Minimal surface designs for porous materials: from microstructures to mechanical properties
- 82 Downloads
In this work, we present four types of topological bicontinuous porous structures, namely Gyroid (G), Schwarz Diamond (D), Schwarz Primitive (P), and iWp (W), which are generated from mathematically defined triply periodic minimal surfaces. A systematic semi-theoretical investigation is performed to analyze the relations between the microstructures and the macroscopic mechanical behavior. Benefiting from the straightforward controllability on parameters, the scaling laws of the geometrical properties and mechanical properties are determined as functions of the relative density according to numerical analysis and computational simulation. An application to additive manufacturing accompanying with uniaxial compression testing is also performed, and the results show a highly agreement with the above scaling laws. Moreover, the simulation results indicate that the mechanical properties are highly dependent on topological architectures, which affect the deformation behavior of porous materials. It is shown that P topology has the highest stiffness and strength with stretching-dominated mode, while the rest exhibit a flexibly bending-dominated deformation behavior. The present study provides not only new insights into the structure–property relations of such topologies, but also a practical guide for their fabrication and application.
This work was supported by Longshan academic talent research supporting program of SWUST (17LZX408). The authors gratefully acknowledge Dr. Li Bo and Mr. Zhong Shengyuan for equipment and technique support.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
- 13.e Sá AM, Mello VM, Echavarria KR, Covill D (2015) Adaptive voids. Vis Comput 31(6):799Google Scholar
- 16.Dementjev A, Tarakanov O (1970) Influence of the cellular structure of foams on their mechanical properties. Mech Polym 4:594Google Scholar
- 19.Lord EA, Mackay AL (2003) Periodic minimal surfaces of cubic symmetry. Curr Sci 85(3):346–362Google Scholar
- 33.Eymard R, Gallouët T, Herbin R (2000) Finite volume methods. Handb Numer Anal 7:713Google Scholar
- 34.Kabel M, Andrä H (2012) Fast numerical computation of precise bounds of effective elastic moduli. Berichte des Fraunhofer ITWM 224(224):1Google Scholar
- 38.http://www.msri.org/ (2018). Accessed 1 Jan 2018
- 41.https://www.geodict.com/ (2018). Accessed 1 Jan 2018
- 42.https://www.formlabs.com/ (2018). Accessed 1 Jan 2018
- 43.ASTM International (2015) Standard test method for compressive properties of rigid plastics. ASTM International, West ConshohockenGoogle Scholar
- 45.Gibson LJ, Ashby MF (1999) Cellular solids: structure and properties. Cambridge University Press, CambridgeGoogle Scholar
- 47.S.S.S. of America (2008) Glossary of soil science terms 2008. ASA-CSSA-SSSA, MadisonGoogle Scholar