Practical Design of Additively Manufactured Auxetic Metamaterials

: (Alternative Format Thesis)

Abstract

In biology, useful strain responses are often created not by rigid mechanisms but by soft structures with variable local properties. These structures create bespoke strain responses out of sparse mechanisms far below the scale of the resulting object. They form the natural analogue to mechanical metamaterials and the inspiration for them. Being able to utilise mechanical metamaterials in design requires the ability to leverage the Poisson’s ratio to create custom deformation patterns in bulk structures. Ideal elastic isotropic structures have two fundamental properties: the Young’s Modulus and the Poisson’s ratio. The former controls the magnitude of a response to load, the latter the transverse spread. Useful mechanisms of this type require the direction of the spread to be controlled, so need both volume conserving and auxetic behaviours to be locally present. This thesis investigated practical design of these auxetic structures, with a focus on behaviour at and below a unit cell scale to allow for precise leveraging of deformation and to develop structures which mirror the beneficial properties found in nature.

A review of recent literature revealed a wide array of structures with high complexity that achieve a range of desired properties, but only do so in theory. Such structures typically under-perform when homogenised or manufactured and often are not manufacturable at all. The range of designs and their common impracticality attest to the fact that sub-cell behaviour and the impact of this on auxetic structure design is not well understood. To address this research gap, a layered ontology was created which builds mechanical metamaterials from paradigms in free space, through functions and parameters. It allows manufacturing and simplicity constraints to be applied to the structures at the fundamental level of structural design.

Applying the paradigm ontology allowed the design of several improved auxetic structures. A series of cells in the star re-entrant paradigm were trialled to create near-isotropic lattice metamaterials with minimised Poisson’s ratios, resulting in the identification of rhombic dodecahedral tessellation as a potential route to increase the directional consistency of auxetic behaviour with increased stiffness and reduced Poisson’s ratios. The cubic cell showed a baseline Poisson’s ratio of -0.449 and anisotropic range of 0.022, but the dodecahedral cells demonstrated higher stiffness with a Poisson’s ratio of -0.401 and range of 0.085 as a viable alternative structural design, with a 2.5× higher infill percentage. The function form section of the ontology was also used to create curved link auxetic structures which were able to take the known cube-celled re-entrant auxetic structure and reduce the Poisson’s ratio by around 0.3, with consistent reductions across the entire strain range. This was done without significantly impacting manufacturability, and the link curvature allowed for reduction of the peak stress at the concave joint which increased the elastic range of the structures. These studies were able to link auxetic behaviour to the edge length per unit volume, a theory which reversed the conventional wisdom of design for re-entrant structures that links the stress concentration to the Poisson’s ratio and creating a new form of auxetic lattice with more useful and robust auxetic behaviour.

During these tests, it became clear that the impact of sub-cell deformation at the concave joint on global structural properties was significant. The literature review found that due to the complexity of mapping local behaviour in situ it is a remarkably little discussed part of auxetic behaviour. High energy X-ray diffraction on aluminium alloy prints from the re-entrant paradigm was used to investigate print scale and the true distribution of the strains in the structures in situ. This gave an unparalleled resolution of the sub-cell deformation patterns and provided useful data for comparison to a range of existing models. The literature-derived benchmark of a 5 × 5 cell array showing a good representation of infinite grid behaviour was validated, with this being the point at which a constant expansion plateau begins to be evident in strained structures. Further, the concave joint was experimentally confirmed to be the critical area for auxetic cell design. This location was found to be the nucleation point for plastic deformation, and the peak stresses at this location were shown to dominate the load bearing efficiency of the whole structure. To assess the impact of scale-dependent print defects that abridge the re-entrant joint, various fillet radii were imposed onto the samples and tested in situ in this manner. The imposed fillets reduced auxetic behaviour but were able to increase the specific energy absorption of the structure at yield by 63%. Despite this, imposed abridgements of the concave joints were found to severely diminish auxetic behaviour. Balancing these competing factors with measures of the influence of boundary conditions allowed for the derivation of ideal auxetic scales and demonstrated the fundamental divide in optimal scales between load bearing and deforming auxetic structures.

None of these findings would be useful without ensuring manufacturability. A series of studies were undertaken detailing approaches to ensuring cell manufacturing is robust in both stereolithography and fused filament printing methods. The need to address the complexity of design for additive manufacturing culminated in the creation of a Bayesian algorithmic tool designed to assess parts for print viability in a geometry agnostic manner. This was shown to be adaptable to new technologies and transparent to users when highlighting risk regions in designs.

This PhD has resulted in a set of improved auxetic metamaterials with Poisson’s ratios up to 60% lower than the equivalent structures in literature throughout a widened elastic strain domain. It has created new approaches to design and new understandings of the causes of auxetic behaviour. All resulting structures have been validated through physical testing and adhered to design for manufacturing principles, while providing useful insights and meaningful developments to the practically achievable behaviour of auxetic structures. These pave the way to graded structures encoded with complex designed strain responses that have applications across engineering; sports, medical and beyond. The capability for designers to leverage graded behaviour to encode mechanisms in bulk structures as seen across nature has been increased through the developments that were made.

Date of Award	24 Jun 2026
Original language	English
Awarding Institution	University of Bath
Supervisor	Vimal Dhokia (Supervisor), Elise Pegg (Supervisor), Alexander Lunt (Supervisor) & Neill Campbell (Supervisor)