Numerical and Analytical Modelling of Nacre-Inspired Auxetic Mechanical Metamaterials

Nacre, known for its brick-and-mortar structure consisting of 95% aragonite and 5% organic matrix, exhibits auxetic behaviour, as shown through experimental analyses. The auxeticity of nacre is still widely unexplored, with no conclusive answer as to the mechanism causing this unexpected property. This project aims to investigate the speculative theories on the mechanisms causing the auxeticity of nacre and further look into how the negative Poisson’s ratio (NPR) can be enhanced. This project utilises analytical and numerical modelling to create and optimise nacre-inspired mechanical metamaterial with negative Poisson’s ratio. The focus of the models was to explore the mechanisms that could explain nacre’s auxeticity but also to find the correlation between Poisson’s ratio (PR) and the geometrical parameters. Four different models were presented in the literature review, and three of them were further modelled. Focus was given to mechanism 1, which speculated on the role of the mortar in the nacre's auxeticity. Mechanisms 2 and 3 were explored and investigated the role of brick morphology and connectivity. Analyses of mechanism 1 revealed dependencies of PR on volume ratio (the ratio of volume of bricks and mortar) and geometry, indicating that higher volume ratio models had lower PR but were prone to experienced yielding at lower strains. Combined bending and axial deformation of the struts in the X-shaped mortar was identified as a significant factor in the NPR of the 2D model of mechanism 1. The 2D numerical model of mechanism 1 exhibited the same behaviour pattern as nacre but with lower PR, signifying the model’s validity and making it a good contender for an explanation of nacre’s auxetic behaviour. Mechanism 1 was then explored as a 3D numerical model. The 3D models showed altered deformation mechanisms and NPR behaviour. It was recognised that the depth of the 3D models prevented the structures from showing the same behaviours as 2D models. The structure was not slender enough to experience the same type of deformation. The out-of-plane deformation was thought to be another contributing factor. To rectify this, a thin structure with beam elements was created. The beam 3D structure showed similar variability of PR as the 2D models, but no exact match was found. The lowest PR achieved through numerical modelling of mechanism 1 was during the 2D analysis showing a PR of approximately -0.80 for the volume ratio of 0.91. The project underscores the significance of understanding geometric properties and deformation behaviours in auxetic materials, providing insights into optimising NPR in nacre-inspired mechanical metamaterials.