Novel lattice structures based on triply periodic minimal surfaces
Creators: name: Peng, Chenxi
Publisher: name: RMIT University
Year: 2024
Subjects: classificationCode: 400505
subject: Construction materials
classificationCode: 401706
subject: Numerical modelling and mechanical characterisation

description: Lattice structures present exciting properties, such as high stiffness-to-weight ratio, strength-to-weight ratio, and energy absorption, which are potential candidates for various engineering applications. The mechanical properties of these materials are mainly determined by the architecture and relative density (RD) of the structure and the property of the base material. At the early research stage on lattice structures, foams were extensively investigated for their mechanical performance and utilised for various engineering applications. However, their stochastic topology led to challenges in controlling and optimising the mechanical responses of foams. With the advances in manufacturing techniques, it is now feasible to fabricate complicated geometries with excellent accuracy at different length scales. More attention has been drawn to designing appropriate topologies for lattice structures to enhance mechanical properties and multifunctionality and improve manufacturability. Recently, a novel family of bio-inspired lattice structures, namely triply periodic minimal surfaces (TPMS), has attracted attention from the research community since they exhibited superior mechanical and promising multifunctional properties. 

This work aims to study the mechanical properties and energy absorption of TPMS-based lattice structures under various loading conditions. Meanwhile, the strategies for improving the mechanical properties and energy absorption of TPMS-based lattices are also explored. Firstly, the flexural properties and energy absorption of TPMS lattices are evaluated in Chapter 2. A numerical model and analytical formulation were developed and validated by experimental data to predict the mechanical responses of sandwich beams with TPMS lattice cores under 3-point bending. A comprehensive parametric study was conducted to evaluate the effect of TPMS type, lattice core density and face-panel thickness on the flexural properties of sandwich structures with TPMS lattice cores. The results showed that the geometrical parameters and the relative density of the TPMS lattices had a considerable influence on their flexural properties and energy absorption. Among the TPMS lattices investigated, TPMS IWP lattices presented the highest flexural stiffness and strength. 

As the most current research mainly focused on the mechanical responses of TPMS lattices fabricated by a single material, the idea of improving the compressive properties of TPMS lattices by fibre-reinforced polymer (FRP) composites is evaluated in Chapter 3. A comprehensive analysis of the number of unit cells, print direction and relative density effects on the mechanical properties of 3D printed composite TPMS gyroid lattices was conducted experimentally and numerically. The impact of the slenderness ratio on the compression buckling properties of FRP TPMS gyroid lattices was also studied. The results showed that FRP TPMS gyroid lattices presented higher elastic modulus when loaded along the printing direction. FRP composite TPMS gyroid lattices showed a bending and stretching mixed deformation mode under compression. The critical buckling load was more sensitive to the changes in slenderness ratio at higher relative density. A transition from plastic yielding to elastic buckling occurred with an increase in the slenderness ratio. 

Apart from incorporating FRP composite as base material to improve the mechanical properties and energy absorption of TPMS lattices, a novel strategy to design honeycomb-like lattices with exceptional and tuneable mechanical properties and energy absorption based on the topology of TPMS is introduced in Chapter 4. Firstly, the method to create honeycomb-like structures based on the topology of TPMS was presented. Then, a numerical model was developed and validated by experimental results to evaluate the mechanical properties of G-Honeycomb and P-Honeycomb lattices. The mechanical performances of  P-Honeycomb and G-Honeycomb were analysed at various relative densities and compared with conventional square honeycombs. G-Honeycomb and P-Honeycomb presented higher elastic modulus and plateau stress than conventional square honeycombs at the same relative density. The idea of designing TPMS lattices with tuneable mechanical responses was demonstrated by introducing a density gradient and creating a G-P hybrid structure with the topology of G-Honeycomb and P-Honeycomb in different regions. The linear elastic, plateau, and densification three stages behaviour under compressive loadings of G-Honeycomb and P-Honeycomb can be turned into a gradual stiffening response, presenting tailorable and progressive failure modes. The G-P hybrid structure can also present distinct properties at different compressive strains, which can be controlled by the level-set approximation equation. 

Moreover, the mechanical properties and energy absorption of TPMS lattice under high strain rate compression and close-in blast are investigated in Chapter 5. The mechanical responses of TPMS lattice under high strain rate compression were evaluated based on numerical simulations and validated by analytical analysis. The results showed that TPMS gyroid lattices presented higher dynamic compression strength than conventional honeycomb structures. A comprehensive parametric study on the effects of core thickness, the number of layers and TPMS topology on the blast resistance of TPMS lattices were conducted. It is found that the initial peak of reaction force transmitted through the TPMS lattices increased with an increase in the thickness while the specific energy absorption reduced. By comparison, the number of layers in the TPMS lattices posed a negligible effect on the maximum reaction and energy absorption. Among the TPMS types investigated, TPMS primitive exhibited the best performance under blast loading compared to other TPMS lattices in terms of energy absorption. Additionally, uneven energy absorption across layers and stress concentration on top layers were found when TPMS lattices were subjected to impulsive loadings. 

The idea of designing functionally graded (FG) TPMS lattices to improve their mechanical properties and energy absorption when subjected to dynamic compression and blast loading is discussed in Chapter 6. A finite element model was developed and validated by experimental results. The performances of the composite sandwich panel made of functionally graded TPMS gyroid lattice core and steel facets under blast were evaluated. The results showed that for the uniform TPMS gyroid lattices, most impulsive energy was absorbed by only part of the core, while there was insignificant plastic deformation found at the bottom layers. Clear material densification was observed near the blast centre's core section. The introduction of the functionally graded TPMS gyroid lattice core noticeably improved the performance of the sandwich panel when subjected to shock impact. All the structures with FG gyroid cores can effectively reduce the stress transmitted to the concrete base compared to the baseline design. Furthermore, uniform distribution of the stress field was observed within the FG TPMS lattice. 

Overall, this work evaluates the mechanical properties and energy absorption of TPMS lattices under various loading conditions and proposes design strategies to improve the mechanical performance of TPMS lattices. TPMS lattices demonstrated promising flexural properties and resistance against dynamic loading. Meanwhile, fabricating TPMS lattices with fibre-reinforced material and designing honeycomb-like structures based on TPMS topology could improve their compressive properties and energy absorption. The results of this study could provide insights into future research on designing lightweight and functional lattice materials for various engineering applications.