Architectural Optimisation of Self-Supporting 3D Printable Lattice Structures

Abstract

Lattice materials have a cellular architecture that comprises structural members, such as struts and/or beams, which are arranged in regular spatial patterns and connected at common nodes. This class of cellular materials are of growing interest for aerospace applications, because of their unique combination of highly tailorable mechanical properties, such as specific stiffness and energy dissipation. These properties are controlled by the unit-cell topology of the lattices and are in general superior to those of other cellular materials, such as foams. Moreover, architected lattices exhibit properties that are typical of metamaterials, such as auxeticity.
Recent advances in additive manufacturing methods, in particular 3D printing, offer cheap and versatile routes for the fabrication of lattice materials and their integration in structural components. In the open literature, a wide range of design methods have been proposed to optimise the architecture of cellular lattices, aiming to enhance specific mechanical properties. A key common objective of all these approaches is to achieve a stretching dominated behaviour for the lattices, which requires the individual structural members to behave like struts rather than beams, thus minimising local flexural deformations and maximising stiffness. Nonetheless, several of these optimisation approaches assume that the structural element in the lattices can be described as essentially 1D elastic bodies (i.e. struts or beams) connected by rigid nodes. This assumption often leads to a significant underestimation of the actual compliance of the lattices. Moreover, current optimisation methods for the design of lattice-material architectures do not consider the inherent limitations of additive manufacturing methods, especially in terms of the level of geometric fidelity that can be achieved and the unavoidable presence of defects.

This dissertation presents the development of a novel high-fidelity evolutionary optimisation framework for lattice materials, which is based on modelling architected unit cells via 3D finite element analysis with periodic boundary conditions. This implies that no restrictive “a priori” assumptions are introduced regarding the kinematics of the structural members comprised in the unit cell, which are meshed using quadratic tetrahedral elements to fully capture their 3D response. Eight different lattice topologies are considered in this thesis. These comprise architectures inspired by common crystal structures, as well as their combination/superposition. The optimisation procedure involves tailoring the aspect ratio of the unit cell, as well as the geometrical dimensions (e.g. radius) of the lattice members, considering ranges of variation that exceed those than can be investigated with classical beam theories (i.e. Euler and Timoshenko). In terms of quasi-static behaviour, this study considers the compressive stiffness and the out-of-plane shear stiffness as primary performance metrics to be optimised, both individually (single-objective) and in combination (multi-objective).

The optimisation process is first carried out at unit-cell level. The results are then validated by means of experimental tests on prototype optimised lattices 3D-printed via stereolithography, under both quasi-static (compression) and dynamic (vibration transmission) conditions. Moreover, full finite-element models of the prototype lattices have been built and run to study the influence of edge effects on the mechanical performance at coupon level. Overall, it is found that the compressive stiffness of the lattices can be enhanced by 70% compared to counterparts with same topology and relative density, while the out-of-plane stiffness can be increased by a more modest 10%. The numerical simulations are in excellent agreement with the experimental results, with relative errors that typically do not exceed 10% for all the quasi-static and dynamic properties investigated. However, larger deviations (up to 30%) of the quasi-static compression modulus have been observed for two of the proposed lattice architectures. These discrepancies are caused by the presence of manufacturing defects, which are hereby characterised by high-resolution X-ray CT scans.

Date of Award	17 Jun 2025
Original language	English
Awarding Institution	University of Bristol
Supervisor	Giuliano Allegri (Supervisor), Fabrizio Scarpa (Supervisor) & Bing Zhang (Supervisor)