Novel superior materials based on aperiodic tilings
Lead Research Organisation:
The Open University
Department Name: Faculty of Sci, Tech, Eng & Maths (STEM)
Abstract
Our world contains ample manifestations of order, both in products of human civilisation (such as art, music or architecture) and in the natural world (with crystals representing the ultimate ordered structure). The surprise discovery of quasicrystals, honoured with the 2011 Nobel Prize in Chemistry, inspires continuing research into properties and applications of these fascinating materials, which exhibit order without periodicity, and are formalised in the mathematics of aperiodically ordered structures.
Aperiodically ordered spatial arrangements open up fascinating opportunities of purpose-made structures, including smart materials. Additive Manufacturing makes it possible to produce such materials cheaply and reliably, with potentially huge impact across a vast area of applications, such as bespoke orthopaedic implants, one of a kind space components and aerospace components produced from valuable raw materials. The investigation of aperiodic metamaterials has only just begun, with an emphasis on photonic materials; there have been no attempts as yet to explore materials with superior mechanical properties based on aperiodic arrangements.
For instance, cellular structures are used as a means of tailoring the stiffness of orthopaedic implants to match that of the receiving bone. The current state of the art employs cubic or hexagonal lattices, which result in undesirable mechanical anisotropy, often requiring over-engineering to ensure sufficient mechanical performance. To recreate the pseudo-random structures present in bone in a repeatable fashion using digital manufacturing is a key limitation in the realisation of 'print-to-order' orthopaedic implants. Aperiodic structures have a key advantage: they can realise higher symmetries that are incompatible with lattice periodicity, making it possible to avoid anisotropies while maintaining a well-defined, deterministic, algorithmically reproducible structure.
The proposed research will lay the mathematical groundwork for applications. We will create, establish, evaluate and verify mathematical models to determine the elastic properties of nearly isotropic cellular materials based on aperiodic tilings.
Aperiodically ordered spatial arrangements open up fascinating opportunities of purpose-made structures, including smart materials. Additive Manufacturing makes it possible to produce such materials cheaply and reliably, with potentially huge impact across a vast area of applications, such as bespoke orthopaedic implants, one of a kind space components and aerospace components produced from valuable raw materials. The investigation of aperiodic metamaterials has only just begun, with an emphasis on photonic materials; there have been no attempts as yet to explore materials with superior mechanical properties based on aperiodic arrangements.
For instance, cellular structures are used as a means of tailoring the stiffness of orthopaedic implants to match that of the receiving bone. The current state of the art employs cubic or hexagonal lattices, which result in undesirable mechanical anisotropy, often requiring over-engineering to ensure sufficient mechanical performance. To recreate the pseudo-random structures present in bone in a repeatable fashion using digital manufacturing is a key limitation in the realisation of 'print-to-order' orthopaedic implants. Aperiodic structures have a key advantage: they can realise higher symmetries that are incompatible with lattice periodicity, making it possible to avoid anisotropies while maintaining a well-defined, deterministic, algorithmically reproducible structure.
The proposed research will lay the mathematical groundwork for applications. We will create, establish, evaluate and verify mathematical models to determine the elastic properties of nearly isotropic cellular materials based on aperiodic tilings.
Organisations
Publications
Clarke D
(2024)
Identification of mechanically representative samples for aperiodic honeycombs
in Materials Today Communications
Clarke D
(2023)
A systematic numerical and experimental study into the mechanical properties of five honeycombs
in Composites Part B: Engineering
Clarke D
(2023)
An isotropic zero Poisson's ratio metamaterial based on the aperiodic 'hat' monotile
in Applied Materials Today
Imediegwu C
(2023)
Mechanical characterisation of novel aperiodic lattice structures
in Materials & Design
Imediegwu C
(2023)
A computational method for determining the linear elastic properties of 2D aperiodic lattice structures
in The Journal of Strain Analysis for Engineering Design
Moat R
(2022)
Compressive behaviour of cellular structures with aperiodic order
in Results in Materials
Moat R
(2024)
A class of aperiodic honeycombs with tuneable mechanical properties
in Applied Materials Today
Description | Aperiodic tilings exhibition |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | Regional |
Primary Audience | Public/other audiences |
Results and Impact | The event consisted of a formal interdisciplinary academic conference, Art exhibition and hands on engagement activities in memory of the passing of Prof Uwe Grimm. This brought together engineers, mathematicians, artists and educators with a common interest in tilings and patterns. The event was extremely successful with over 700 visitors to the exhibition over two days, including 450 school students. Comments from those who attended included: 'I was greatly impressed by the range and depth of art displayed. For me, this was the largest collection of aperiodic art I have ever seen' and 'The exhibition was a unique experience bringing together mathematicians, engineers, artists, educators, school children and members of the local community.' Teachers of students who attended further commented "They certainly were given the opportunity to see maths in a very different way" and "This has had such an effect on one pupil that they have set up a geometric art club in the library at lunchtime back in school." Researchers from the NOVMAT team exhibited work from the project, presented in the formal academic session and led groups during the student sessions. The event resulted in internal collaboration and interest from new external partners. |
Year(s) Of Engagement Activity | 2022 |
URL | https://www.open.ac.uk/stem/mathematics-and-statistics/aperiodic-tilings-2022 |