A Taxonomy for Representing Prismatic Cellular Materials

2016 ◽  
Author(s):  
Mohammad Fazelpour ◽  
Joshua D. Summers ◽  
Vincent Y. Blouin
Keyword(s):  
Cellular Materials ◽  
Unit Cell ◽  
Structural Members ◽  
Cellular Topology

A taxonomy is developed to describe prismatic cellular materials (PCM) explicitly to allow for unambiguous discussion of cellular topology. The taxonomy represents a PCM through describing (1) the unit cell (UC) and (2) the tiling or unit cell arrangements. The UC is described through three characteristics: boundary, interior, and connections of the unit cell with its adjacent structural members. Each of these are further refined into sub-divisions. The taxonomy is evaluated through three metrics: completeness, perceptual orthogonality, and depth. Using this descriptive taxonomy, researchers can more uniformly describe the development efforts that they are pursuing.

Multifunctional Topology Design of Cellular Material Structures

2006 ◽  
Author(s):  
Carolyn Conner Seepersad ◽  
Janet K. Allen ◽  
David L. McDowell ◽  
Farrokh Mistree
Keyword(s):  
Heat Transfer ◽  
Topology Optimization ◽  
Cell Walls ◽  
Cellular Structure ◽  
Optimization Methods ◽  
Cellular Materials ◽  
Design Methods ◽  
Topology Design ◽  
Cellular Topology ◽  
Multifunctional Properties

Prismatic cellular or honeycomb materials exhibit favorable properties for multifunctional applications such as ultra-light load bearing combined with active cooling. Since these properties are strongly dependent on the underlying cellular structure, design methods are needed for tailoring cellular topologies with customized multifunctional properties that may be unattainable with standard cell designs. Topology optimization methods are available for synthesizing the form of a cellular structure—including the size, shape, and connectivity of cell walls and the number, shape, and arrangement of cell openings—rather than specifying these features a priori. To date, the application of these methods for cellular materials design has been limited primarily to elastic and thermo-elastic properties, however, and limitations of standard topology optimization methods prevent direct application to many other phenomena such as conjugate heat transfer with internal convection. In this paper, we introduce a practical, two-stage, flexibility-based, multifunctional topology design approach for applications that require customized multifunctional properties. As part of the approach, robust topology design methods are used to design flexible cellular topology with customized structural properties. Dimensional and topological flexibility is embodied in the form of robust ranges of cell wall dimensions and robust permutations of a nominal cellular topology. The flexibility is used to improve the heat transfer characteristics of the design via addition/removal of cell walls and adjustment of cellular dimensions, respectively, without degrading structural performance. We apply the method to design stiff, actively cooled prismatic cellular materials for the combustor liners of next-generation gas turbine engines.

Multifunctional Topology Design of Cellular Material Structures

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Carolyn Conner Seepersad ◽  
Janet K. Allen ◽  
David L. McDowell ◽  
Farrokh Mistree
Keyword(s):  
Heat Transfer ◽  
Topology Optimization ◽  
Cell Walls ◽  
Cellular Structure ◽  
Optimization Methods ◽  
Cellular Materials ◽  
Design Methods ◽  
Topology Design ◽  
Cellular Topology ◽  
Multifunctional Properties

Prismatic cellular or honeycomb materials exhibit favorable properties for multifunctional applications such as ultralight load bearing combined with active cooling. Since these properties are strongly dependent on the underlying cellular structure, design methods are needed for tailoring cellular topologies with customized multifunctional properties. Topology optimization methods are available for synthesizing the form of a cellular structure—including the size, shape, and connectivity of cell walls and openings—rather than specifying these features a priori. To date, the application of these methods for cellular materials design has been limited primarily to elastic and thermoelastic properties, and limitations of classic topology optimization methods prevent a direct application to many other phenomena such as conjugate heat transfer with internal convection. In this paper, a practical, two-stage topology design approach is introduced for applications that require customized multifunctional properties. In the first stage, robust topology design methods are used to design flexible cellular topology with customized structural properties. Dimensional and topological flexibility is embodied in the form of robust ranges of cell wall dimensions and robust permutations of a nominal cellular topology. In the second design stage, the flexibility is used to improve the heat transfer characteristics of the design via addition/removal of cell walls and adjustment of cellular dimensions without degrading structural performance. The method is applied to design stiff, actively cooled prismatic cellular materials for the combustor liners of next-generation gas turbine engines.

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.

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.

The Linear Elastic Properties of Open-Cell Foams

1988 ◽  
Vol 55 (2) ◽  
pp. 341-346 ◽  
Author(s):  
W. E. Warren ◽  
A. M. Kraynik
Keyword(s):  
Young’S Modulus ◽  
Elastic Properties ◽  
Cross Section ◽  
Elastic Constants ◽  
Volume Fraction ◽  
Cellular Materials ◽  
Unit Cell ◽  
Open Cell ◽  
Linear Elastic ◽  
Open Cell Foams

A theoretical model for the linear elastic properties of three-dimensional open-cell foams is developed. We consider a tetrahedral unit cell, which contains four identical half-struts that join at equal angles, to represent the essential microstructural features of a foam. The effective continuum stress is obtained for an individual tetrahedral element arbitrarily oriented with respect to the principal directions of strain. The effective elastic constants for a foam are determined under the assumption that all possible orientations of the unit cell are equally probable in a representative volume element. The elastic constants are expressed as functions of compliances for bending and stretching of a strut, whose cross section is permitted to vary with distance from the joint, so the effect of strut morphology on effective elastic properties can be determined. Strut bending is the primary distortional mechanism for low-density foams with tetrahedral microstructure. For uniform strut cross section, the effective Young’s modulus is proportional to the volume fraction of solid material squared, and the coefficient of proportionality depends upon the specific strut shape. A similar analysis for cellular materials with cubic microstructure indicates that strut extension is the dominant distortional mechanism and that the effective Young’s modulus is linear in volume fraction. Our results emphasize the essential role of microstructure in determining the linear elastic properties of cellular materials and provide a theoretical framework for investigating nonlinear behavior.

Some Topics in Recent Advances and Applications of Structural Impact Dynamics

2011 ◽  
Vol 64 (3) ◽  
Author(s):  
X. M. Qiu ◽  
T. X. Yu
Keyword(s):  
Experimental Studies ◽  
Rate Sensitivity ◽  
Cellular Materials ◽  
Dynamic Responses ◽  
Stress Wave Propagation ◽  
Impact Dynamics ◽  
Structural Members ◽  
Transverse Loading ◽  
Time Dynamic ◽  
Structural Impact

This paper reviews some topics related to the advances and applications of structural impact dynamics in recent years. Dynamic behavior of structural members including tubes, beams and plates under axial or transverse loading, and cellular materials and sandwich structures under impact or blast loading are summarized here. The research methodology involves experimental studies, theoretical modeling, as well as numerical simulations. However, as we mainly focus on the longer time dynamic responses of structures and cellular materials, studies of stress wave propagation and the material's strain-rate sensitivity are not included.

A User Study on Exploring the Sequencing of Unit Cell Design Guidelines

2017 ◽  
Author(s):  
Mohammad Fazelpour ◽  
Apurva Patel ◽  
Prabhu Shankar ◽  
Joshua D. Summers
Keyword(s):  
User Study ◽  
Cellular Materials ◽  
Design Guidelines ◽  
Unit Cell ◽  
Structural Behavior ◽  
Cell Design ◽  
Unit Cells ◽  
Meso Scale

The objective of this user study is to evaluate the effect of sequencing of unit cell design guidelines. The unit cell design guidelines support engineers in intentionally redesigning the topology and shape of unit cells for a desired structural behavior. In this study, four different unit cell design guidelines are selected to enable designers in increasing the shear flexure in meso-scale periodic cellular materials. These guidelines are not necessarily objective and may result in different modified unit cells when applied by different designers. Therefore, this user study was designed to evaluate the effect of sequencing the guidelines on the subjectivity and the modified unit cells. Twelve different sequencing sets are tested and it is found that certain sequencing of guidelines resulted in more novel ideas than other cases with less subjective guidelines.

Shape Design of Periodic Cellular Materials Under Cyclic Loading

2011 ◽  
Author(s):  
Ehsan Masoumi Khalil Abad ◽  
Sajad Arabnejad Khanoki ◽  
Damiano Pasini
Keyword(s):  
Fatigue Strength ◽  
Cellular Materials ◽  
Unit Cell ◽  
Cellular Material ◽  
Cellular Solid ◽  
Lattice Materials ◽  
Cell Topology ◽  
A Cell ◽  
Continuous Curvature ◽  
Geometric Changes

This paper presents a method to improve the fatigue strength of 2D periodic cellular materials under a fully-reversed loading condition. For a given cell topology, the shape of the unit cell is synthesized to minimize any stress concentration caused by discontinuities in the cell geometry. We propose to reduce abrupt geometric changes emerging in the periodic microstructure through the synthesis of a cell shape defined by curved boundaries with continuous curvature, i.e. G2-continous curves. The bending moments caused by curved cell elements are reduced by minimizing the curvature of G2-continuous cell elements so as to make them as straight as possible. The asymptotic homogenization technique is used to obtain the homogenized stiffness matrix and the fatigue strength of the synthesized cellular material. The proposed methodology is applied to synthesize a unit cell topology described by smooth boundary curves. Numeric simulations are performed to compare the performance of the synthesized cellular solid with that of common two dimensional lattice materials having hexagonal, circular, square, and Kagome shape of the unit cell. The results show that the methodology enables to obtain a cellular material with improved fatigue strength. Finally, a parametric study is performed to examine the effect of different geometric parameters on the performance of the proposed cellular geometries.

Design of periodic unit cell in cellular materials with extreme properties using topology optimization

2016 ◽  
Vol 232 (10) ◽  
pp. 852-869 ◽  
Author(s):  
Wenjiong Chen ◽  
Liyong Tong ◽  
Shutian Liu
Keyword(s):  
Topology Optimization ◽  
Effective Properties ◽  
Optimization Method ◽  
Homogenization Method ◽  
Cellular Materials ◽  
Unit Cell ◽  
Threshold Method ◽  
Penalization Method ◽  
Modulus Maximum ◽  
Periodic Unit Cell

This paper presents a topology optimization method to design periodic unit cell in cellular materials with extreme properties using a moving iso-surface threshold method. The aim is to determine the optimal distribution of material within the periodic unit cell. The effective properties of cellular material are obtained by using a finite element-based homogenization method. The penalty function approach is introduced to construct the objective function for designing material with extreme properties under condition of square or isotropic symmetry. New characteristic response functions of moving iso-surface threshold are proposed for maximum shear or bulk modulus, maximum shear modulus or negative Poisson’s ratio under isotropic symmetry. Several examples are presented and the results are compared to those obtained with the solid isotropic material with penalization method to demonstrate the validity of the method. A series of new and interesting microstructures with extreme properties are found and presented.

High-resolution structure determination by ALCHEMI

1983 ◽  
Vol 41 ◽  
pp. 178-181 ◽  
Author(s):  
Peter G. Self ◽  
Peter R. Buseck
Keyword(s):  
Site Occupancy ◽  
Real Space ◽  
Unit Cell ◽  
Bragg Angle ◽  
Electron Current ◽  
High Resolution Structure ◽  
Beam Incident ◽  
Crystallographic Planes ◽  
Electron Beam Incident ◽  
Resolution Structure

ALCHEMI (Atom Location by CHanneling Enhanced Microanalysis) enables the site occupancy of atoms in single crystals to be determined. In this article the fundamentals of the method for both EDS and EELS will be discussed. Unlike HRTEM, ALCHEMI does not place stringent resolution requirements on the microscope and, because EDS clearly distinguishes between elements of similar atomic number, it can offer some advantages over HRTEM. It does however, place certain constraints on the crystal. These constraints are: a) the sites of interest must lie on alternate crystallographic planes, b) the projected charge density on the alternate planes must be significantly different, and c) there must be at least one atomic species that lies solely on one of the planes.An electron beam incident on a crystal undergoes elastic scattering; in reciprocal space this is seen as a diffraction pattern and in real space this is a modulation of the electron current across the unit cell. When diffraction is strong (i.e., when the crystal is oriented near to the Bragg angle of a low-order reflection) the electron current at one point in the unit cell will differ significantly from that at another point.

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