Topological Design of Three-Dimensional Microstructure Based on Homogenization Effective Method

2006 ◽  
Vol 532-533 ◽  
pp. 705-708
Author(s):  
Ke Peng Qiu ◽  
Wei Hong Zhang ◽  
Shi Ping Sun ◽  
Ji Hong Zhu
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Optimization Method ◽  
Homogenization Method ◽  
The Finite Element Method ◽  
Topological Design ◽  
Unit Cells ◽  
Material Volume ◽  
Specific Material ◽  
Optimal Material

Nowadays, the topology optimization method is extensively adopted for the design of material microstructures to achieve desired behaviors. The present work is concerned with the optimal design of the stiffness and thermal conductivity of 3D microstructure unit cells with the specific material volume fraction in conjunction with the homogenization method and the finite element method. Numerical examples are given to demonstrate that optimal material layouts are successfully achieved and the initial layout has a great effect on the optimal microstructure.

Prediction of internal geometry and tensile behavior of 3D woven solid structures by mathematical coding

2021 ◽  
pp. 152808372110013
Author(s):  
Vivek R Jayan ◽  
Lekhani Tripathi ◽  
Promoda Kumar Behera ◽  
Michal Petru ◽  
BK Behera
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Areal Density ◽  
Woven Fabrics ◽  
Tensile Behavior ◽  
Geometrical Parameters ◽  
Fiber Volume ◽  
Acceptable Error ◽  
Internal Geometry ◽  
Unit Cells

The internal geometry of composite material is one of the most important factors that influence its performance and service life. A new approach is proposed for the prediction of internal geometry and tensile behavior of the 3 D (three dimensional) woven fabrics by creating the unit cell using mathematical coding. In many technical applications, textile materials are subjected to rates of loading or straining that may be much greater in magnitude than the regular household applications of these materials. The main aim of this study is to provide a generalized method for all the structures. By mathematical coding, unit cells of 3 D woven orthogonal, warp interlock and angle interlock structures have been created. The study then focuses on developing code to analyze the geometrical parameters of the fabric like fabric thickness, areal density, and fiber volume fraction. Then, the tensile behavior of the coded 3 D structures is studied in Ansys platform and the results are compared with experimental values for authentication of geometrical parameters as well as for tensile behavior. The results show that the mathematical coding approach is a more efficient modeling technique with an acceptable error percentage.

Large-scale three-dimensional anisotropic topology optimization of variable-axial lightweight composite structures

2021 ◽  
pp. 1-15
Author(s):  
Yuqing Zhou ◽  
Tsuyoshi Nomura ◽  
Enpei Zhao ◽  
Kazuhiro Saitou
Keyword(s):  
Topology Optimization ◽  
Composite Structures ◽  
Large Scale ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Optimization Method ◽  
Optimized Design ◽  
Adaptive Meshing ◽  
Design Synthesis ◽  
Fiber Placement

Abstract Variable-axial fiber-reinforced composites allow for local customization of fiber orientation and thicknesses. Despite their significant potential for performance improvement over the conventional multiaxial composites and metals, they pose challenges in design optimization due to the vastly increased design freedom in material orientations. This paper presents an anisotropic topology optimization method for designing large-scale, 3D variable-axial lightweight composite structures subject to multiple load cases. The computational challenges associated with large-scale 3D anisotropic topology optimization with extremely low volume fraction are addressed by a tensor-based representation of 3D orientation that would avoid the 2π periodicity of angular representations such as Euler angles, and an adaptive meshing scheme, which, in conjunction with PDE regularization of the density variables, refines the mesh where structural members appear and coarsens where there is void. The proposed method is applied to designing a heavy-duty drone frame subject to complex multi-loading conditions. Finally, the manufacturability gaps between the optimized design and the fabrication-ready design for Tailored Fiber Placement (TFP) is discussed, which motivates future work toward a fully-automated design synthesis.

Three-dimensional braided composites with zero, negative and isotropic thermal expansion behavior

2020 ◽  
Vol 54 (13) ◽  
pp. 1761-1781
Author(s):  
SA Pottigar ◽  
B Santhosh ◽  
RG Nair ◽  
P Punith ◽  
PJ Guruprasad ◽  
...  
Keyword(s):  
Thermal Expansion ◽  
Volume Fraction ◽  
Coefficient Of Thermal Expansion ◽  
Three Dimensional ◽  
Braided Composites ◽  
Fiber Volume ◽  
Braided Composite ◽  
Expansion Behavior ◽  
Unit Cells ◽  
Composite Configuration

Three-dimensional braided composites with zero, negative and isotropic coefficient of thermal expansion are presented based on an analytical homogenization technique. The configuration of the braided composites is worked out considering the exact jamming condition leading to higher fiber volume fraction. A total of four configurations of three-dimensional-braided composite representative unit cells were analyzed. Among these, two arrangements are 4-axes and the other two are 5-axes. Special emphasis is given on the detailed description of the representative unit cells. Analysis reveals that a three-dimensional-braided composite configuration with thermoelastic isotropic properties having same coefficient of thermal expansion along x-, y-, and z-axes is achievable. As a special case, the homogenization model is used to predict, for the first time, a configuration of braided architecture and material leading to zero coefficient of thermal expansion along x-, y- and z-directions.

scholarly journals Optimization of Heat Transfer Properties of Nanofluid Flow Over a Shrinking Surface Through Mathematical Modeling

2020 ◽  
Vol 25 (2) ◽  
pp. 40-56 ◽  
Author(s):  
A. Bhandari ◽  
R.K. Pavan Kumar Pannala
Keyword(s):  
Magnetic Parameter ◽  
Volume Fraction ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Nanofluid Flow ◽  
Thermal Buoyancy ◽  
Similarity Transformations ◽  
Permeability Parameter ◽  
Shrinking Surface ◽  
Transfer Properties

AbstractIn the current study, a three dimensional incompressible magnetohydrodynamic (MHD) nanofluid flow over a shrinking surface with associated thermal buoyancy, thermal radiation, and heating absorption effects, as well as viscous dissipation have been investigated. The model has been represented in a set of partial differential equations and is transformed using suitable similarity transformations which are then solved by using the finite element method through COMSOL. The results for velocity and temperature profiles are provided for various values of the shrinking parameter, Biot’s number, heat generation/absorption parameter, thermal Grashof number, nanoparticle volume fraction, permeability parameter, magnetic parameter and radiation parameter.

scholarly journals Homogenization of fully nonlinear rod lattice structures: on the size of the RVE and micro structural instabilities

2021 ◽  
Author(s):  
Ludwig Herrnböck ◽  
Paul Steinmann
Keyword(s):  
Large Deformations ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Homogenization Method ◽  
Volume Element ◽  
Lattice Structures ◽  
Micro Scale ◽  
Macro Scale ◽  
Unit Cells ◽  
Structural Instabilities

AbstractThis work investigates the possibility of applying two-scale computational homogenization to rod lattice structures emerging, for instance, from additive manufacturing. The influence of the number of unit cells within the representative volume element (RVE), thus, the RVE’s size on the homogenized mechanical response is studied for occurring microscopic structural instabilities. Therein, the macro-scale, described in terms of three-dimensional continuum mechanics, is coupled to the micro-scale described by geometrically exact rods, enabling arbitrary large deformations and rotations. A special feature of the presented framework is that the rods building the lattice structures are not restricted to deform purely elastically but may deform inelastically. The mechanical response of lattice structures is investigated by applying the developed homogenization method to an exemplary lattice. Under special loads the structure reaches an instable state and may buckle. The appearance of instabilities depends on the geometric properties of the lattice’s underlying rods and the RVE’s size.

scholarly journals Electromagnetic characterization of millimetre-scale replicas of the gyroid photonic crystal found in the butterfly Parides sesostris

2012 ◽  
Vol 2 (5) ◽  
pp. 645-650 ◽  
Author(s):  
C. Pouya ◽  
P. Vukusic
Keyword(s):  
Photonic Crystal ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Normal Incidence ◽  
Electromagnetic Response ◽  
Transmission Minimum ◽  
Index Contrast ◽  
Material Volume ◽  
Microwave Regime

We have used three-dimensional stereolithography to synthetically replicate the gyroid photonic crystal (PC) structure that occurs naturally in the butterfly Parides sesostris . We have experimentally characterized the transmission response of this structure in the microwave regime at two azimuthal angles ( ϕ ) over a comprehensive range of polar angles ( θ ). We have modelled its electromagnetic response using the finite-element method (FEM) and found excellent agreement with experimental data. Both theory and experiment show a single relatively broad transmission minimum at normal incidence ( θ = 0°) that comprises several narrow band resonances which separate into clearly identifiable stop-bands at higher polar angles. We have identified the specific effective geometric planes within the crystal, and their associated periodicities that give rise to each of these stop-bands. Through extensive theoretical FEM modelling of the gyroid PC structure, using varying filling fractions of material and air, we have shown that a gyroid PC with material volume fraction of 40 per cent is appropriate for optimizing the reflected bandwidth at normal incidence (for a refractive index contrast of 1.56). This is the same gyroid PC material volume fraction used by the butterfly P. sesostris itself to produce its green structurally coloured appearance. This infers further optimization of this biological PC beyond that of its lattice constant alone.

Thermal Modeling of Randomly Distributed Multi-Walled Carbon Nanotube/Polymer Composites

2012 ◽  
Vol 548 ◽  
pp. 123-127
Author(s):  
Xiao Tuo Li ◽  
Xin Yu Fan ◽  
Ying Dan Zhu ◽  
Juan Li
Keyword(s):  
Thermal Conductivity ◽  
Carbon Nanotube ◽  
Thermal Resistance ◽  
Polymer Composites ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Interfacial Thermal Resistance ◽  
The Finite Element Method ◽  
Multi Walled Carbon Nanotube ◽  
The Relationship

A three-dimensional computational model based on the finite element method was developed to predict the thermal properties of randomly distributed multi-walled carbon nanotube (MWCNT)/polymer composites. The numerical results agree very well with the experimental data for MWCNT/epoxy composites with the MWCNT loading below ~10 vol% at the interfacial thermal resistance of ~1.0×10-8 m2K/W, which may give insight into the relationship between the thermal behavior of MWCNT-matrix interfaces and the thermal conductivity of composites. This model is also a useful tool to evaluate the effects of MWCNT-matrix interfacial thermal resistance, volume fraction, thermal conductivity and diameter of MWCNTs on the thermal conductivity of other types of MWCNT/ polymer composites.

scholarly journals A Lattice Model for Elastic Particulate Composites

Materials ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 1584 ◽  
Author(s):  
Darius Zabulionis ◽  
Vytautas Rimša
Keyword(s):  
Mechanical Response ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Particulate Composite ◽  
High Volume ◽  
Spherical Particles ◽  
Particulate Composites ◽  
The Finite Element Method ◽  
Network Method

In the present article, a version of the lattice or spring network method is proposed to model the mechanical response of elastic particulate composites with a high volume fraction of spherical particles and with a much weaker matrix compared to the stiffness of the particles. The main subject of the article is the determination of the axial stiffnesses of the springs of the cell. A comparison of the mechanical response of a three-dimensional particulate composite cube obtained using the finite element method and the proposed methodology showed that the efficiency of the proposed methodology increases with an increasing volume fraction of the particles.

scholarly journals Design and fabrication considerations for three dimensional scaffold structures

2017 ◽  
Vol 2 (2) ◽  
pp. 120 ◽  
Author(s):  
Mazher Iqbal Mohammed
Keyword(s):  
3D Printing ◽  
Three Dimensional ◽  
Porous Structures ◽  
Dimensional Changes ◽  
Design Engineers ◽  
Wide Range ◽  
Unit Cells ◽  
Traditional Manufacturing ◽  
Optimal Material ◽  
Accuracy And Repeatability

<p>Porous three dimensional structures have seen extensive investigation among design engineers for a wide range of novel applications. The fabrication of such designs would not be possible using traditional manufacturing approaches owing to the dimensional intricacy of such structures, but have now become a distinct possibility owing to the maturity of 3D printing technologies. In this study, we have examined the creation of novel unit cells from mathematic surface renderings as a basis for creating tailored porous structures, before realising the final designs through Fuse Deposition Modelling (FDM) 3D printing. We examined the use of Gyroid and Schwarz primitive (P) surfaces to create novel unit cells not typically found in design software libraries. We then transpose these structures into several test geometries comprising a cylinder, cuboid and tetrahedron, which will adequately test limits of design and fabrication in regular and irregularly shaped structures. It was found that the porosities of the resulting models could be adjusted through discrete dimensional changes in the unit cell and digital wrapping procedures. It was also found that models could be fabricated using FDM printing to a minimum pore diameter of approximately 1mm with a high degree of accuracy and repeatability. Ultimately this work will provide guidance to engineering's when creating porous structures and could find usefulness in applications where optimal material usage versus porosity are required, such as in high throughput 3D fluidic applications, such as heat exchangers and tissue engineered structures.</p>

scholarly journals Influence of unit cell parameters of tetrachiral mechanical metamaterial on its effective properties

2021 ◽  
Vol 8 (1) ◽  
pp. 150-157
Author(s):  
Linar R. Akhmetshin ◽  
◽  
Igor Yu. Smolin ◽  
◽  
◽  
...  
Keyword(s):  
Rotation Angle ◽  
Effective Properties ◽  
Three Dimensional ◽  
Unit Cell ◽  
The Finite Element Method ◽  
Unit Cell Parameters ◽  
Cell Parameters ◽  
Chiral Structures ◽  
Unit Cells ◽  
Loading Axis

In the paper, we study the mechanical behavior of a three-dimensional chiral mechanical metamaterial using numerical modeling. A feature of chiral structures is that during their uniaxial loading a twisting is observed along the loading axis. A rod of the mechanical metamaterial composed of 3 × 3 × 9 unit cells along the corresponding three orthogonal axes. The relative strain of uniaxial compression of the sample in the simulation did not exceed 3.3%. The simulation was performed by the finite element method in a threedimensional case. Original results on the dependencies of the rotation angle and the reaction of the rigidly fixed support of the metamaterial sample on the parameters characterizing the structure of the unit cell of the metamaterial are presented in this context. All the dependencies, except one, are nonlinear with portions of large and small changes.

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