Machine Learning Aided Optimisation of Mechanical Metamaterials

Abstract

Mechanical metamaterials are a group of specially designed periodic material structures that exhibit properties not found in naturally occurring materials. These structures often consist of lattices of repeated unit cells of translational symmetry. The novel properties of these structures are often a result of their unique geometry features or material compositions. In this thesis, two main categories of mechanical metamaterials are investigated in detail. They are elastic metamaterials (EMMs) and auxetic metamaterials (AMMs). Elastic metamaterials are known for their ability of wave manipulation. In particular, the EMMs of interest in our work present complete bandgaps in the wave band structure, indicating attenuation of all wave propagation through the structure within the corresponding frequency spectra. AMMs are a group of material structures known for their unusual behavioural patterns under mechanical deformation. More specifically, the cross-chiral metamaterial structures (CMSs) investigated in this work exhibit simultaneous expansion or compression in both the longitudinal (parallel to loading) and the transverse (perpendicular to loading) directions. This behaviour is characterised as having a negative Poisson's ratio (NPR), which contradicts the natural deformation pattern of natural homogenous materials. Collectively, these two categories of materials share the focus of the research presented in this thesis for their novel properties and wide range of applications. A great deal of challenges in engineering designs of metamaterial structures stems from attempting to their structure in a fine but controllable geometry based on a performance criterion. The main goal of this study is to develop an accurate and rapid optimisation approach that combines finite element analysis (FEA) simulation, numerical optimisation methods, and surrogate models to alleviate the high demand for computational powers by FEA solvers. In this thesis, the parametric optimisation of EMMs and AMMs is discussed and validated with physical experiments. Numerical optimisation methods are explored, including the Nelder-Mead (NM) downhill simplex method and Genetic Algorithm (GA) based methods. For EMM structures, the main performance benchmark is determined to be the relative width of the primary bandgap, while several structural characteristics are considered in the CMSs, namely, maximum von Mises stress, NPR, volume-specific energy absorption and buckling resistance. Comparison between the optimised structure and the original in all cases reveals improvement in the mechanical performance of the metamaterial structure, which subsequently proves the proposed optimisation approach to be effective and efficient. One of the fundamental challenges of structural optimization of metamaterial structures with complex geometry lies within the high consumption of computational power associated with finite element analysis (FEA) simulations, which often renders the numerical solution an ineffective and costly attempt. Additionally, due to the inherent mesh dependence of the FEA method, minuscule geometry features, which often arise during optimization, demand very fine elements, resulting in enormously high time consumption, especially when repetitive solutions are needed for objective function validations. To cope with this drawback, a surrogate model is developed based on machine learning techniques to reduce computational time in the structural optimization of EMMs and CMSs. The surrogate model is constructed based on a multilayer feedforward artificial neural network (ANN) architecture, trained with machine learning techniques and optimized through a genetic algorithm (GA) program to improve its accuracy. Numerical optimisation methods are employed to build optimisation algorithms with the trained and optimized ANN surrogate at the core. Show more