Effective properties of 0-3, 1-3, and 2-2 composites based on unified unit-cell micromechanics model

2021 ◽  
pp. 103807
Author(s):  
Chien-hong Lin
Keyword(s):  
Effective Properties ◽  
Unit Cell ◽  
Micromechanics Model ◽  
Cell Micromechanics

Locally resonant effective phononic crystals for subwavelength vibration control of torsional cylindrical waves

2021 ◽  
pp. 1-30
Author(s):  
Ignacio Arretche ◽  
Kathryn Matlack
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Effective Properties ◽  
Equations Of Motion ◽  
Phononic Crystal ◽  
Phononic Crystals ◽  
Unit Cell ◽  
Periodic Coefficients ◽  
Bloch Theorem ◽  
Plane Wave Propagation

Abstract Locally resonant materials allow for wave propagation control in the sub-wavelength regime. Even though these materials do not need periodicity, they are usually designed as periodic systems since this allows for the application of the Bloch theorem and analysis of the entire system based on a single unit cell. However, geometries that are invariant to translation result in equations of motion with periodic coefficients only if we assume plane wave propagation. When wave fronts are cylindrical or spherical, a system realized through tessellation of a unit cell does not result in periodic coefficients and the Bloch theorem cannot be applied. Therefore, most studies of periodic locally resonant systems are limited to plane wave propagation. In this paper, we address this limitation by introducing a locally resonant effective phononic crystal composed of a radially-varying matrix with attached torsional resonators. This material is not geometrically periodic but exhibits effective periodicity, i.e. its equations of motion are invariant to radial translations, allowing the Bloch theorem to be applied to radially propagating torsional waves. We show that this material can be analyzed under the already developed framework for metamaterials. To show the importance of using an effectively periodic system, we compare its behavior to a system that is not effectively periodic but has geometric periodicity. We show considerable differences in transmission as well as in the negative effective properties of these two systems. Locally resonant effective phononic crystals open possibilities for subwavelength elastic wave control in the near field of sources.

scholarly journals Effective properties of a porous inhomogeneously polarized by direction piezoceramic material with full metalized pore boundaries: Finite element analysis

2020 ◽  
Vol 10 (05) ◽  
pp. 2050018
Author(s):  
Andrey Nasedkin ◽  
Mohamed Elsayed Nassar
Keyword(s):  
Finite Element ◽  
Effective Properties ◽  
Dielectric Material ◽  
Unit Cell ◽  
Dielectric Constants ◽  
Polarization Field ◽  
Electrostatic Problem ◽  
Element Analysis ◽  
Piezoceramic Material ◽  
Homogenization Problems

This paper concerns the homogenization problems for porous piezocomposites with infinitely thin metalized pore surfaces. To determine the effective properties, we used the effective moduli method and the finite element approaches, realized in the ANSYS package. As a simple model of the representative volume, we applied a unit cell of porous piezoceramic material in the form of a cube with one spherical pore. We modeled metallization by introducing an additional layer of material with very large permittivity coefficients along the pore boundary. Then we simulated the nonuniform polarization field around the pore. For taking this effect into account, we previously solved the electrostatic problem for a porous dielectric material with the same geometric structure. From this problem, we obtained the polarization field in the porous piezomaterial; after that, we modified the material properties of the finite elements from dielectric to piezoelectric with element coordinate systems whose corresponding axes rotated along the polarization vectors. As a result, we obtained the porous unit cell of an inhomogeneously polarized piezoceramic matrix. From the solutions of these homogenization problems, we observed that the examined porous piezoceramics composite with metalized pore boundaries has more extensive effective transverse and shear piezomoduli, and effective dielectric constants compared to the conventional porous piezoceramics. The analysis also showed that the effect of the polarization field inhomogeneity is insignificant on the ordinary porous piezoceramics; however, it is more significant on the porous piezoceramics with metalized pore surfaces.

A New Micromechanics Model for Predicting Thermal Properties of Heterogeneous Materials

2006 ◽  
Author(s):  
Wenbin Yu ◽  
Tian Tang
Keyword(s):  
Thermal Properties ◽  
Heterogeneous Materials ◽  
Present Theory ◽  
Unit Cell ◽  
Micromechanics Model ◽  
Micromechanics Models ◽  
Unit Cells ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method ◽  
Complete Set

A new micromechanics model, namely, the variational asymptotic method for unit cell homogenization (VAMUCH), is extended to predict thermal properties of heterogeneous anisotropic materials. In comparison to existing micromechanics models, VAMUCH is unique in the following three aspects: (1) it invokes only essential assumptions within the concept of micromechanics and achieves the same accuracy as mathematical homogenization theories; (2) it calculates the complete set of properties simultaneously without applying any loads; and (3) the dimensionality of the problem is determined by the dimension of the unit cell and the complete set of material properties can be obtained for one-dimensional unit cells. The present theory is implemented in the computer program VAMUCH, a recently developed, versatile engineering code for homogenization of heterogeneous materials. Several examples will be used to demonstrate the application and accuracy of the theory and the code of VAMUCH.

Design for Additive Manufacturing: Effectiveness of Unit Cell Design Guidelines As Ideation Tools

2019 ◽  
Author(s):  
I’Shea Boyd ◽  
Mohammad Fazelpour
Keyword(s):  
Additive Manufacturing ◽  
Effective Properties ◽  
Cellular Materials ◽  
Design Guidelines ◽  
Unit Cell ◽  
Cell Design ◽  
Recent Approach ◽  
Wide Range ◽  
Unit Cells ◽  
High Flexibility

Abstract The periodic cellular materials are comprised of repeatable unit cells. Due to outstanding effective properties of the periodic cellular materials such as high flexibility or high stiffness at low relative density, they have a wide range of applications in lightweight structures, crushing energy absorption, compliant structures, among others. Advancement in additive manufacturing has led to opportunities for making complex unit cells. A recent approach introduced four unit cell design guidelines and verified them through numerical simulation and user studies. The unit cell design guidelines aim to guide designers to re-design the shape or topology of a unit cell for a desired structural behavior. While the guidelines were identified as ideation tools, the effectiveness of the guidelines as ideation tools has not been fully investigated. To evaluate the effectiveness of the guidelines as ideation tools, four objective metrics have been considered: novelty, variety, quality, and quantity. The results of this study reveal that the unit cell design guidelines can be considered as ideation tools. The guidelines are effective in aiding engineers in creating novel unit cells with improved shear flexibility while maintaining the effective shear modulus.

Prediction of Electrical Properties of Plain-Weave Fabric Composites for Printed Wiring Board Design

1993 ◽  
Vol 115 (2) ◽  
pp. 219-224 ◽  
Author(s):  
R. K. Agarwal ◽  
A. Dasgupta
Keyword(s):  
Dielectric Constant ◽  
Loss Tangent ◽  
Effective Properties ◽  
Mechanistic Model ◽  
Three Dimensional ◽  
Unit Cell ◽  
Woven Fabric ◽  
Effective Dielectric Constant ◽  
Low Loss ◽  
Dielectric Constant And Loss

A mechanistic model is presented for predicting the effective dielectric constant and loss tangent of woven-fabric reinforced composites with low-loss constituents. A two-scale asymptotic homogenization scheme is used to predict the orthotropic effective properties. A three-dimensional unit-cell enclosing the characteristic periodic repeat pattern in the fabric weave is isolated and modeled mathematically. Electrostatic boundary value problems (BVP’s) are formulated in the unit-cell and are solved analytically to predict effective dielectric constant of the composite, using three-dimensional series-parallel reactance nets. Results are also verified numerically, using finite element methods. The effective dielectric constant and the effective loss tangent are then obtained, analogous to mechanical viscoelastic problems for low-loss materials. The predicted dielectric constant and loss tangent are compared with experimental results for E-glass/epoxy laminates. Frequency dependence of the effective dielectric constant and loss tangent is obtained from the corresponding behavior of the constituent materials. Trade-off studies are conducted to investigate the effect of the constituent material properties on orthotropic effective dielectric permittivity.

scholarly journals Second order homogenization of quasi-periodic structures

2018 ◽  
Vol 40 (4) ◽  
pp. 325-348
Author(s):  
Duc Trung Le ◽  
Jean-Jacques Marigo
Keyword(s):  
General Framework ◽  
Volume Fraction ◽  
Effective Properties ◽  
Periodic Structures ◽  
Expansion Method ◽  
Second Order ◽  
Unit Cell ◽  
One Dimensional ◽  
Minimization Problems ◽  
Asymptotic Expansion Method

The paper develops a general framework to derive the effective properties of quasi-periodic elastic medium. By using the asymptotic expansion method, the solution is expanded to the second order by solving a sequence of minimization problems. The effective stiffness tensors fields entering in the expression of the macroscopic energy are obtained by solving several families of microscopic problems posed on the unit cell and which bring into play only the microstructure. As an illustrative example, we consider an anti-plane elastic case of a heterogeneous cylinder made of a bi-layer laminate and submitted to the gravity. The unit cell being one-dimensional, all the associated elementary problems can be solved in a closed form and one shows that the effective energy of the medium expanded up to the second order depends not only on the strain gradient, but also on the gradient of the volume fraction \(\theta\) characterizing the repartition of the two materials in the laminate.

scholarly journals Multiscale Evaluation of The Elastic Behavior for The Metal-Coated Lattice Structures

2020 ◽  
Author(s):  
Sina Soleimanian ◽  
Xiang Wang ◽  
Min Chen ◽  
Yanqing Yu ◽  
Ji Li ◽  
...  
Keyword(s):  
Elastic Modulus ◽  
Film Thickness ◽  
Volume Fraction ◽  
Effective Properties ◽  
Unit Cell ◽  
Homogenization Theory ◽  
Elastic Behavior ◽  
Coating Film ◽  
Specific Modulus ◽  
The Impact

Abstract Well-developed Additive Manufacturing leads to a variety of material and structure design. With the combination of 3D printing and plating technique, metal-coated resin lattice is investigated to achieve a light weight design with minimal economic cost and admirable material properties. In this paper, numerical approaches integrated with classical homogenization theory is adopted to study the effective mechanical characterizations of the BCC (Body-Centered-Cubic) metal-coated lattices. The selection of RVE (Representative Volume Element) is discussed for obtaining objective effective properties. Moreover, the impact of unit cell rod diameter and coating film thickness are investigated. A sensitivity analysis of these two parameters is conducted based on the advanced hypercube sampling methods. The results reveal that multiple-unit-cells lead to more stable homogenized properties than single unit cell. The Increase of volume fraction may improve the elastic modulus and specific modulus remarkably. However, the increase of thickness of coating film only leads to monotonously increased elastic modulus. For this reason, there exists an optimal coating film thickness for the specific modulus of the lattice structure.

A Multiphysics Micromechanics Model of Smart Materials Using the Variational Asymptotic Method

2008 ◽  
Author(s):  
Tian Tang ◽  
Wenbin Yu
Keyword(s):  
Asymptotic Method ◽  
Smart Materials ◽  
Effective Properties ◽  
Primary Objective ◽  
Local Fields ◽  
New Model ◽  
Micromechanics Model ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method ◽  
Micromechanics Modeling

The primary objective of the present paper is to develop a micromechanics model for the prediction of the effective properties and the distribution of local fields of smart materials which are responsive to fully coupled electric, magnetic, thermal and mechanical fields. This work is based on the framework of the variational asymptotic method for unit cell homogenization (VAMUCH), a recently developed micromechanics modeling scheme. For practicle use of this theory, we implement this new model using the finite element method into the computer program VAMUCH. For validation, several examples will be presented in the full paper to compare with existing models and demonstrate the application and advantages of the new model.

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