Acoustic band gaps and elastic stiffness of PMMA cellular solids based on triply periodic minimal surfaces

2018 ◽  
Vol 145 ◽  
pp. 20-27 ◽  
Author(s):  
Diab W. Abueidda ◽  
Iwona Jasiuk ◽  
Nahil A. Sobh
Keyword(s):  
Minimal Surfaces ◽  
Elastic Stiffness ◽  
Band Gaps ◽  
Cellular Solids ◽  
Triply Periodic Minimal Surfaces ◽  
Triply Periodic

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.

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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