Modeling Symmetric Minimal Surfaces by Mesh Subdivision

Stefano Rosso,Andrea Curtarello,Federico Basana,Gianmaria Concheri,Gianpaolo Savio,Luca Grigolato,Roberto Meneghello

doi:10.1007/978-3-030-70566-4_40

Abstract

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.

Highlights

The spreading of additive manufacturing (AM) technologies makes it possible to produce parts with unprecedented complexity, such as biomimicry products, organic shapes and lightweight components
Minimal surfaces repeating themselves in three dimensions are called triply periodic minimal surfaces (TPMS) [8]
The findings show the accuracy of the proposed modeling method; more, the numerical model allows to relate the thickness of the part to the mechanical properties by simulating a single cell inside the lattice structure, saving computational time, and giving directions for tailored applications with lattices that present variable properties in the design volume

Summary

Introduction

The spreading of additive manufacturing (AM) technologies makes it possible to produce parts with unprecedented complexity, such as biomimicry products, organic shapes and lightweight components. Minimal surfaces repeating themselves in three dimensions are called triply periodic minimal surfaces (TPMS) [8]. These surfaces have received huge attention in the research community due to their intrinsic properties [9], especially in the biomedical field, where it is mandatory to use porous scaffolds designed to allow fluid exchange and tissue regrowth [10, 11]. Due to their curvature continuity, the stress concentration at nodal points is eliminated and fatigue life is improved compared to beam-like lattice structures [12]

Methods

Results

Conclusion