Predicting the effective properties of 3D needled carbon/carbon composites by a hierarchical scheme with a fiber-based representative unit cell

2017 ◽  
Vol 172 ◽  
pp. 198-209 ◽  
Author(s):  
Songhe Meng ◽  
Leying Song ◽  
Chenghai Xu ◽  
Wei Wang ◽  
Weihua Xie ◽  
...  
Keyword(s):  
Effective Properties ◽  
Unit Cell ◽  
Carbon Composites ◽  
Representative Unit Cell ◽  
Hierarchical Scheme

scholarly journals Prediction of Effective Thermal Conductivities of Four-Directional Carbon/Carbon Composites by Unit Cells with Different Sizes

2021 ◽  
Vol 11 (3) ◽  
pp. 1171
Author(s):  
Chang Xu ◽  
Zhihong Sun ◽  
Guowei Shao
Keyword(s):  
Carbon Fiber ◽  
Longitudinal Direction ◽  
Unit Cell ◽  
Carbon Composites ◽  
Temperature Boundary ◽  
The Matrix ◽  
Unit Cells ◽  
Experimental Values ◽  
Different Diameters ◽  
Thermal Conductivities

Two-unit cells developed to predict the effective thermal conductivities of four-directional carbon/carbon composites with the finite element method are proposed in this paper. The smaller-size unit cell is formulated from the larger-size unit cell by two 180° rotational transformations. The temperature boundary conditions corresponding to the two-unit cells are derived, and the validity is verified by the temperature and heat flux distributions at specific positions of the larger-size unit cell and the smaller-size unit cell. The thermal conductivities of the carbon fiber bundles and carbon fiber rods are measured firstly. Then, combined with the properties of the matrix, the effective thermal conductivities of the four-directional carbon/carbon composites are numerically predicted. The results in transverse direction predicted by the larger-size unit cell and the smaller-size unit cell are both higher than experimental values, which are 5.8 to 6.2% and 7.3 to 8.2%, respectively. In longitudinal direction, the calculated thermal conductivities of the larger-size unit cell and the smaller-size unit cell are 6.8% and 6.2% higher than the experimental results, respectively. In addition, carbon fiber rods with different diameters are set to clarify the influence on the effective thermal conductivities of the four-directional carbon/carbon composites.

scholarly journals Thermo-Viscoelastic Response of 3D Braided Composites Based on a Novel FsMsFE Method

Materials ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 271
Author(s):  
Jun-Jun Zhai ◽  
Xiang-Xia Kong ◽  
Lu-Chen Wang
Keyword(s):  
Finite Element ◽  
Cell Model ◽  
Structural Parameters ◽  
Thermal Relaxation ◽  
Viscoelastic Behavior ◽  
Unit Cell ◽  
Time Dependent ◽  
3D Braided Composites ◽  
Equivalent Time ◽  
Representative Unit Cell

A homogenization-based five-step multi-scale finite element (FsMsFE) simulation framework is developed to describe the time-temperature-dependent viscoelastic behavior of 3D braided four-directional composites. The current analysis was performed via three-scale finite element models, the fiber/matrix (microscopic) representative unit cell (RUC) model, the yarn/matrix (mesoscopic) representative unit cell model, and the macroscopic solid model with homogeneous property. Coupling the time-temperature equivalence principle, multi-phase finite element approach, Laplace transformation and Prony series fitting technology, the character of the stress relaxation behaviors at three scales subject to variation in temperature is investigated, and the equivalent time-dependent thermal expansion coefficients (TTEC), the equivalent time-dependent thermal relaxation modulus (TTRM) under micro-scale and meso-scale were predicted. Furthermore, the impacts of temperature, structural parameters and relaxation time on the time-dependent thermo-viscoelastic properties of 3D braided four-directional composites were studied.

SEA model for structural acoustic coupling by means of periodic finite element models of the structural subsystems

2021 ◽  
Vol 263 (1) ◽  
pp. 5301-5309
Author(s):  
Luca Alimonti ◽  
Abderrazak Mejdi ◽  
Andrea Parrinello
Keyword(s):  
Finite Element ◽  
Numerical Approach ◽  
Unit Cell ◽  
Analytical Models ◽  
Finite Element Models ◽  
Fe Model ◽  
Acoustic Coupling ◽  
Representative Unit Cell ◽  
Definition Of ◽  
Acoustic Treatment

Statistical Energy Analysis (SEA) often relies on simplified analytical models to compute the parameters required to build the power balance equations of a coupled vibro-acoustic system. However, the vibro-acoustic of modern structural components, such as thick sandwich composites, ribbed panels, isogrids and metamaterials, is often too complex to be amenable to analytical developments without introducing further approximations. To overcome this limitation, a more general numerical approach is considered. It was shown in previous publications that, under the assumption that the structure is made of repetitions of a representative unit cell, a detailed Finite Element (FE) model of the unit cell can be used within a general and accurate numerical SEA framework. In this work, such framework is extended to account for structural-acoustic coupling. Resonant as well as non-resonant acoustic and structural paths are formulated. The effect of any acoustic treatment applied to coupling areas is considered by means of a Generalized Transfer Matrix (TM) approach. Moreover, the formulation employs a definition of pressure loads based on the wavenumber-frequency spectrum, hence allowing for general sources to be fully represented without simplifications. Validations cases are presented to show the effectiveness and generality of the approach.

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.

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.

Micromechanical Modeling of Two-Dimensional Periodic Cellular Materials

2013 ◽  
Author(s):  
K. Alzebdeh ◽  
A. Al-Shabibi ◽  
T. Pervez
Keyword(s):  
Elastic Moduli ◽  
Cellular Materials ◽  
Unit Cell ◽  
Cellular Material ◽  
Micromechanical Modeling ◽  
Beam Model ◽  
Essential Boundary Condition ◽  
Representative Unit Cell ◽  
Structural Applications ◽  
Equivalent Continuum

The mechanical behavior of 2-D periodic cellular materials is investigated using a continuum-based modeling approach. Two micromechanical models are developed on the basis of representative unit cell concept in which skeleton of cellular material is modeled as elastic beams. The ANSYS finite element code is used to solve the beam model of skeleton. Elastic moduli of square and triangular networks comprising the microstructure of the cellular material are calculated based on an equivalent continuum model. This is achieved by equating the stored energy in skeleton of a unit cell to the strain energy of the equivalent continuum under a set of prescribed boundary conditions. A proper displacement-controlled (essential) boundary condition generates a uniform strain field in both models which corresponds to calculation of one elastic modulus at a time. Then, effective Young’s modulus and Poisson’s ratio of continuum are extracted from the calculated elastic moduli. The dependence of effective elastic constants on relative density and thickness to length ratio of the microstructure is investigated. Furthermore, the in-plane behavior of cellular solids in compression is explored with the help of current modeling. The proposed models may contribute to optimal designs of a new class of materials with tailored geometry and material properties which could be useful in a broad range of structural applications.

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.

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