses within each constituents of Nacre. Homogenized material model is then tested for macroscopic structure under three point bending condition and the results obtained are comparable with the results obtained for detailed microstructure based structure, thus homogenization provides a bridge between macroscopic scale and microscopic scale and homogenized material properties obtained from microstructural (RVE) analysis could be used in large scale structural analysis.

Keywords: Homogenization, finite element, staggered arrangement, inelastic deformation

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7 A Novel Geometrical Approach toward the Mechanical Properties of Particle Reinforced Composites

Authors: Hamed Khezrzadeh


Many investigations on the micromechanical structure of materials indicate that there exist fractal patterns at the micro scale in some of the main construction and industrial materials. A recently presented micro-fractal theory brings together the well-known periodic homogenization and the fractal geometry to construct an appropriate model for determination of the mechanical properties of particle reinforced composite materials. The proposed multi-step homogenization scheme considers the mechanical properties of different constituent phases in the composite together with the interaction between these phases throughout a step-by-step homogenization technique. In the proposed model the interaction of different phases is also investigated. By using this method the effect of fibers grading on the mechanical properties also could be studied. The theory outcomes are compared to the experimental data for different types of particle-reinforced composites which very good agreement with the experimental data is observed.

Keywords: Fractal geometry, Homogenization, micromehcanics, particulate composites

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6 Limit State of Heterogeneous Smart Structures under Unknown Cyclic Loading

Authors: X. Wang, M. Chen, S-Q. Zhang, D. Tate


This paper presents a numerical solution, namely limit and shakedown analysis, to predict the safety state of smart structures made of heterogeneous materials under unknown cyclic loadings, for instance, the flexure hinge in the micro-positioning stage driven by piezoelectric actuator. In combination of homogenization theory and finite-element method (FEM), the safety evaluation problem is converted to a large-scale nonlinear optimization programming for an acceptable bounded loading as the design reference. Furthermore, a general numerical scheme integrated with the FEM and interior-point-algorithm based optimization tool is developed, which makes the practical application possible.

Keywords: Homogenization, limit state, shakedown analysis, heterogeneous structure

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5 A Numerical Study on Micromechanical Aspects in Short Fiber Composites

Authors: I. Ioannou, I. M. Gitman


This study focused on the contribution of micro-mechanical parameters on the macro-mechanical response of short fiber composites, namely polypropylene matrix reinforced by glass fibers. In the framework of this paper, an attention has been given to the glass fibers length, as micromechanical parameter influences the overall macroscopic material’s behavior. Three dimensional numerical models were developed and analyzed through the concept of a Representative Volume Element (RVE). Results of the RVE-based approach were compared with analytical Halpin-Tsai’s model.

Keywords: Homogenization, representative volume element, effective properties, short fiber reinforced composites

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4 Processing Methods for Increasing the Yield, Nutritional Value and Stability of Coconut Milk

Authors: Archana G. Lamdande, Shyam R. Garud, K. S. M. S. Raghavarao


Coconut has two edible parts, that is, a white kernel (solid endosperm) and coconut water (liquid endosperm). The white kernel is generally used in fresh or dried form for culinary purposes. Coconut testa, is the brown skin, covering the coconut kernel. It is removed by paring of wet coconut and obtained as a by-product in coconut processing industries during the production of products such as desiccated coconut, coconut milk, whole coconut milk powder and virgin coconut oil. At present, it is used as animal feed component after drying and recovering the residual oil (by expelling). Experiments were carried out on expelling of coconut milk for shredded coconut with and without testa removal, in order to explore the possibility of increasing the milk yield and value addition in terms of increased polyphenol content. The color characteristics of coconut milk obtained from the grating without removal of testa were observed to be L* 82.79, a* 0.0125, b* 6.245, while that obtained from grating with removal of testa were L* 83.24, a* -0.7925, b* 3.1. A significant increase was observed in total phenol content of coconut milk obtained from the grating with testa (833.8 µl/ml) when compared to that from without testa (521.3 µl/ml). However, significant difference was not observed in protein content of coconut milk obtained from the grating with and without testa (4.9 and 5.0% w/w, respectively). Coconut milk obtained from grating without removal of testa showed higher milk yield (62% w/w) when compared to that obtained from grating with removal of testa (60% w/w). The fat content in coconut milk was observed to be 32% (w/w), and it is unstable due to such a high fat content. Therefore, several experiments were carried out for examining its stability by adjusting the fat content at different levels (32, 28, 24, and 20% w/w). It was found that the coconut milk was more stable with a fat content of 24 % (w/w). Homogenization and ultrasonication and their combinations were used for exploring the possibility of increasing the stability of coconut milk. The microscopic study was carried out for analyzing the size of fat globules and the degree of their uniform distribution.

Keywords: Stability, Homogenization, ultrasonication, coconut milk, testa

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3 Characterization of Thin Woven Composites Used in Printed Circuit Boards by Combining Numerical and Experimental Approaches

Authors: Sébastien Mercier, Gautier Girard, Marion Martiny, Mohamad Jrad, Mohamed-Slim Bahi, Laurent Bodin, Francois Lechleiter, David Nevo, Sophie Dareys


Reliability of electronic devices has always been of highest interest for Aero-MIL and space applications. In any electronic device, Printed Circuit Board (PCB), providing interconnection between components, is a key for reliability. During the last decades, PCB technologies evolved to sustain and/or fulfill increased original equipment manufacturers requirements and specifications, higher densities and better performances, faster time to market and longer lifetime, newer material and mixed buildups. From the very beginning of the PCB industry up to recently, qualification, experiments and trials, and errors were the most popular methods to assess system (PCB) reliability. Nowadays OEM, PCB manufacturers and scientists are working together in a close relationship in order to develop predictive models for PCB reliability and lifetime. To achieve that goal, it is fundamental to characterize precisely base materials (laminates, electrolytic copper, …), in order to understand failure mechanisms and simulate PCB aging under environmental constraints by means of finite element method for example. The laminates are woven composites and have thus an orthotropic behaviour. The in-plane properties can be measured by combining classical uniaxial testing and digital image correlation. Nevertheless, the out-of-plane properties cannot be evaluated due to the thickness of the laminate (a few hundred of microns). It has to be noted that the knowledge of the out-of-plane properties is fundamental to investigate the lifetime of high density printed circuit boards. A homogenization method combining analytical and numerical approaches has been developed in order to obtain the complete elastic orthotropic behaviour of a woven composite from its precise 3D internal structure and its experimentally measured in-plane elastic properties. Since the mechanical properties of the resin surrounding the fibres are unknown, an inverse method is proposed to estimate it. The methodology has been applied to one laminate used in hyperfrequency spatial applications in order to get its elastic orthotropic behaviour at different temperatures in the range [-55°C; +125°C]. Next; numerical simulations of a plated through hole in a double sided PCB are performed. Results show the major importance of the out-of-plane properties and the temperature dependency of these properties on the lifetime of a printed circuit board. Acknowledgements—The support of the French ANR agency through the Labcom program ANR-14-LAB7-0003-01, support of CNES, Thales Alenia Space and Cimulec is acknowledged.

Keywords: Homogenization, printed circuit board, orthotropic behaviour, woven composites

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2 Micromechanical Modeling of Fiber-Matrix Debonding in Unidirectional Composites

Authors: M. Palizvan, M. T. Abadi, M. H. Sadr


Due to variations in damage mechanisms in the microscale, the behavior of fiber-reinforced composites is nonlinear and difficult to model. To make use of computational advantages, homogenization method is applied to the micro-scale model in order to minimize the cost at the expense of detail of local microscale phenomena. In this paper, the effective stiffness is calculated using the homogenization of nonlinear behavior of a composite representative volume element (RVE) containing fiber-matrix debonding. The damage modes for the RVE are considered by using cohesive elements and contacts for the cohesive behavior of the interface between fiber and matrix. To predict more realistic responses of composite materials, different random distributions of fibers are proposed besides square and hexagonal arrays. It was shown that in some cases, there is quite different damage behavior in different fiber distributions. A comprehensive comparison has been made between different graphs.

Keywords: Homogenization, cohesive zone model, fiber-matrix debonding, RVE

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1 A Numerical Method to Evaluate the Elastoplastic Material Properties of Fiber Reinforced Composite

Authors: M. Palizvan, M. T. Abadi, M. H. Sadr


The representative volume element (RVE) plays a central role in the mechanics of random heterogeneous materials with a view to predicting their effective properties. In this paper, a computational homogenization methodology, developed to determine effective linear elastic properties of composite materials, is extended to predict the effective nonlinear elastoplastic response of long fiber reinforced composite. Finite element simulations of volumes of different sizes and fiber volume fractures are performed for calculation of the overall response RVE. The dependencies of the overall stress-strain curves on the number of fibers inside the RVE are studied in the 2D cases. Volume averaged stress-strain responses are generated from RVEs and compared with the finite element calculations available in the literature at moderate and high fiber volume fractions. For these materials, the existence of an RVE is demonstrated for the sizes of RVE corresponding to 10–100 times the diameter of the fibers. In addition, the response of small size RVE is found anisotropic, whereas the average of all large ones leads to recover the isotropic material properties.

Keywords: Homogenization, RVE, periodic boundary condition, elastoplastic properties

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