scholarly journals REDUCTION OF THE RESONANCE ERROR — PART 1: APPROXIMATION OF HOMOGENIZED COEFFICIENTS

2011 ◽  
Vol 21 (08) ◽  
pp. 1601-1630 ◽  
Author(s):  
ANTOINE GLORIA
Keyword(s):  
Elliptic Equations ◽  
Length Scale ◽  
Numerical Homogenization ◽  
Cell Problem ◽  
Typical Size ◽  
Effective Coefficients ◽  
Homogenization Methods

This paper is concerned with the approximation of effective coefficients in homogenization of linear elliptic equations. One common drawback among numerical homogenization methods is the presence of the so-called resonance error, which roughly speaking is a function of the ratio ε/η, where η is a typical macroscopic length scale and ε is the typical size of the heterogeneities. In the present work, we propose an alternative for the computation of homogenized coefficients (or more generally a modified cell-problem), which is a first brick in the design of effective numerical homogenization methods. We show that this approach drastically reduces the resonance error in some standard cases.

MULTISCALE CONTINUOUS AND DISCONTINUOUS MODELING OF HETEROGENEOUS MATERIALS: A REVIEW ON RECENT DEVELOPMENTS

2011 ◽  
Vol 03 (04) ◽  
pp. 229-270 ◽  
Author(s):  
VINH PHU NGUYEN ◽  
MARTIJN STROEVEN ◽  
LAMBERTUS JOHANNES SLUYS
Keyword(s):  
Strain Localization ◽  
Computational Cost ◽  
Heterogeneous Materials ◽  
Computational Homogenization ◽  
Cohesive Crack ◽  
Multiscale Simulations ◽  
Numerical Homogenization ◽  
Recent Developments ◽  
Computational Aspects ◽  
Homogenization Methods

This paper reviews the recent developments in the field of multiscale modelling of heterogeneous materials with emphasis on homogenization methods and strain localization problems. Among other topics, the following are discussed (i) numerical homogenization or unit cell methods, (ii) continuous computational homogenization for bulk modelling, (iii) discontinuous computational homogenization for adhesive/cohesive crack modelling and (iv) continuous-discontinuous computational homogenization for cohesive failures. Different boundary conditions imposed on representative volume elements are described. Computational aspects concerning robustness and computational cost of multiscale simulations are presented.

Asymptotic and numerical homogenization methods applied to fibrous viscoelastic composites using Prony’s series

2020 ◽  
Vol 231 (7) ◽  
pp. 2761-2771 ◽  
Author(s):  
J. A. Otero ◽  
R. Rodríguez-Ramos ◽  
R. Guinovart-Díaz ◽  
O. L. Cruz-González ◽  
F. J. Sabina ◽  
...  
Keyword(s):  
Numerical Homogenization ◽  
Homogenization Methods ◽  
Viscoelastic Composites

scholarly journals Introduction to Macroscopic Optimal Design in the Mechanics of Composite Materials and Structures

2021 ◽  
Vol 5 (2) ◽  
pp. 36
Author(s):  
Aleksander Muc
Keyword(s):  
Composite Materials ◽  
Composite Structures ◽  
Constitutive Relations ◽  
A Priori ◽  
Chemical Properties ◽  
Composite Plates ◽  
Failure Criteria ◽  
Lagrange Equations ◽  
Homogenization Methods ◽  
Mechanics Of Composite Materials

The main goal of building composite materials and structures is to provide appropriate a priori controlled physico-chemical properties. For this purpose, a strengthening is introduced that can bear loads higher than those borne by isotropic materials, improve creep resistance, etc. Composite materials can be designed in a different fashion to meet specific properties requirements.Nevertheless, it is necessary to be careful about the orientation, placement and sizes of different types of reinforcement. These issues should be solved by optimization, which, however, requires the construction of appropriate models. In the present paper we intend to discuss formulations of kinematic and constitutive relations and the possible application of homogenization methods. Then, 2D relations for multilayered composite plates and cylindrical shells are derived with the use of the Euler–Lagrange equations, through the application of the symbolic package Mathematica. The introduced form of the First-Ply-Failure criteria demonstrates the non-uniqueness in solutions and complications in searching for the global macroscopic optimal solutions. The information presented to readers is enriched by adding selected review papers, surveys and monographs in the area of composite structures.

scholarly journals Numerical Homogenization of Multi-Layered Corrugated Cardboard with Creasing or Perforation

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3786
Author(s):  
Tomasz Garbowski ◽  
Anna Knitter-Piątkowska ◽  
Damian Mrówczyński
Keyword(s):  
Computational Models ◽  
Load Capacity ◽  
Torsional Stiffness ◽  
Numerical Homogenization ◽  
Corrugated Board ◽  
3D Geometry ◽  
Corrugated Cardboard ◽  
Numerical Tools ◽  
Packaging Industry ◽  
Theoretical Considerations

The corrugated board packaging industry is increasingly using advanced numerical tools to design and estimate the load capacity of its products. This is why numerical analyses are becoming a common standard in this branch of manufacturing. Such trends cause either the use of advanced computational models that take into account the full 3D geometry of the flat and wavy layers of corrugated board, or the use of homogenization techniques to simplify the numerical model. The article presents theoretical considerations that extend the numerical homogenization technique already presented in our previous work. The proposed here homogenization procedure also takes into account the creasing and/or perforation of corrugated board (i.e., processes that undoubtedly weaken the stiffness and strength of the corrugated board locally). However, it is not always easy to estimate how exactly these processes affect the bending or torsional stiffness. What is known for sure is that the degradation of stiffness depends, among other things, on the type of cut, its shape, the depth of creasing as well as their position or direction in relation to the corrugation direction. The method proposed here can be successfully applied to model smeared degradation in a finite element or to define degraded interface stiffnesses on a crease line or a perforation line.

scholarly journals Permeability of Sand-Clay Mixtures

2010 ◽  
Vol 56 (4) ◽  
pp. 299-320 ◽  
Author(s):  
G. Kacprzak ◽  
C. Boutin ◽  
T. Doanh
Keyword(s):  
Experimental Data ◽  
Actual State ◽  
Load Step ◽  
Qualitative And Quantitative ◽  
Experimental Data Point ◽  
Saturated Clay ◽  
Simplifying Assumptions ◽  
Data Point ◽  
Homogenization Methods

Abstract This study deals with the behavior of composite blends constituted of rigid and impervious grains included in saturated clay paste of kaolin, considered as permeable and deformable. Permeability tests performed during standard oedometr tests (before each load step) highlight the key role of the original and actual state of the clay paste, and show the existence of a threshold of sand grain concentration above which a structuring effect influences its permeability. In the light of these experiments some usual homogenization methods (with simplifying assumptions to make the problem manageable) are considered in order to model the mixture permeability. Qualitative and quantitative comparisons with experimental data point out their respective domain of interest and limitations of such approaches

scholarly journals Evaluation of homogenization methods for seasonal snow depth data in the Austrian Alps, 1930–2010

2019 ◽  
Vol 39 (11) ◽  
pp. 4514-4530 ◽  
Author(s):  
Giorgia Marcolini ◽  
Roland Koch ◽  
Barbara Chimani ◽  
Wolfgang Schöner ◽  
Alberto Bellin ◽  
...  
Keyword(s):  
Snow Depth ◽  
Depth Data ◽  
Seasonal Snow ◽  
Austrian Alps ◽  
Homogenization Methods
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