scholarly journals Evaluation of Cellular Solids Derived From Triply Periodic Minimal Surfaces

2016 ◽  
Author(s):  
Daniel Cellucci ◽  
Kenneth C. Cheung
Keyword(s):  
Minimal Surfaces ◽  
Three Dimensional ◽  
Cellular Solids ◽  
Cellular Solid ◽  
Multi Scale ◽  
Triply Periodic Minimal Surfaces ◽  
Triply Periodic ◽  
Digital Cellular ◽  
Octet Truss ◽  
Periodic Frameworks

Cellular solids are a class of materials that have many interesting engineering applications, including ultralight structural materials [1]. The traditional method for analyzing these solids uses convex uniform polyhedral honeycombs to represent the geometry of the material [2], and this approach has carried over into the design of digital cellular solids [3]. However, the use of such honeycomb-derived lattices makes the problem of decomposing a three-dimensional lattice into a library of two-dimensional parts non-trivial. We introduce a method for generating periodic frameworks from Triply Periodic Minimal Surfaces (TPMS), which result in geometries that are easier to decompose into digital parts. Additionally, we perform multi-scale analysis of two cellular solids generated from two TPMS, the P- and D-Schwarz, and two cellular solids, the Kelvin and Octet honeycombs. We show that the simulated behavior of these TMPS-derived structures shows the expected modulus of the cellular solid scaling linearly with relative density, and matches the behavior of the octet truss.

Forced Convection Computational Fluid Dynamics Analysis of Architected and Three-Dimensional Printable Heat Sinks Based on Triply Periodic Minimal Surfaces

2020 ◽  
Vol 13 (2) ◽  
Author(s):  
Oraib Al-Ketan ◽  
Mohamed Ali ◽  
Mohamad Khalil ◽  
Reza Rowshan ◽  
Kamran A. Khan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Heat Transfer Coefficient ◽  
Minimal Surfaces ◽  
Heat Sink ◽  
Three Dimensional ◽  
Heat Sinks ◽  
Triply Periodic Minimal Surfaces ◽  
Triply Periodic

Abstract The drive for small and compact electronic components with higher processing capabilities is limited by their ability to dissipate the associated heat generated during operations, and hence, more advanced heat sink designs are required. Recently, the emergence of additive manufacturing techniques facilitated the fabrication of complex structures and overcame the limitation of traditional techniques such as milling, drilling, and casting. Therefore, complex heat sink designs are now easily realizable. In this study, we propose a design procedure for mathematically realizable architected heat sinks and investigate their performance using the computational fluid dynamics (CFD) approach. The proposed heat sinks are mathematically designed with topologies based on triply periodic minimal surfaces (TPMSs). Three-dimensional CFD models are developed using the starccm+ platform for uniform heat sinks and topologically graded heat sinks to study the heat transfer performance in forced convection domains. The overall heat transfer coefficient, surface temperature, and pressure drop versus the input heat sources as well as the Reynolds number are used to evaluate the heat sink performance. Moreover, temperature contours and velocity streamlines were examined to analyze the fluid flow behavior within the heat sinks. Results showed that the tortuosity and channel complexity of the Diamond solid-networks heat sink result in a 32% increase in convective heat transfer coefficient compared with the Gyroid solid-network heat sink which has the comparable surface area under the examined flow conditions. This increase is at the expense of increased pressure drops which increases by the same percentage. In addition, it was found that expanding channel size along flow direction using the porosity grading approach results in significant pressure drop (27.6%), while the corresponding drop in convective heat transfer is less significant (15.7%). These results show the importance of employing functional grading in the design of heat sinks. Also, the manufacturability of the proposed designs was assessed using computerized tomography (CT) scan and scanning electron microscopy (SEM) imaging performed on metallic samples fabricated using powder bed fusion techniques. A visible number of internal manufacturing defects can affect the performance of the proposed heat sinks.

scholarly journals Unification and classification of two-dimensional crystalline patterns using orbifolds

2014 ◽  
Vol 70 (4) ◽  
pp. 319-337 ◽  
Author(s):  
S. T. Hyde ◽  
S. J. Ramsden ◽  
V. Robins
Keyword(s):  
Euclidean Space ◽  
Minimal Surfaces ◽  
Three Dimensional ◽  
Hyperbolic Groups ◽  
Dimensional Euclidean Space ◽  
Two Dimensional ◽  
Triply Periodic Minimal Surfaces ◽  
Triply Periodic ◽  
Simple Rules

The concept of an orbifold is particularly suited to classification and enumeration of crystalline groups in the euclidean (flat) plane and its elliptic and hyperbolic counterparts. Using Conway's orbifold naming scheme, this article explicates conventional point, frieze and plane groups, and describes the advantages of the orbifold approach, which relies on simple rules for calculating the orbifold topology. The article proposes a simple taxonomy of orbifolds into seven classes, distinguished by their underlying topological connectedness, boundedness and orientability. Simpler `crystallographic hyperbolic groups' are listed, namely groups that result from hyperbolic sponge-like sections through three-dimensional euclidean space related to all known genus-three triply periodic minimal surfaces (i.e.theP,D,Gyroid,CLPandHsurfaces) as well as the genus-fourI-WPsurface.

Description of a 3-periodic minimal surface family with trigonal symmetry

1994 ◽  
Vol 209 (1) ◽  
Author(s):  
A. Fogden
Keyword(s):  
Minimal Surface ◽  
Minimal Surfaces ◽  
Weierstrass Representation ◽  
Systematic Analysis ◽  
Trigonal Symmetry ◽  
Triply Periodic Minimal Surfaces ◽  
Periodic Minimal Surface ◽  
Triply Periodic ◽  
The Family

AbstractA systematic analysis of a family of triply periodic minimal surfaces of genus seven and trigonal symmetry is given. The family is found to contain five such surfaces free from self-intersections, three of which are previously unknown. Exact parametrisations of all surfaces are provided using the Weierstrass representation.

scholarly journals Porous polylactic acid scaffolds for bone regeneration: A study of additively manufactured triply periodic minimal surfaces and their osteogenic potential

2020 ◽  
Vol 11 ◽  
pp. 204173142095654
Author(s):  
Anna Diez-Escudero ◽  
Hugo Harlin ◽  
Per Isaksson ◽  
Cecilia Persson
Keyword(s):  
Polylactic Acid ◽  
Cancellous Bone ◽  
Minimal Surfaces ◽  
Pore Distribution ◽  
Osteogenic Potential ◽  
Osteoblastic Cell ◽  
Triply Periodic Minimal Surfaces ◽  
Triply Periodic ◽  
3D Printed ◽  
Grade Material

Three different triply periodic minimal surfaces (TPMS) with three levels of porosity within those of cancellous bone were investigated as potential bone scaffolds. TPMS have emerged as potential designs to resemble the complex mechanical and mass transport properties of bone. Diamond, Schwarz, and Gyroid structures were 3D printed in polylactic acid, a resorbable medical grade material. The 3D printed structures were investigated for printing feasibility, and assessed by morphometric studies. Mechanical properties and permeability investigations resulted in similar values to cancellous bone. The morphometric analyses showed three different patterns of pore distribution: mono-, bi-, and multimodal pores. Subsequently, biological activity investigated with pre-osteoblastic cell lines showed no signs of cytotoxicity, and the scaffolds supported cell proliferation up to 3 weeks. Cell differentiation investigated by alkaline phosphatase showed an improvement for higher porosities and multimodal pore distributions, suggesting a higher dependency on pore distribution and size than the level of interconnectivity.

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