Parametric Studies and Data Development of Two-dimensional Cellular Structures and Crystals at Different Length Scales

Abstract

The work presented in the thesis is focused on developing effective data-led simulation approaches for studying the behaviour and properties of auxetic structures and crystals with a particular focus on the Poisson’s ratio, auxeticity and anisotropy. Python based parametric programs are developed and integrated with Finite element modelling (Abaqus) and ab initio quantum mechanical programs (Materials Studio CASTEP) for structure development and data processing. A range of auxetic structures have been studied including missing rib structures in tension, missing rib and mixed cellular structures in compression and self-similar hierarchical structures in compression. A Python program is also developed for calculating and tracking of the area changes for cellular structures under compression and tension loads. The use of Python programs in developing Voronoi random structures and random structures with auxetic behaviors is also presented. The models are used to establish the effect of key dimensional parameters on the deformation process, Poisson’s ratio and stability of auxeticity. The results show that the area analysis is effective in studying the changes in cell shape and area; the areas of the missing rib and honeycomb cell follows a more uniform cell deformation trend in tension than in compression. The area changes of the missing rib model under compression reflect the main deformation stages including the corner edge-cell wall contact. The work shows that deformation and instability auxeticity of normal missing rib structure and mixed structures are associated with the corner edge wall contact. The mixed model showed different beam–wall contact patterns, which contributes to the much higher critical strain of stable auxeticity and overall shape stability. The work with ab initio quantum mechanical program (Materials Studio CASTEP) is focused on developing a Python-based data system for systematic crystal structure processing and establishing the link between crystal structures and key ground state properties of crystals based on first principle calculations with Materials Studio. A range of ground state properties (e.g., elastic constants (Cij), bulk modulus (K), Young’s modulus (E), shear modulus (G), Poisson’s ratio (v), etc.) have been studied with a particular focus on the Poisson’s ratio and anisotropy. The correlation between the ground state elastic parameters and other properties are analysed. Some typical results on key engineering carbides including simple cubic systems (TiC, VC and NbC) are presented together with the mathematical operation to calculate the K, E, G, v. 3D surface constructions of the ground state parameters including anisotropic features are presented with an integrated program. The Python graphical user interface developed is effective for systematic calculation and visualization of the key structures, properties and anisotropy features. The relationship between maxima and minima of Poisson’s ratio and the anisotropy index of a range of carbides showed a good agreement with the other published data based on a large quantity of data. Some compounds with low or negative Poisson’s ratio were identified and detailed structures and properties data are given. The data highlighted the source of uncertainty in Poisson’s ratio and the link between property data. The Data for structures with Negative Poisson’s ratio is briefly presented and analysed including links between the auxetic crystal structure and some macro lattice structure with auxetic behaviors. The procedure for modelling surface energy, oxygen reduction reaction (ORR), crystals with doping elements and the effect of temperatures are also presented and showed a good agreement with published works. Future use of the framework developed, and main research focuses in both FE modelling and ab initio quantum mechanical simulation are discussed.