Consistent Hashin-Shtrikman Bounds on the Effective Properties of Periodic Composite Materials

1999 ◽  
Vol 66 (4) ◽  
pp. 858-866
Author(s):  
P. Bisegna ◽  
R. Luciano
Keyword(s):  
Composite Materials ◽  
Saddle Point ◽  
Variational Principles ◽  
Effective Properties ◽  
The Other ◽  
Constitutive Behavior ◽  
Homogenization Problem ◽  
Numerical Examples ◽  
Periodic Composites ◽  
Periodic Composite

In this paper the four classical Hashin-Shtrikman variational principles, applied to the homogenization problem for periodic composites with a nonlinear hyperelastic constitutive behavior, are analyzed. It is proved that two of them are indeed minimum principles while the other two are saddle point principles. As a consequence, every approximation of the former ones provide bounds on the effective properties of composite bodies, while approximations of the latter ones may supply inconsistent bounds, as it is shown by two numerical examples. Nevertheless, the approximations of the saddle point principles are expected to provide better estimates than the approximations of the minimum principles.

scholarly journals Transport of Temperature Fluctuations Across a Two-Phased Laminate Conductor

2020 ◽  
Vol 22 (3) ◽  
pp. 775-788
Author(s):  
Łukasz Wodzyński ◽  
Dorota Kula ◽  
Ewaryst Wierzbicki
Keyword(s):  
Heat Transfer ◽  
Composite Materials ◽  
Boundary Effect ◽  
Temperature Fluctuations ◽  
Periodic Composites ◽  
Periodic Composite ◽  
Oscillating Boundary ◽  
Tolerance Model

AbstractIn the periodic composite materials temperature or displacement fluctuations suppressed in directions perpendicular to the periodicity surfaces should expect a damping reaction from the composite. This phenomenon, known as the boundary effect behavior has been investigated only in the framework of approximated models. In this paper extended tolerance model of heat transfer in periodic composites is used as a tool allows analytical investigations of highly oscillating boundary thermal loadings. It has been shown that mentioned reaction is dual – different for even and odd fluctuations.

Two-Scale Algorithm of Simulating the Approximation for the Piezoelectric Problem in Small Periodic Composites

2016 ◽  
Vol 880 ◽  
pp. 90-94
Author(s):  
Ming Xiang Deng ◽  
Yong Ping Feng
Keyword(s):  
Finite Element ◽  
Piezoelectric Material ◽  
Numerical Algorithm ◽  
Asymptotic Method ◽  
Computational Algorithm ◽  
Numerical Examples ◽  
Periodic Composites ◽  
Periodic Composite ◽  
Small Periodic

The piezoelectric material plays an important role in some special fields. Based on two-scale asymptotic method, the two-scale finite element computational algorithm of simulating the piezoelectric problem in periodic composite is given, the finite element approximate errors are analyzed, and some numerical examples are presented so as to show the effectiveness of the numerical algorithm.

scholarly journals Macroscopic response of regular masonry from homogenization: comparison of isotropic and orthotropic damage models

2020 ◽  
Vol 310 ◽  
pp. 00052
Author(s):  
Tomáš Krejčí ◽  
Tomáš Koudelka ◽  
Vasco Bernardo ◽  
Michal Šejnoha
Keyword(s):  
Reinforced Concrete ◽  
Constitutive Model ◽  
Effective Properties ◽  
Damage Model ◽  
Masonry Structure ◽  
The Other ◽  
Homogenization Problem ◽  
Material Parameters ◽  
Damage Models ◽  
The One

This paper outlines prediction of macroscopic effective properties of a regular masonry from homogenization. It focuses on the derivation of nonlinear macroscopic stress strain curves adopting either classical isotropic or more advanced orthotropic damage model. The response resulting from both tensile and compressive uniaxial loading is examined in the light of strain and stress loading regimes. A masonry structure typical of ”Placa” buildings (mixed masonry- reinforced concrete buildings) built in Portugal is selected as one particular example to illustrate the differences in the predictive capabilities of the two constitute models on the one hand and the formulation of the homogenization problem on the other hand. It is suggested that the mixed loading conditions are essentially required when estimating all macroscopic material parameters needed in the corresponding macroscopic constitutive model

scholarly journals Effective properties of multiphase composites made of elastic materials with hierarchical structure

2015 ◽  
Vol 22 (4) ◽  
pp. 751-770 ◽  
Author(s):  
Dimitrios Tsalis ◽  
Nicolas Charalambakis ◽  
Kevin Bonnay ◽  
George Chatzigeorgiou
Keyword(s):  
Analytical Solution ◽  
Hierarchical Structure ◽  
Effective Properties ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Elastic Materials ◽  
Homogenization Problem ◽  
Numerical Examples ◽  
Multiphase Composites ◽  
Homogenization Scheme

In this paper, the analytical solution of the multi-step homogenization problem for multi-rank composites with generalized periodicity made of elastic materials is presented. The proposed homogenization scheme may be combined with computational homogenization for solving more complex microstructures. Three numerical examples are presented, concerning locally periodic stratified materials, matrices with wavy layers and wavy fiber-reinforced composites.

Hybrid polymer composite materials. Part 2. Preparation technology

2020 ◽  
pp. 8-13
Keyword(s):  
Composite Materials ◽  
Impact Toughness ◽  
Polymer Composites ◽  
The Other ◽  
Polymer Materials ◽  
Hybrid Polymer ◽  
Preparation Technology ◽  
Advantages And Disadvantages ◽  
Hybrid Polymer Composite ◽  
The One

The main methods (pressing and winding) of the processing of hybrid polymer composites to obtain items were examined. Advantages and disadvantages of the methods were noted. Good combinations of different-module fibers (carbon, glass, boron, organic) in hybrid polymer materials are described, which allow one to prepare materials with high compression strength on the one hand, and to increase fracture energy of samples and impact toughness on the other hand.

scholarly journals Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mohsen Alipour ◽  
Dumitru Baleanu ◽  
Fereshteh Babaei
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Convergence Analysis ◽  
Bernstein Polynomials ◽  
Linear Equations ◽  
The Other ◽  
New Combination ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Block Pulse Functions

We introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block-Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.

scholarly journals On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Sendren Sheng-Dong Xu ◽  
Chih-Chiang Chen
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Switched Systems ◽  
The Other ◽  
Linear Control ◽  
Linear Control Systems ◽  
Problem Statement ◽  
Theoretical Derivation ◽  
Control Laws ◽  
Numerical Examples

The equivalence of two conditions, condition (3) and condition (4) stated in Problem Statement section, regarding the existence of stabilizing switching laws between two unstable linear systems first appeared in (Feron 1996). Although Feron never published this result, it has been referenced in almost every survey on switched systems; see, for example, (Liberzon and Morse 1999). This paper proposes another way to prove the equivalence of two conditions regarding the existence of stabilizing switching laws between two unstable linear systems. One is effective for theoretical derivation, while the other is implementable, and a class of stabilizing switching laws have been explicitly constructed by Wicks et al. (1994). With the help of the equivalent relation, a condition for the existence of controllers and stabilizing switching laws between two unstabilizable linear control systems is then proposed. Then, the study is further extended to the issue concerning the construction of quadratically stabilizing switching laws among unstable linear systems and unstabilizable linear control systems. The obtained results are employed to study the existence of control laws and quadratically stabilizing switching laws within a class of unstabilizable linear control systems. The numerical examples are illustrated and simulated to show the feasibility and effectiveness of the proposed methods.

A Friendly Iterative Technique for Solving Nonlinear Integro-Differential and Systems of Nonlinear Integro-Differential Equations

2018 ◽  
Vol 15 (03) ◽  
pp. 1850016 ◽  
Author(s):  
A. A. Hemeda
Keyword(s):  
Approximate Solution ◽  
Differential Operator ◽  
Differential Equations ◽  
The Other ◽  
Iterative Technique ◽  
Restrictive Assumption ◽  
Numerical Examples ◽  
Linear And Nonlinear ◽  
Computational Procedures ◽  
Adomian’S Polynomials

In this work, a simple new iterative technique based on the integral operator, the inverse of the differential operator in the problem under consideration, is introduced to solve nonlinear integro-differential and systems of nonlinear integro-differential equations (IDEs). The introduced technique is simpler and shorter in its computational procedures and time than the other methods. In addition, it does not require discretization, linearization or any restrictive assumption of any form in providing analytical or approximate solution to linear and nonlinear equations. Also, this technique does not require calculating Adomian’s polynomials, Lagrange’s multiplier values or equating the terms of equal powers of the impeding parameter which need more computational procedures and time. These advantages make it reliable and its efficiency is demonstrated with numerical examples.

The Mechanical Performance Evaluation of a Mechanism with Curved Edge Driving Component

2013 ◽  
Vol 834-836 ◽  
pp. 1290-1294
Author(s):  
Xin Qin Liu
Keyword(s):  
Performance Evaluation ◽  
Fast Moving ◽  
Mechanical Performance ◽  
Gain Coefficient ◽  
The Other ◽  
Force Transmission ◽  
Transmission Performance ◽  
Connecting Rod ◽  
Numerical Examples ◽  
Straight Line

Mechanicalmethods were employed to study the motion and force transmission performance ofa kind of connecting rod slider mechanism with a curved edge driving component.The deduction methods and the computation formulae of the slider displacement,velocity, acceleration and the executive force gain coefficient were given.Considering two cases of the driving components with straight line edge andexponential function edge, the numerical examples was computed respectively,the results show that the former one is suitable for the force transmission andcan be used in the grip design and the other one is suitable for the motiontransmission which can be used in the fast moving mechanism

Elastic Fields in a Polygon-Shaped Inclusion With Uniform Eigenstrains

1997 ◽  
Vol 64 (3) ◽  
pp. 495-502 ◽  
Author(s):  
H. Nozaki ◽  
M. Taya
Keyword(s):  
Composite Materials ◽  
Closed Form ◽  
Strain Field ◽  
Strain Energy ◽  
Convex Polygon ◽  
Numerical Examples ◽  
Elastic Fields ◽  
Closed Form Solutions ◽  
Arbitrary Convex ◽  
Shaped Inclusion

In this paper the elastic fields in an arbitrary, convex polygon-shaped inclusion with uniform eigenstrains are investigated under the condition of plane strain. Closed-form solutions are obtained for the elastic fields in a polygon-shaped inclusion. The applications to the evaluation of the effective elastic properties of composite materials with polygon-shaped reinforcements are also investigated for both dilute and dense systems. Numerical examples are presented for the strain field, strain energy, and stiffness of the composites with polygon shaped fibers. The results are also compared with some existing solutions.

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