Numerical Analysis and Parametric Study of Phononic Band Gap Structures

2016 ◽  
Vol 846 ◽  
pp. 120-126
Author(s):  
Yang Fan Li ◽  
Xiao Dong Huang ◽  
Shi Wei Zhou
Keyword(s):  
Finite Element ◽  
Band Gap ◽  
Density Ratio ◽  
Critical Density ◽  
Base Material ◽  
Phononic Crystals ◽  
Unit Cell ◽  
Element Analysis ◽  
Phononic Band Gap ◽  
Periodic Composite

Phononic band gap crystals (PnCs) are periodic composite materials and well known for their novel property that can prohibit the propagation of mechanical waves in certain range of frequency. This paper develops the finite element method to calculate band structures of bi-material phononic crystals. Through finite element analysis, complete band gap for longitudinal and transverse waves are obtained by characterizing the dispersion relation in phononic crystals. Phononic crystals with different inclusion shapes in a square and hexagonal unit cell are investigated to study the influence of unit cell topology on band gap size. For a specific pattern, the existence of complete band gap in relation to the density and Lamé constant modulus of composites is studied and critical density ratio and Lamé constant ratio of inclusions versus base material for opening complete band gap are given. The results provide theoretical guidance for designing phononic crystals in practical applications.

Micromechanical properties of unidirectional composites filled with single and clustered shaped fibers

2018 ◽  
Vol 25 (1) ◽  
pp. 143-152 ◽  
Author(s):  
Yong-Peng Lei ◽  
Hui Wang ◽  
Qing-Hua Qin
Keyword(s):  
Finite Element ◽  
Composite Materials ◽  
Micromechanical Model ◽  
Unit Cell ◽  
Micromechanical Modeling ◽  
Element Formulation ◽  
Element Analysis ◽  
Cross Sectional ◽  
Periodic Composite ◽  
Representative Unit Cell

AbstractComputational micromechanics provides an efficient strategy to optimize composite materials by addressing the effect of different material and geometric parameters involved. In the present paper, the effective transverse elastic properties for periodic composite materials reinforced with single and clustered polygonal fibers are evaluated using the micromechanical finite element formulation subject to periodic displacement boundary conditions. The cross-sectional shapes of polygonal fibers are assumed to be triangular, square, pentagonal, hexagonal, octagonal, and circular to perform comprehensive investigation. By applying a periodic displacement constraint along the boundary of the representative unit cell of the composite to meet the requirement of straight-line constraint during the deformation of the unit cell, the computational micromechanical modeling based on homogenization technology is established for evaluating the effects of fiber shape and cluster on the overall properties. Subsequently, the micromechanical model is divided into four submodels, which are solved by means of the finite element analysis for determining the traction distributions along the cell boundary. Finally, the effective orthotropic elastic constants of composites are obtained using the solutions of the linear system of equations involving traction integrations to investigate the effects of fiber shape and cluster on the overall properties.

EFFECT OF BOUNDARY CONDITIONS ON PROCESS- INDUCED STRESSES IN A PLAIN WEAVE UNIT CELL

2021 ◽  
Author(s):  
K. BUKENYA ◽  
M. N. OLAYA ◽  
E. J. PINEDA ◽  
M. MAIARU
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Process Modeling ◽  
Complex Geometry ◽  
Polymer Matrix Composites ◽  
Unit Cell ◽  
Modeling Framework ◽  
Element Analysis ◽  
Finite Element Software ◽  
Aerospace Applications

Woven polymer matrix composites (PMCs) are leveraged in aerospace applications for their desirable specific properties, yet they are vulnerable to high residual stresses during manufacturing and their complex geometry makes experimental results difficult to observe. Process modeling is needed to characterize the effects of the curing and predict end stress states. Finite element software can be used to model woven architectures, however accurate representation of processing conditions remains a challenge when it comes to selecting boundary conditions. The effect of BCs on process-induced stress within woven PMCs is studied. The commercial Finite Element Analysis (FEA) software Abaqus is coupled with user-written subroutines in a process modeling framework. A two-dimensionally (2D) woven PMC repeating unit cell (RUC) is modeled with TexGen and Abaqus. Virtual curing is imposed on the bulk matrix. The BC study is conducted with Free, Periodic, Flat, and Flat-Free configurations. Results show that the end stress state is sensitive to the boundary condition assumptions. Flat BC results show great agreement with Periodic BCs. Residual stress results from process modeling are then compared with a linear-elastic thermal cooldown analysis in Abaqus. Cooldown results indicate an overestimation in matrix stresses compared with process modeling.

Experimental and numerical study on stiffness and damage of glass/epoxy biaxial weft-knitted reinforced composites

2020 ◽  
pp. 073168442093844 ◽  
Author(s):  
Navid Shekarchizadeh ◽  
Reza Jafari Nedoushan ◽  
Tohid Dastan ◽  
Hossein Hasani
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Numerical Study ◽  
Unit Cell ◽  
Analytical Equation ◽  
Reinforced Composites ◽  
Element Analysis ◽  
Composite Strength ◽  
Failure Theories ◽  
Meso Scale

This paper deals with investigating the tensile characteristics of biaxial weft-knitted reinforced composites in terms of stiffness, strength and failure mechanism. The biaxial weft-knitted fabric was produced on an electronic flat knitting machine by E-glass yarns and then was impregnated with epoxy resin. Using an accurate geometrical model, the composite unit cell was designed in Abaqus software’s environment. Tensile tests were simulated in different directions on the created unit cell and the stiffness was calculated. By applying the proper failure theories, the composite strength was predicted and then critical regions of the unit cell were determined. In the next step, a micromechanical approach was also applied to estimate the same tensile features. Failure theories were also applied to predict the strength and most susceptible areas for failure phenomenon in the composite unit cell. The tensile properties of the produced composites were measured and compared with outputs of the finite element and micromechanical approaches. The results showed that the meso-scale finite element analysis approach can well predict the composite strength. In contrast, the meso-scale analytical equation model was not able to predict it acceptably because this model ignores the strain concentration. Both meso-scale finite element analysis and meso-scale analytical equation approaches predicted the similar locations for the composite failure in wale and course directions.

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.

Full Band-Gap Silicon Phononic Crystals for Surface Acoustic Waves

2006 ◽  
Author(s):  
Saeed Mohammadi ◽  
Abdelkrim Khelif ◽  
Ryan Westafer ◽  
Eric Massey ◽  
William D. Hunt ◽  
...  
Keyword(s):  
Band Gap ◽  
Acoustic Waves ◽  
Phononic Crystal ◽  
Surface Acoustic Waves ◽  
Hexagonal Lattice ◽  
Phononic Crystals ◽  
Bulk Wave ◽  
Filling Fraction ◽  
Phononic Band Gap ◽  
Wide Range

Periodic elastic structures, called phononic crystals, show interesting frequency domain characteristics that can greatly influence the performance of acoustic and ultrasonic devices for several applications. Phononic crystals are acoustic counterparts of the extensively-investigated photonic crystals that are made by varying material properties periodically. Here we demonstrate the existence of phononic band-gaps for surface acoustic waves (SAWs) in a half-space of two dimensional phononic crystals consisting of hexagonal (honeycomb) arrangement of air cylinders in a crystalline Silicon background with low filling fraction. A theoretical calculation of band structure for bulk wave using finite element method is also achieved and shows that there is no complete phononic band gap in the case of the low filling fraction. Fabrication of the holes in Silicon is done by optical lithography and deep Silicon dry etching. In the experimental characterization, we have used slanted finger interdigitated transducers deposited on a thin layer of Zinc oxide (sputtered on top of the phononic crystal structure to excite elastic surface waves in Silicon) to cover a wide range of frequencies. We believe this to be the first reported demonstration of phononic band-gap for SAWs in a hexagonal lattice phononic crystal at such a high frequency.

On the Influence of Internal Void Size on the Fracture Stress of Constrained Solder Joints

2016 ◽  
Vol 258 ◽  
pp. 229-232
Author(s):  
Martin Lederer ◽  
Golta Khatibi ◽  
Julien Magnien
Keyword(s):  
Finite Element ◽  
Intermetallic Compound ◽  
Fracture Stress ◽  
Solder Joints ◽  
Base Material ◽  
Gradient Elasticity ◽  
Bulk Solder ◽  
Element Analysis ◽  
Dominant Influence

The fracture strengths of thin solder joints were investigated experimentally and with Finite Element Analysis. Due to a constraining effect, thin solder joints can carry loads which are much higher than the ultimate tensile strength of bulk solder material. On the other hand, thin solder joints show a tendency of being brittle. In fact, the tensile properties show a dependence on the quality of the intermetallic compound at the interface to the base material. Consequently, the size of microscopic defects in the intermetallic compound has a dominant influence on the fracture stress. This behavior could nicely be explained with Finite Element simulations based on strain gradient elasticity.

Band Gap Engineering in N-Dimensional Phononic Crystals

2006 ◽  
Author(s):  
Manvir S. Kushwaha
Keyword(s):  
Photonic Crystals ◽  
Band Structure ◽  
Band Gap ◽  
Photonic Band Gap ◽  
Phononic Crystals ◽  
Spectral Gaps ◽  
Phononic Band Gap ◽  
Acoustic Waveguides ◽  
Photonic Band Gap Materials ◽  
Acoustic Filters

Periodic binary elastic/acoustic composites can give rise to genuine band gaps in the band structure. The term genuine refers to the complete gaps, which persist independently of the polarization of the wave and of its direction of propagation. Within these complete gaps sound and vibrations are forbidden, the "acoustic crystals" stand still, and the total silence reigns. Thus a vibrator (or defect) introduced into a periodic elastic composite would be unable to generate sound or vibrations within the gap. The existence of complete gaps in the band structure is closely associated with the (classical) Anderson localization of sound and vibrations. The search for phononic band-gap materials is of comparable interest to the pursuit of photonic band-gap materials. Thus the phononic crystals are to acoustics as photonic crystals are to optics. In comparison to the photonic crystals, there are additional parameters (the mass densities and two velocities - longitudinal and transverse) involved in the phononic crystals, which make the physics richer and leaves us with more options in the quest of creating full stop bands in the system. As regards the applications, the phononic crystals are envisioned to find ways in the acoustic waveguides, improvements in designing the transducers, elastic/acoustic filters, noise control, ultrasonics, and medical imaging, to name a few. Since the interesting phenomena emerging from the phononic crystals are all consequences of the existence of the gap(s), a major part of the research efforts has focused on the search for phononic band-gap crystals. As such, we report and emphasize on the spectral gaps in the band structure for cleverly synthesized N-dimensional (N = 1, 2, 3) phononic crystals. PACS numbers:

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