Periodic Reporting for period 1 - ANIMODD (Achieving animate properties with nonlinear odd solids)
Periodo di rendicontazione: 2023-09-01 al 2025-08-31
Living materials, from the cellular scale up to plants and animals, are animate: they sense, compute, and respond to their environment. These capabilities yield an impressive palette of functionality: from robust locomotion to programmable shape-change and pattern formation. Inspired by living matter, recent progress in materials science attempts to realise these animate properties in synthetic materials. A recent report from the Royal Society identifies these animate materials as ‘a new and potentially transformative class of materials’, with application anywhere a material is required to function in an unpredictable, dynamic, and potentially damaging, environment. Examples include devices operating in deep space, in contact with moving animals, or in a changing climate.
How should we design such synthetic animate materials? A particularly promising approach is the idea of an active solid: a solid material embedded with a distribution of sensors and actuators. These materials use the central concept of emergence from condensed matter physics to achieve functionality like self-folding, shape-morphing, and collective oscillation. Such robot-like behaviours do not come from any central controller. Instead, they emerge, bottom-up, from solid-body interactions between many interchangeable active units. Emergent behaviours are inherently robust, and as such are prime choices for designing adaptable functionality: if one active unit breaks, the collective behaviour of the whole solid remains unchanged.
There are many possible interactions between active units that could be designed, but one recent class stands out as a distinguished route towards animacy: non-reciprocal, or odd, interactions, in which microscopic energy injection is used to break basic symmetries like Newton’s Third Law. These odd interactions cause the internal dynamics of the material to spontaneously undergo work cycles, converting energy injection into coherent motion and making them a natural candidate for programming animate mechanical behaviours, like robust crawling and rolling, or reconfigurable pattern formation. Indeed, recent work has shown that odd interactions yield linear phenomena that are forbidden in a passive material, such as unidirectional wave amplification, and mechanical waves in overdamped media.
These linear phenomena suggest building blocks for designing animate properties. However, the wave amplification which odd interactions cause inherently leads to nonlinear mechanical deformations: indeed, the finite-amplitude cycles necessary for tasks like locomotion can only come from a balance of energy injection and nonlinearity. This nonlinear regime presents a tremendous opportunity for programming stable modes of actuation, built on excitations which are fundamentally nonlinear, like patterns and topological defects. Yet, understanding nonlinear odd solids remains a fundamental challenge, and key questions remain unanswered: can we realise and control stable nonlinear excitations in odd solids? How do these excitations react in response to environmental cues? And most crucially, how can nonlinear excitations be used to achieve animate properties?
How should we design such synthetic animate materials? A particularly promising approach is the idea of an active solid: a solid material embedded with a distribution of sensors and actuators. These materials use the central concept of emergence from condensed matter physics to achieve functionality like self-folding, shape-morphing, and collective oscillation. Such robot-like behaviours do not come from any central controller. Instead, they emerge, bottom-up, from solid-body interactions between many interchangeable active units. Emergent behaviours are inherently robust, and as such are prime choices for designing adaptable functionality: if one active unit breaks, the collective behaviour of the whole solid remains unchanged.
There are many possible interactions between active units that could be designed, but one recent class stands out as a distinguished route towards animacy: non-reciprocal, or odd, interactions, in which microscopic energy injection is used to break basic symmetries like Newton’s Third Law. These odd interactions cause the internal dynamics of the material to spontaneously undergo work cycles, converting energy injection into coherent motion and making them a natural candidate for programming animate mechanical behaviours, like robust crawling and rolling, or reconfigurable pattern formation. Indeed, recent work has shown that odd interactions yield linear phenomena that are forbidden in a passive material, such as unidirectional wave amplification, and mechanical waves in overdamped media.
These linear phenomena suggest building blocks for designing animate properties. However, the wave amplification which odd interactions cause inherently leads to nonlinear mechanical deformations: indeed, the finite-amplitude cycles necessary for tasks like locomotion can only come from a balance of energy injection and nonlinearity. This nonlinear regime presents a tremendous opportunity for programming stable modes of actuation, built on excitations which are fundamentally nonlinear, like patterns and topological defects. Yet, understanding nonlinear odd solids remains a fundamental challenge, and key questions remain unanswered: can we realise and control stable nonlinear excitations in odd solids? How do these excitations react in response to environmental cues? And most crucially, how can nonlinear excitations be used to achieve animate properties?
In this project, we characterised the nonlinear excitations of an odd solid, and used these excitations as a toolkit for designing animate properties. These fundamental results have opened a new line of research in active matter and animate materials, as well as unlocking the potential of odd solids for applications like robust locomotion and reconfigurable pattern formation.
Our work resulted in 4 publications, either published or under review, with further publications under preparation:
Publications
1. J. Veenstra, C. Scheibner, M. Brandenbourger, J. Binysh, A. Souslov, V. Vitelli and C. Coulais, Adaptive locomotion of active solids, Nature 639 935-941 (2025). https://www.nature.com/articles/s41586-025-08646-3(si apre in una nuova finestra)
2. J. Binysh, G. Baardink, J. Veenstra, C. Coulais & A. Souslov, More is less in unpercolated active solids. Preprint: arXiv: 2504.18362.
3. J. Veenstra, J. Binysh, V. Seinen, R. Naber, D. Robledo-Poisson, A. Hunt, W. v. Saarloos, A. Souslov and C. Coulais, Wave coarsening drives time crystallization in active solids, Preprint: arXiv:2508.20052.
4. S. Al-Izzi, Y.Du J. Veenstra A. Carlson, R. Morris, A. Souslov and C. Coulais, J. Binysh, Non-reciprocal Buckling Makes Active Filaments Polyfunctional, arXiv: 2510.14725
Our work resulted in 4 publications, either published or under review, with further publications under preparation:
Publications
1. J. Veenstra, C. Scheibner, M. Brandenbourger, J. Binysh, A. Souslov, V. Vitelli and C. Coulais, Adaptive locomotion of active solids, Nature 639 935-941 (2025). https://www.nature.com/articles/s41586-025-08646-3(si apre in una nuova finestra)
2. J. Binysh, G. Baardink, J. Veenstra, C. Coulais & A. Souslov, More is less in unpercolated active solids. Preprint: arXiv: 2504.18362.
3. J. Veenstra, J. Binysh, V. Seinen, R. Naber, D. Robledo-Poisson, A. Hunt, W. v. Saarloos, A. Souslov and C. Coulais, Wave coarsening drives time crystallization in active solids, Preprint: arXiv:2508.20052.
4. S. Al-Izzi, Y.Du J. Veenstra A. Carlson, R. Morris, A. Souslov and C. Coulais, J. Binysh, Non-reciprocal Buckling Makes Active Filaments Polyfunctional, arXiv: 2510.14725
ANIMODD has laid the groundwork for autonomous metamaterials that use non-reciprocity to shape shift and locomote in a multimodal way. We have built 2D prototype technologies that embody these advances, as shown in the attached images. Beyond building these structures, we have also developed a fundamental understanding of their mechanics. We now estimate the TRL of our robotic metamaterials to be between 2 and 3. Beyond the project, we will leverage these advances towards 3D materials and application. We will target end-users interested in advanced vibration damping and autonomous robotics. These end-users include Prof. Coulais’ own spinout company with Tata Steel, ATG Europe, Airbus, ASML, and the prosthetics company Livit. We anticipate non-reciprocal solids becoming a new tool for designing autonomous robotics which complements more traditional centralized approaches based on control.