Graph-based Learning and design of Advanced Mechanical Metamaterials
Lead Research Organisation:
University of Cambridge
Department Name: Engineering
Abstract
The emergence of additive manufacturing techniques has enabled the creation of complex 3D shapes with topological feature sizes spanning length scales from nanometres upwards. These manufacturing technologies have facilitated the creation of new materials (metamaterials) with previously unattainable properties such as light and recoverable ceramics. However, defects (deviations from the design) caused by manufacturing variabilities proliferate in topologically complex printed samples comprising millions of micro-scale elements. Traditional numerical simulations do not capture these a priori unknown defects, and thus the measured properties of fabricated metamaterials invariably deviate substantially from the designed/simulated properties. This low fidelity of the metamaterial simulation tools has left a vast portion of the metamaterial design space untapped. Leveraging recent foundational advances in machine learning and graph neural networks (GNNs), now is the ideal time for designing new additively manufactured materials with fully tailorable static and dynamic properties wherein, for example, a designer inputs a wave transmission spectrum from which a metamaterial that fully replicates the input response in an experimental setting is inversely designed and printed. Graph-based data-driven methods can address this challenge by their ability to learn from experimental data and efficiently encode the 3D material topology. The proposal will break new ground by exploiting breakthroughs in graph-based generative machine learning models to inversely generate metamaterials and thereby fuse the field of GNNs with mechanics, materials science, and additive manufacturing. This represents a fundamentally new realm of engineered material creation and discovery paradigm that will bridge the longstanding gap between simulation and experimental data of 3D printed metamaterials. The project will lay the scientific foundations for new engineering material designs and solutions.
People |
ORCID iD |
| Vikram Deshpande (Principal Investigator) |
Publications
AlMahri S
(2023)
Underexcitation prevents crystallization of granular assemblies subjected to high-frequency vibration.
in Proceedings of the National Academy of Sciences of the United States of America
Carlsson J
(2024)
The compressive response of the filled Kelvin foam
in European Journal of Mechanics - A/Solids
Cheng L
(2023)
Effect of water content on the constitutive response of a cellulose foam
in European Journal of Mechanics - A/Solids
Das R
(2024)
Imbibition of water into a cellulose foam: The kinetics
in Journal of the Mechanics and Physics of Solids
Das R
(2025)
Capillary rise in a packing of glass spheres
in Journal of the Mechanics and Physics of Solids
Grega I
(2022)
Gravity enables self-assembly
in Natural Sciences
Grega I
(2025)
Graph neural networks for strut-based architected solids
in Journal of the Mechanics and Physics of Solids
Grega, I
(2024)
Energy-conserving equivariant GNN for elasticity of lattice architected metamaterials
in Energy-conserving equivariant GNN for elasticity of lattice architected metamaterials
Grega, I
(2024)
Neural rendering enables dynamic tomography
in Neural rendering enables dynamic tomography
Ha CS
(2023)
Rapid inverse design of metamaterials based on prescribed mechanical behavior through machine learning.
in Nature communications
| Description | Engineering polymers, including rubbers, find extensive applications across diverse industries, from aerospace to medicine. Beginning with Hooke's law in the 1660s to the 1930s and 1940s work of Flory on polymer chains (1974 Nobel prize), the understanding of rubber elasticity was formalised in the 1940s via the Neo-Hookean model. This established the idea that, under isothermal conditions, stress is (non)linearly related to strain and no other state variable. Wang et al have made striking three-dimensional (3D) measurements to show that this fundamental concept needs to be revisited. They designed laboratory-based X-ray tomography experiments to show that a motile un-crosslinked phase exists within rubber and many engineering polymers, such as Nylon and HDPE. This adds an additional state variable and consequently, spatial variations of gradient of stress (or strain) play a role in setting their mechanical behaviour. The implication is that material properties of polymers cannot be defined solely in terms of the local material strain over-turning long established and pervasive assumptions. The measurements of Wang et al. show that in the presence of spatial gradients in deformation (which are ubiquitous in applications): (i) There are significant local volume changes (±10%) over millimetre length scales, but the specimen overall is incompressible. (ii) Locally, the material volume can decrease even if the hydrostatic stress (pressure) is tensile, giving rise to an apparent negative bulk modulus. They have rationalised these observations within a new thermodynamic framework to replace the classical Neo-Hookean ideas of elasticity. These findings open new directions to understand and manipulate rubber elasticity and the behaviour of widely used polymers. Polymers represent a very wide class of materials that find significant applications especially in bioengineering. The work of Wang et al. opens new directions for the efficient design and application of this wide class of materials. |
| Exploitation Route | The findings of Wang et al. revise some of the most established ideas in the mechanical behaviour of polymers. However, as with any ground-breaking study, this paper opens new avenues of research across many disciplines. The immediate ideas that come to mind are: (i) Wang et al. show via direct observations that the mobile phase within rubbers has a mobility that is more than 1000x higher than water in a hydrogel- what are the molecular mechanisms that endow such a high mobility to large polymeric molecules? (ii) A corollary to their study is that the mobile phase crystallises within the rubber much like a liquid crystal. Can this unique mixture of a liquid crystal within a solid be exploited for novel multi-functional applications? (iii) A key part of the study was the development of the X-ray technique (Flux Enhanced Tomography for Correlation). This technique provides, for the first time, a general method for generating measured 3D deformation field datasets. Such data is a key and currently missing ingredient for the burgeoning field of data-driven mechanics. The combination of such measurements with emerging machine learning (ML) techniques has the potential to fundamentally transform the nature of modelling of materials. |
| Sectors | Education |
| Description | Adaptable mechanical metamaterials with tailorable toughness and energy absorption |
| Amount | $430,000 (USD) |
| Funding ID | N000142412519 |
| Organisation | US Navy |
| Department | US Office of Naval Research Global |
| Sector | Academic/University |
| Country | United States |
| Start | 08/2024 |
| End | 08/2028 |
| Description | Architected Materials for flow control |
| Amount | $296,718 (USD) |
| Organisation | Intellectual Ventures |
| Sector | Private |
| Country | United States |
| Start | 03/2024 |
| End | 06/2025 |
| Description | CMMI-EPSRC Damage Tolerant 3D microarchitectured brittle materials |
| Amount | £398,867 (GBP) |
| Funding ID | EP/Y032489/1 |
| Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
| Sector | Public |
| Country | United Kingdom |
| Start | 01/2024 |
| End | 12/2026 |
| Description | Multimaterial blisk design via high throughput tomographic full-field characterization and unsupervised ML models |
| Amount | $1,726,065 (USD) |
| Funding ID | HR001123S0029-METALS-FP |
| Organisation | University of Virginia (UVa) |
| Sector | Academic/University |
| Country | United States |
| Start | 02/2024 |
| End | 02/2026 |
| Description | Using Data-Driven Mechanics to create high-fidelity soft composite material constitutive models for improved process simulation |
| Amount | $578,139 (USD) |
| Funding ID | #2024-UI-PA-086 |
| Organisation | Boeing |
| Sector | Private |
| Country | United States |
| Start | 01/2025 |
| End | 12/2027 |
| Title | Research Data supporting "3D observations provide striking findings in rubber elasticity" |
| Description | There are five .rar files, corresponding to Figure 1 to Figure 5. Please unzip to access the dataset. In each figure folder, there are subfolders (named as "A", "B", "C", ) that contain data of each subfigure, namely Figure 1A, Figure 1B, etc... There are four types of data format, namely vtk, xlsx, mat, and opju. Here is a detailed guidance |
| Type Of Material | Database/Collection of data |
| Year Produced | 2024 |
| Provided To Others? | Yes |
| Impact | related to a PNAS paper by PI |
| URL | https://www.repository.cam.ac.uk/items/af0c1ebe-132f-4fa9-84c9-a7c28279eee8 |
| Description | Hexcel research collaboration |
| Organisation | Hexcel Composites Ltd |
| Country | United Kingdom |
| Sector | Private |
| PI Contribution | collaborative work on wire knotting |
| Collaborator Contribution | knowledge exchange |
| Impact | paper |
| Start Year | 2022 |
| Description | Ivan Grega (PhD student) on secondment to Mila - Quebec AI Institute |
| Organisation | Mila - Quebec AI Institute |
| Country | Canada |
| Sector | Private |
| PI Contribution | PhD student expanded his knowledge |
| Collaborator Contribution | knowledge transfer |
| Impact | papers |
| Start Year | 2024 |
| Title | Energy-conserving equivariant GNN for elasticity of lattice architected metamaterials |
| Description | This is the code for "Energy-conserving equivariant GNN for elasticity of lattice architected metamaterials" Work presented at the International Conference on Learning Representations (ICLR) 2024. Link to paper: https://openreview.net/forum?id=smy4DsUbBo https://arxiv.org/abs/2401.16914 |
| Type Of Technology | Software |
| Year Produced | 2024 |
| Open Source License? | Yes |
| Impact | Work presented at the International Conference on Learning Representations (ICLR) 2024. |
| Description | ASME meeting - Portland, Oregon, USA |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | meeting other academics in our field |
| Year(s) Of Engagement Activity | 2024 |
| Description | Barty Wardell - talk at EuroMech 2023 conference Eindhoven, Netherlands |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | presenting research |
| Year(s) Of Engagement Activity | 2023 |
| Description | EMMC19 - Talk |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | giving presentation |
| Year(s) Of Engagement Activity | 2024 |
| Description | EMMC19 Madrid, Spain - Talk by Ivan Grega |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Presenting research |
| Year(s) Of Engagement Activity | 2024 |
| Description | EMMC19 Madrid, Spain - Talk by Dr Vatsa Gandi |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Presenting research |
| Year(s) Of Engagement Activity | 2024 |
| Description | EMMC19 Madrid, Spain - Talk by Dr Zifan Wang |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Presenting research |
| Year(s) Of Engagement Activity | 2024 |
| Description | EMMC19 Madrid, Spain - Talk by Dr Shuvrangsu Das |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Presenting research |
| Year(s) Of Engagement Activity | 2024 |
| Description | ETH visit |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Postgraduate students |
| Results and Impact | Workshop on advances on fracture mechanics for post-grad students |
| Year(s) Of Engagement Activity | 2023 |
| Description | EuroMech Symposium Sirmione, Italy |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | meetings with other academics |
| Year(s) Of Engagement Activity | 2023 |
| Description | EuroMech symposium Sirmione 2023 |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | Giving a presentation |
| Year(s) Of Engagement Activity | 2023 |
| Description | Keynote lecture at IUTAM symposium 'Frontiers of Solid Mechanics for Energy Transition' |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | Talk to solids mechanics community |
| Year(s) Of Engagement Activity | 2024 |
| Description | Plenary Lecture CFRAC |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Plenary lecture at the CFRAC2023 in Prague |
| Year(s) Of Engagement Activity | 2023 |
| Description | RAM3 conference - Rome, Italy |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | presenting my work |
| Year(s) Of Engagement Activity | 2024 |
| Description | SES Prager medal lecture |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Prager Medal Lecture |
| Year(s) Of Engagement Activity | 2022 |
| Description | Talk at EMMC 19 Madrid Spain |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | meetings with other academics |
| Year(s) Of Engagement Activity | 2024 |
| Description | University of California Santa Barbra - Workshop |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | working with colleagues |
| Year(s) Of Engagement Activity | 2024 |
| Description | Visit to MIT |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | Presenting my work to colleagues |
| Year(s) Of Engagement Activity | 2024 |
| Description | Visit to Princeton University |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | Presenting my work to colleagues |
| Year(s) Of Engagement Activity | 2024 |
| Description | walker lecture a&m |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Postgraduate students |
| Results and Impact | Named lecture "Walker Eminent lecture" at Texas A&M |
| Year(s) Of Engagement Activity | 2023 |