Design and optimization of lattice structures and mechanical metamaterials for additive manufacturing

This PhD thesis focuses on the design, optimization, and additive manufacturing (AM) of lattice structures and mechanical metamaterials. These materials, characterized by their cellular nature, possess unique properties primarily determined by the design of their individual cells rather than the properties of the bulk material from which they are constructed. Mechanical metamaterials exhibit properties which are uncommon in nature, indicating a spectrum of potential applications. This study proposes various modelling strategies, based on explicit, implicit, and parametric functions, for the design of lattice structures and mechanical metamaterials. The responses of these structures are investigated through numerical simulations and experimental testing. For tailored responses, these structures are tuned using an optimization strategy using a genetic algorithm (GA). The study develops, simulates, and tests a range of different designs exhibiting unique properties, such as programmable permeability, auxetic response, and dual-stiffness characteristics. Various AM processes, including Digital Light Processing (DLP), Fused Deposition Modelling (FDM), and Selective Laser Sintering (SLS), are employed for the fabrication of the designed lattice structures and metamaterials.

The thesis begins with a comprehensive literature review on lattice structure and mechanical metamaterial design for AM. Subsequently, the mechanical properties of different lattice structures fabricated through SLS and DLP are investigated. The numerical and experimental results from compression testing are compared and discussed, revealing the effect of these AM processes on the mechanical response and the discrepancy between numerical and experimental outcomes.

Evolving the understanding of the mechanical behaviour of the lattice structures, a multi-objective GA is utilized to optimize the shape of a body-centred cubic (BCC) lattice structure for maximum stiffness and minimum von Mises stress. An implicit model of BCC is integrated with Finite Element Analysis (FEA) and GA to perform shape optimization for the best response. The numerical results obtained from this method are compared with those of a classical model of a BCC structure to assess the efficiency of the presented optimization approach. These findings are supported by experimental testing of selected designs fabricated through DLP.

The methodology is further applied to the design of a 2D auxetic metamaterial featuring variable permeability. A parametric equation defines the unit cell of the auxetic structure, which is then utilized as a programmable filtering medium capable of filtering particles of specific sizes. GA is employed to optimize the geometry of the auxetic structure for effective particle filtration under uniaxial applied strain. A prototype is fabricated through FDM and tested to evaluate the effectiveness of the developed filtering medium.

Furthermore, the design methodology is expanded to the development of 3D metamaterials offering a spectrum of mechanical properties. An explicit equation-based model consisting of three design variables is employed to construct a unit cell. The effect of varying each design variable on the resulting geometry and its corresponding mechanical response is investigated. A variety of design configurations possessing unique properties are presented and discussed, including 3D auxetic structures and dual-stiffness materials, which are designed, simulated, and experimentally tested.

This work has achieved significant milestones, including the creation of a versatile programmable lattice metamaterial designed for various functions and applications. An important objective was met by integrating a multi-objective optimization approach, seamlessly incorporating a parametric design algorithm into the optimization process. To demonstrate the practicality of these lattice metamaterial designs, a variety of applications were explored by fabrication of the developed metamaterials through AM processes. The study concludes by showcasing the proposed programmable metamaterial designs, categorizing lattice metamaterials systematically, evaluating current limitations in metamaterial design and fabrication technologies, and offering recommendations for future research directions. These recommendations focus on expanding and implementing innovative techniques and tools for metamaterial development.