The triply periodic minimal surfaces of Alan Schoen and their constant mean curvature companions

1989 ◽  
Vol 64 (3) ◽  
pp. 291-357 ◽  
Author(s):  
Hermann Karcher
Keyword(s):  
Minimal Surfaces ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Triply Periodic Minimal Surfaces ◽  
Triply Periodic

scholarly journals Modeling Symmetric Minimal Surfaces by Mesh Subdivision

2021 ◽  
pp. 249-254
Author(s):  
Stefano Rosso ◽  
Andrea Curtarello ◽  
Federico Basana ◽  
Luca Grigolato ◽  
Roberto Meneghello ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Minimal Surfaces ◽  
Mean Curvature ◽  
Geometric Modeling ◽  
Mechanical Response ◽  
Triply Periodic Minimal Surfaces ◽  
Triply Periodic ◽  
Enhanced Properties ◽  
Manufacturing Technologies ◽  
Zero Mean Curvature

AbstractThanks to the great diffusion of additive manufacturing technologies, the interest in lattice structures is growing. Among them, minimal surfaces are characterized by zero mean curvature, allowing enhanced properties such as mechanical response and fluidynamic behavior. Recent works showed a method for geometric modeling triply periodic minimal surfaces (TPMS) based on subdivision surface. In this paper, the deviation between the subdivided TPMS and the implicit defined ones is investigated together with mechanical properties computed by numerical methods. As a result, a model of mechanical properties as a function of the TPMS thickness and relative density is proposed.

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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