scholarly journals A Generalized Strain Energy-Based Homogenization Method for 2-D and 3-D Cellular Materials with and without Periodicity Constraints

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1870
Author(s):  
Ahmad I. Gad ◽  
Xin-Lin Gao
Keyword(s):  
Strain Energy ◽  
Homogenization Method ◽  
Cellular Materials ◽  
Cellular Material ◽  
Equilibrium Equations ◽  
New Approach ◽  
Cubic Symmetry ◽  
Representative Cell ◽  
The Matrix ◽  
Hill’S Lemma

A generalized strain energy-based homogenization method for 2-D and 3-D cellular materials with and without periodicity constraints is proposed using Hill’s Lemma and the matrix method for spatial frames. In this new approach, the equilibrium equations are enforced at all boundary and interior nodes and each interior node is allowed to translate and rotate freely, which differ from existing methods where the equilibrium conditions are imposed only at the boundary nodes. The newly formulated homogenization method can be applied to cellular materials with or without symmetry. To illustrate the new method, four examples are studied: two for a 2-D cellular material and two for a 3-D pentamode metamaterial, with and without periodic constraints in each group. For the 2-D cellular material, an asymmetric microstructure with or without periodicity constraints is analyzed, and closed-form expressions of the effective stiffness components are obtained in both cases. For the 3-D pentamode metamaterial, a primitive diamond-shaped unit cell with or without periodicity constraints is considered. In each of these 3-D cases, two different representative cells in two orientations are examined. The homogenization analysis reveals that the pentamode metamaterial exhibits the cubic symmetry based on one representative cell, with the effective Poisson’s ratio v¯ being nearly 0.5. Moreover, it is revealed that the pentamode metamaterial with the cubic symmetry can be tailored to be a rubber-like material (with v¯ ≅0.5) or an auxetic material (with v¯< 0).

Design of Frame-Like Periodic Solids for Isotropic Symmetry by Member Sizing

2016 ◽  
Vol 33 (1) ◽  
pp. 41-54 ◽  
Author(s):  
K. Theerakittayakorn ◽  
P. Suttakul ◽  
P. Sam ◽  
P. Nanakorn
Keyword(s):  
Closed Form ◽  
Elastic Constants ◽  
Strain Energy ◽  
Equivalent Strain ◽  
Homogenization Method ◽  
Unit Cell ◽  
Cubic Symmetry ◽  
Effective Elastic Constants ◽  
Common Unit ◽  
2D And 3D

AbstractIn this study, a methodology to design frame-like periodic solids for isotropic symmetry by appropriate sizing of unit-cell struts is presented. The methodology utilizes the closed-form effective elastic constants of 2D frame-like periodic solids with square symmetry and 3D frame-like periodic solids with cubic symmetry, derived using the homogenization method based on equivalent strain energy. By using the closed-form effective elastic constants, an equation to enforce isotropic symmetry can be analytically constructed. Thereafter, the equation can be used to determine relative unit-cell strut sizes that are required for isotropic symmetry. The methodology is tested with 2D and 3D frame-like periodic solids with some common unit-cell topologies. Satisfactory results are observed.

scholarly journals On the Modular Operator of Mutli-component Regions in Chiral CFT

2021 ◽  
Author(s):  
Stefan Hollands
Keyword(s):  
Field Theory ◽  
Integral Equation ◽  
Hilbert Problem ◽  
Matrix Elements ◽  
New Approach ◽  
Conformal Field ◽  
The Matrix ◽  
Kms Condition ◽  
Modular Operator ◽  
Riemann Hilbert Problem

AbstractWe introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.

Effect of temperature on matrix multicracking evolution of C/SiC fiber-reinforced ceramic-matrix composites

2020 ◽  
Vol 39 (1) ◽  
pp. 189-199
Author(s):  
Longbiao Li
Keyword(s):  
Strain Energy ◽  
Ceramic Matrix Composites ◽  
Critical Value ◽  
Matrix Cracking ◽  
Interface Debonding ◽  
Matrix Composites ◽  
Temperature Dependent ◽  
Damage State ◽  
The Matrix ◽  
Sic Composites

AbstractIn this paper, the temperature-dependent matrix multicracking evolution of carbon-fiber-reinforced silicon carbide ceramic-matrix composites (C/SiC CMCs) is investigated. The temperature-dependent composite microstress field is obtained by combining the shear-lag model and temperature-dependent material properties and damage models. The critical matrix strain energy criterion assumes that the strain energy in the matrix has a critical value. With increasing applied stress, when the matrix strain energy is higher than the critical value, more matrix cracks and interface debonding occur to dissipate the additional energy. Based on the composite damage state, the temperature-dependent matrix strain energy and its critical value are obtained. The relationships among applied stress, matrix cracking state, interface damage state, and environmental temperature are established. The effects of interfacial properties, material properties, and environmental temperature on temperature-dependent matrix multiple fracture evolution of C/SiC composites are analyzed. The experimental evolution of matrix multiple fracture and fraction of the interface debonding of C/SiC composites at elevated temperatures are predicted. When the interface shear stress increases, the debonding resistance at the interface increases, leading to the decrease of the debonding fraction at the interface, and the stress transfer capacity between the fiber and the matrix increases, leading to the higher first matrix cracking stress, saturation matrix cracking stress, and saturation matrix cracking density.

scholarly journals The Influence of Filler Size and Crosslinking Degree of Polymers on Mullins Effect in Filled NR/BR Composites

Polymers ◽  
2021 ◽  
Vol 13 (14) ◽  
pp. 2284
Author(s):  
Miaomiao Qian ◽  
Bo Zou ◽  
Zhixiao Chen ◽  
Weimin Huang ◽  
Xiaofeng Wang ◽  
...  
Keyword(s):  
Particle Size ◽  
Strain Energy ◽  
Mathematical Expression ◽  
Rubber Matrix ◽  
Mullins Effect ◽  
Butadiene Rubber ◽  
Crosslinking Degree ◽  
Test Range ◽  
Two Factors ◽  
The Matrix

Two factors, the crosslinking degree of the matrix (ν) and the size of the filler (Sz), have significant impact on the Mullins effect of filled elastomers. Herein, the result. of the two factors on Mullins effect is systematically investigated by adjusting the crosslinking degree of the matrix via adding maleic anhydride into a rubber matrix and controlling the particle size of the filler via ball milling. The dissipation ratios (the ratio of energy dissipation to input strain energy) of different filled natural rubber/butadiene rubber (NR/BR) elastomer composites are evaluated as a function of the maximum strain in cyclic loading (εm). The dissipation ratios show a linear relationship with the increase of εm within the test range, and they depend on the composite composition (ν and Sz). With the increase of ν, the dissipation ratios decrease with similar slope, and this is compared with the dissipation ratios increase which more steeply with the increase in Sz. This is further confirmed through a simulation that composites with larger particle size show a higher strain energy density when the strain level increases from 25% to 35%. The characteristic dependence of the dissipation ratios on ν and Sz is expected to reflect the Mullins effect with mathematical expression to improve engineering performance or prevent failure of rubber products.

scholarly journals Development of High-Performance SiCp/Al-Si Composites by Equal Channel Angular Pressing

Metals ◽  
2018 ◽  
Vol 8 (10) ◽  
pp. 738 ◽  
Author(s):  
Qiong Xu ◽  
Aibin Ma ◽  
Junjie Wang ◽  
Jiapeng Sun ◽  
Jinghua Jiang ◽  
...  
Keyword(s):  
Wear Resistance ◽  
Equal Channel Angular Pressing ◽  
High Performance ◽  
Adhesive Wear ◽  
Processing Route ◽  
Matrix Composites ◽  
New Approach ◽  
Angular Pressing ◽  
The Matrix ◽  
Industry Applications

Relatively low compactness and unsatisfactory uniformity of reinforced particles severely restrict the performance and widespread industry applications of the powder metallurgy (PM) metal matrix composites (MMCs). Here, we developed a combined processing route of PM and equal channel angular pressing (ECAP) to enhance the mechanical properties and wear resistance of the SiCp/Al-Si composite. The results indicate that ECAP significantly refined the matrix grains, eliminated pores and promoted the uniformity of the reinforcement particles. After 8p-ECAP, the SiCp/Al-Si composite consisted of ultrafine Al matrix grains (600 nm) modified by uniformly-dispersed Si and SiCp particles, and the composite relative density approached 100%. The hardness and wear resistance of the 8p-ECAP SiCp/Al-Si composite were markedly improved compared to the PM composite. More ECAP passes continued a trend of improvement for the wear resistance and hardness. Moreover, while abrasion and delamination dominated the wear of PM composites, less severe adhesive wear and fatigue mechanisms played more important roles in the wear of PM-ECAP composites. This study demonstrates a new approach to designing wear-resistant Al-MMCs and is readily applicable to other Al-MMCs.

scholarly journals Homogenization of very rough three-dimensional interfaces for the poroelasticity theory with Biot's model

2019 ◽  
Author(s):  
Nguyen Thi Kieu ◽  
Pham Chi Vinh ◽  
Do Xuan Tung
Keyword(s):  
Incident Angle ◽  
Three Dimensional ◽  
Homogenization Method ◽  
Reflection And Transmission Coefficients ◽  
Biot Theory ◽  
Rough Interface ◽  
Matrix Formulation ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
The Matrix

In this paper, we carry out the homogenization of a very rough three-dimensional interface separating  two dissimilar generally anisotropic poroelastic solids modeled by the Biot theory. The very rough interface is assumed to be a cylindrical surface that rapidly oscillates between two parallel planes, and the motion is time-harmonic. Using the homogenization method with the matrix formulation of the poroelasicity theory, the explicit  homogenized equations have been derived. Since the obtained  homogenized equations are totally explicit, they are very convenient for solving various practical problems. As an example proving this, the reflection and transmission of SH waves at a very rough interface of tooth-comb type is considered. The closed-form analytical expressions of the reflection and transmission coefficients have been  derived. Based on them, the effect of the incident angle and some material parameters  on the reflection and transmission coefficients are examined numerically.

scholarly journals Impact Study on Social Accounting Matrix by Intrabusiness Analysis

2021 ◽  
Vol 18 (23) ◽  
pp. 12547
Author(s):  
Monica Laura Zlati ◽  
Romeo-Victor Ionescu ◽  
Valentin Marian Antohi
Keyword(s):  
Economic Systems ◽  
Input Output ◽  
Economic Sectors ◽  
Output Analysis ◽  
Regional Economic ◽  
New Approach ◽  
The Matrix ◽  
The Government ◽  
Current Concerns

According to the current concerns about social welfare and environmental protection, integrated in a model assimilated to intrabusiness relations, our research started from the analysis of the initial model SAM, which will be transformed in order to develop the SAMI model under six research objectives. The need of improving SAM matrix started to connect it directly to the regional economic systems and continued to a new approach on Input-Output Analysis. Nowadays, SAM describes the intraregional connections between regional economic actors using the role of different income categories. Moreover, SAM can quantify different regional multipliers. All deficiencies previously identified in connection to SAM model have been reviewed and resolved within the proposed SAMI model by the authors of this paper. The purpose of this research is the launch of an absolutely new mathematical model (SAMI) and its practical testing at regional level. This model is able to systematize the links between the local and regional businesses, under the matrix (SAMI) flow, for all kinds of companies and to assist the regional decision, as well. Czamanski was not able to escape from the input-output prison’s approach. This is why he continued to use the linear interdependencies between the industries, economic sectors and economic actors. The income is able only to approximate the individuals and other economic actors’ welfare. If the increase in the average and aggregate income is doubled by an unfair distribution of income in two countries which have the same average income, the effects on welfare vary a lot. A relatively similar effect comes from the government policy differences in income distribution and redistribution.

Laser direct writing of nanocompounds

2011 ◽  
Vol 1365 ◽  
Author(s):  
Andreas Ostendorf ◽  
M’Barek Chakif ◽  
Qingchuan Guo
Keyword(s):  
Polymer Materials ◽  
Polymerization Process ◽  
Direct Writing ◽  
Laser Direct Writing ◽  
Bioactive Materials ◽  
New Approach ◽  
Photosensitive Polymer ◽  
The Matrix ◽  
Inorganic Nanomaterials ◽  
Huge Variety

ABSTRACTLaser direct polymerization has been proven as a powerful tool to generate microstructures. Often photosensitive polymer materials are used because they can be tuned by photoactive molecules to be susceptible to a specific wavelength of light to initiate the polymerization process. One of the main drawbacks of this technique is the lack of functional polymers, e.g. conductive, magnetic, mechanical, optical or bioactive materials. Nanocomposites (nanocompounds), i.e. polymers with inorganic nanomaterials incorporated in the matrix offer a huge variety of new functionalities. A new approach will be presented how functional nanocomposite polymers can be generated and used for laser direct writing techniques. This can open the door for completely new MEMS and MOEMS devices comprising active and passive subcomponents.

Estimate of the Elastic Property of Microtubule Based on a Multiscale Model

2011 ◽  
Vol 211-212 ◽  
pp. 545-549 ◽  
Author(s):  
Yu Zhou Sun ◽  
Jin Yan Wang ◽  
Bin Gao ◽  
Li Wu Chang
Keyword(s):  
Energy Density ◽  
Elastic Property ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Multiscale Model ◽  
Future Application ◽  
Geometrical Parameters ◽  
Orthotropic Elasticity ◽  
Representative Cell ◽  
Tubular Shape

This paper presents a multiscale method to estimate the elastic property of the 13_3 microtubule. A microtubule is viewed as being formed by rolling up its planar encounter into the tubular shape, and the transformation is written into a set of equations with three geometrical parameters. The representative cell is chosen as an unit of two pairs of tubulin momoners. With the appropriate longitudinal and lateral interactive potentials, the strain energy density is calculated by deviding the cell’s energy by its spacial volume. The elastic property of microtubule is determined by minimizing the strain energy density, and the elastic constants are calculated in the thereotical scheme of orthotropic elasticity due to the geometrical meanings of the induced parameters. The advantage of the proposed method and its future application are discussed.

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