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A Design Methodology for Graded Density Triply Periodic Minimal Surfaces

Abstract:

Functionally Graded Cellular Materials (FGCM), characterized by a gradual change in their properties, have previously reported better mechanical responses than their uniform counterparts. One particular example of FGCM corresponds to the application of a gradient in the density. In this context, the use of variable volume fraction cells can further improve the generation of lightweight internal structures for additive manufacturing. Accordingly, this study considers the implementation of Triply Periodic Minimal Surfaces (TPMS) as elements for cellular constructs, given their advantages compared to traditional CAD lattices. Even though previous efforts in the literature have explored the generation of models with variable density TPMS, a modelling procedure has not been formally defined. Therefore, the main objective of this study is to propose a general design methodology for the development of graded density Primitive and Gyroid surfaces, which are common examples of TPMS, while considering a variation of the unit-cells’ design parameters, i.e. the pattern thickness and unit-cell length. The desired parameter variation is then used for the generation of the TPMS constructs by a manipulation of the TPMS function variables or the meshing process, inside a pre-defined design space. The differences in surface generation depending on TPMS type and input design parameters are presented and discussed, along perspectives for the process’s improvement. Ultimately, graded density TPMS can be developed in combination with topological optimization procedures of penalization algorithms for intermediate densities, while accounting for manufacturability restrictions.