arXiv subjects

Corentin Coulais

Publications and source records attributed to Corentin Coulais.

At least 19 recordsLinked to original sources

arXiv2026

Tuning nonlinear waves in nonreciprocal active filaments

The instabilities of slender structures power biological locomotion across scales, and offer a compelling method to actuate soft robots. Nonreciprocal elastic solids have been found to amplify flexural waves in one direction only, but design principles to tune and stabilize these waves are missing. Here we develop a geometrically exact theory of nonreciprocal filaments and provide simulations that capture their post-instability nonlinear dynamics. We find that nonreciprocity, when coupled to inertia or pre-stress, amplifies and advects curvature variations. The resulting one-way patterns of shape morphing can then be selected via dissipative interactions with the environment. Our work offers a continuum-based strategy for how internal stresses can drive active unidirectional waves without need for additional degrees of freedom.

cond-mat.soft↗

arXiv2026

Dynamical frustration in spacetime metamaterials enables cascading logic and synchronization

Spacetime metamaterials are engineered media whose constitutive parameters such as permittivity, permeability, stiffness, or mass density are modulated simultaneously in both space and time. These additional degrees of freedom, absent in conventional static metamaterials, unlock a cabinet of wave phenomena that cannot be achieved in time-invariant structures, e.g. compact nonreciprocal devices, topological insulators, and devices for efficient frequency conversion and mixing and pulse shaping. The vast majority of these studies, however, operate in the stable regime, where modulation parameters are chosen to yield linear wave propagation. Here, we push spacetime metamaterials into the regime of parametric instability, and discover a novel type of ``dynamically frustrated'' oscillating states, where nonlinear non-reciprocal, topologically protected phase dislocations emerge. We control these dislocations and make them stop, split, and recombine. We harness this control to create devices for cascading logic in branched networks, and synchronization in 2D metamaterials. Our findings are broadly applicable anywhere where spacetime modulation can be pushed beyond linear stability, from cold atoms and superconducting circuits to acoustics and RF circuits.

cond-mat.soft↗

arXiv2026

Multipolar Piezoelectricity and Anisotropic Surface Transport in Alterelectrics

Altermagnets are an emergent class of materials combining features of ferro- and antiferro-magnetic materials. They have spin-separated bands normally associated with ferromagnets, but a vanishing net magnetization. Moreover the symmetries giving rise to $d$-wave altermagnetism can provide them with a particular anisotropic, quadrupolar (i.e. with equal and opposite values when strained in perpendicular directions) piezomagnetism. Observing that the same symmetries provide a natural place to look for hyberbolic wave dispersion, this raises the question which properties are intrinsically linked to magnetism and which are determined by the symmetry. Here, we disentangle these concepts by introducing an alternative to altermagnets, based on electric polarization. These alterelectrics display quadrupolar piezoelectricity and a hyperbolic dispersion, which we demonstrate conceptually within a simplified model as well as a first-principles material realization. We furthermore establish that a counterpart of the spin-separated bands is formed by surface modes which allow for surface dependent anisotropic electronic transport analogous to the spintronic applications proposed for altermagnets.

cond-mat.mtrl-sci↗

arXiv2025

Curved Odd Elasticity

Living materials such as membranes, cytoskeletal assemblies, cell collectives and tissues can often be described as active solids---materials that are energized from within, with elastic response about a well defined reference configuration. These materials often live in complex and curved manifolds, yet most descriptions of active solids are flat. Here, we explore the interplay between curvature and non-reciprocal elasticity via a covariant effective theory on curved manifolds in combination with numerical simulations. We find that curvature spatially patterns activity, gaps the spectrum, modifies exceptional points and introduces non-Hermitian defect modes. Together these results establish a foundation for hydrodynamic and rheological models on curved manifolds, with direct implications for living matter and active metamaterials.

cond-mat.soft↗

arXiv2025

Nonreciprocal buckling makes active filaments polyfunctional

Active filaments are a workhorse for propulsion and actuation across biology, soft robotics and mechanical metamaterials. However, artificial active rods suffer from limited robustness and adaptivity because they rely on external control, or are tethered to a substrate. Here we bypass these constraints by demonstrating that non-reciprocal interactions lead to large-scale unidirectional dynamics in free-standing slender structures. By coupling the bending modes of a buckled beam anti-symmetrically, we transform the multistable dynamics of elastic snap-through into persistent cycles of shape change. In contrast to the critical point underpinning beam buckling, this transition to self-snapping is mediated by a critical exceptional point, at which bending modes simultaneously become unstable and degenerate. Upon environmental perturbation, our active filaments exploit self-snapping for a range of functionality including crawling, digging and walking. Our work advances critical exceptional physics as a guiding principle for programming instabilities into functional active materials.

cond-mat.soft↗

arXiv2025

Wave coarsening drives time crystallization in active solids

When metals are magnetized, emulsions phase separate, or galaxies cluster, domain walls and patterns form and irremediably coarsen over time. Such coarsening is universally driven by diffusive relaxation toward equilibrium. Here, we discover an inertial counterpart - wave coarsening - in active elastic media, where vibrations emerge and spontaneously grow in wavelength, period, and amplitude, before a globally synchronized state called a time crystal forms. We observe wave coarsening in one- and two-dimensional solids and capture its dynamical scaling. We further arrest the process by breaking momentum conservation and reveal a far-from-equilibrium nonlinear analogue to chiral topological edge modes. Our work unveils the crucial role of symmetries in the formation of time crystals and opens avenues for the control of nonlinear vibrations in active materials.

cond-mat.soft↗

arXiv2025

Non-reciprocal topological solitons in active metamaterials

From protein motifs to black holes, topological solitons are pervasive nonlinear excitations that are robust and can be driven by external fields. So far, existing driving mechanisms all accelerate solitons and antisolitons in opposite directions. Here we introduce a local driving mechanism for solitons that accelerates both solitons and antisolitons in the same direction instead: non-reciprocal driving. To realize this mechanism, we construct an active mechanical metamaterial consisting of non-reciprocally coupled oscillators subject to a bistable potential. We find that such nonlinearity coaxes non-reciprocal excitations - so-called non-Hermitian skin waves, which are typically unstable - into robust oneway (anti)solitons. We harness such non-reciprocal topological solitons by constructing an active waveguide capable of transmitting and filtering unidirectional information. Finally, we illustrate this mechanism in another class of metamaterials that displays the breaking of 'supersymmetry' causing only antisolitons to be driven. Our observations and models demonstrate a subtle interplay between non-reciprocity and topological solitons, whereby solitons create their own driving force by locally straining the material. Beyond the scope of our study, non-reciprocal solitons might provide an efficient driving mechanism for robotic locomotion and could emerge in other settings, e.g. quantum mechanics, optics and soft matter.

cond-mat.soft↗

arXiv2025

Non-reciprocal breathing solitons

Breathing solitons consist of a fast beating wave within a compact envelope of stable shape and velocity. They can propagate and carry information and energy in a variety of contexts such as plasmas, optical fibers and cold atoms, but propagating breathers have remained elusive when energy conservation is broken. Here, we report on the observation of breathing, unidirectional, arbitrarily long-lived solitons in non-reciprocal, non-conservative active metamaterials. Combining precision desktop experiments, numerical simulations and perturbation theory on generalizations of the sine-Gordon and nonlinear Schrödinger equations, we demonstrate that unidirectional breathers generically emerge in weakly nonlinear non-reciprocal materials, and that their dynamics are governed by an unstable fixed point. Crucially, breathing solitons can persist for arbitrarily long times provided: (i) this fixed point displays a bifurcation when a delicate balance between energy injection and dissipation is struck; (ii) the initial conditions allow the dynamics to reach this bifurcation point. Importantly, discrete effects tend to stabilize these non-reciprocal breathers over a wider range of initial conditions. Our work establishes non-reciprocity as a promising avenue to generate stable nonlinear unidirectional waves, and could be generalized beyond metamaterials to optics, soft matter and superconducting circuits.

cond-mat.soft↗

arXiv2025

More is less in unpercolated active solids

A remarkable feat of active matter physics is that systems as diverse as collections of self-propelled particles, nematics mixed with molecular motors, and interacting robots can all be described by symmetry-based continuum theories. These descriptions rely on reducing complex effects of individual motors to a few key active parameters, which increase with activity. Here we discover a striking anomaly in the continuum description of non-reciprocal active solids, a ubiquitous class of active materials. We find that as microscopic activity increases, macroscale active response can vanish: more is less. In this highly active regime, non-affine and localized modes prevail and destroy the large-scale signature of microscopic activity. These modes exist in any dilute periodic structure and emerge in random lattices below a percolation transition. Our results unveil a counterintuitive facet of active matter, offering new principles for engineering materials far from equilibrium.

cond-mat.soft↗

arXiv2025

Combinatorial Design of Floppy Modes and Frustrated Loops in Metamaterials

Metamaterials are a promising platform for a range of applications, from shock absorption to mechanical computing. These functionalities typically rely on floppy modes or mechanically frustrated loops, both of which are difficult to design. In particular, how to design multiple modes or loops with target deformations remains an open problem. We introduce a combinatorial approach that allows us to create an arbitrarily large number of floppy modes and frustrated loops. The design freedom of the mode shapes enables us to easily introduce kinematic incompatibility to turn them into frustrated loops. We demonstrate that floppy modes can be sequentially buckled by using a specific instance of elastoplastic buckling. We utilize our combinatorial floppy chains and frustrated loops to achieve matrix-vector multiplication in materia. Our findings bring about new principles for the design and the use of floppiness and geometric frustration in soft matter and metamaterials.

cond-mat.soft↗

arXiv2025

Mechano-optical metasurfaces

Tunable metasurfaces enable active and on-demand control over optical wavefronts through reconfigurable scattering of resonant nanostructures. Here, we present novel insights inspired by mechanical metamaterials to achieve giant tunability in mechano-optical metasurfaces where the mechanical metamaterial and optical metasurfaces are integrated in a single nanopatterned material. In a first design, judiciously engineered cuts in a flexible substrate enable large, strain-induced extension of the inter-particle spacing, tuning a high quality-factor resonance in a silicon nanoparticle array across a very broad spectral range. In a second design, we eliminate the substrate and demonstrate a nanopatterned silicon membrane that simultaneously functions as a mechanical metamaterial and an optical metasurface with large tunability. Our results highlight a promising route toward active metasurfaces, with potential applications in tunable filters, reconfigurable lenses, and dynamic wavefront shaping.

physics.optics↗

arXiv2025

Metamaterials that learn to change shape

Learning to change shape is a fundamental strategy of adaptation and evolution of living organisms, from bacteria and cells to tissues and animals. Human-made materials can also exhibit advanced shape morphing capabilities, but lack the ability to learn. Here, we build metamaterials that can learn complex shape-changing responses using a contrastive learning scheme. By being shown examples of the target shape changes, our metamaterials are able to learn those shape changes by progressively updating internal learning degrees of freedom -- the local stiffnesses. Unlike traditional materials that are designed once and for all, our metamaterials have the ability to forget and learn new shape changes in sequence, to learn multiple shape changes that break reciprocity, and to learn multistable shape changes, which in turn allows them to perform reflex gripping actions and locomotion. Our findings establish metamaterials as an exciting platform for physical learning, which in turn opens avenues for the use of physical learning to design adaptive materials and robots.

cond-mat.soft↗

arXiv2025

Shape Morphing Metamaterials

Mechanical metamaterials leverage geometric design to achieve unconventional properties, such as high strength at low density, efficient wave guiding, and complex shape morphing. The ability to control shape changes builds on the complex relationship between geometry and nonlinear mechanics, and opens new possibilities for disruptive technologies across diverse fields, including wearable devices, medical technology, robotics, and beyond. In this review of shape-morphing metamaterials, we examine the current state of the field and propose a unified classification system for the mechanisms involved, as well as the design principles underlying them. Specifically, we explore two main categories of unit cells-those that exploit structural anisotropy or internal rotations-and two potential approaches to tessellating these cells: based on kinematic compatibility or geometric frustration. We conclude by discussing the available design tools and highlighting emerging challenges in the development of shape-morphing metamaterials.

physics.app-ph↗

arXiv2024

Tuning the buckling sequences of metamaterials using plasticity

Material nonlinearities such as hyperelasticity, viscoelasticity, and plasticity have recently emerged as design paradigms for metamaterials based on buckling. These metamaterials exhibit properties such as shape morphing, transition waves, and sequential deformation. In particular, plasticity has been used in the design of sequential metamaterials which combine high stiffness, strength, and dissipation at low density and produce superior shock absorbing performances. However, the use of plasticity for tuning buckling sequences in metamaterials remains largely unexplored. In this work, we introduce yield area, yield criterion, and loading history as new design tools of plasticity in tuning the buckling load and sequence in metamaterials. We numerically and experimentally demonstrate a controllable buckling sequence in different metamaterial architectures with the above three strategies. Our findings enrich the toolbox of plasticity in the design of metamaterials with more controllable sequential deformations and leverage plasticity to broader applications in multi-functional metamaterials, high-performance soft robotics, and mechanical self-assembly.

cond-mat.soft↗

arXiv2024

Roadmap for Animate Matter

Humanity has long sought inspiration from nature to innovate materials and devices. As science advances, nature-inspired materials are becoming part of our lives. Animate materials, characterized by their activity, adaptability, and autonomy, emulate properties of living systems. While only biological materials fully embody these principles, artificial versions are advancing rapidly, promising transformative impacts across various sectors. This roadmap presents authoritative perspectives on animate materials across different disciplines and scales, highlighting their interdisciplinary nature and potential applications in diverse fields including nanotechnology, robotics and the built environment. It underscores the need for concerted efforts to address shared challenges such as complexity management, scalability, evolvability, interdisciplinary collaboration, and ethical and environmental considerations. The framework defined by classifying materials based on their level of animacy can guide this emerging field encouraging cooperation and responsible development. By unravelling the mysteries of living matter and leveraging its principles, we can design materials and systems that will transform our world in a more sustainable manner.

cond-mat.mtrl-sci↗

arXiv2024

Prospecting for Pluripotency in Metamaterial Design

From self-assembly and protein folding to combinatorial metamaterials, a key challenge in material design is finding the right combination of interacting building blocks that yield targeted properties. Such structures are fiendishly difficult to find; not only are they rare, but often the design space is so rough that gradients are useless and direct optimization is hopeless. Here, we design ultra rare combinatorial metamaterials capable of multiple desired deformations by introducing a two-fold strategy that avoids the drawbacks of direct optimization. We first combine convolutional neural networks with genetic algorithms to prospect for metamaterial designs with a potential for high performance. In our case, these metamaterials have a high number of spatially extended modes; they are pluripotent. Second, we exploit this library of pluripotent designs to generate metamaterials with multiple target deformations, which we finally refine by strategically placing defects. Our pluripotent, multishape metamaterials would be impossible to design through trial-and-error or standard optimization. Instead, our data-driven approach is systematic and ideally suited to tackling the large and intractable combinatorial problems that are pervasive in material science.

cond-mat.soft↗

arXiv2024

Fracture metamaterials with on-demand crack paths enabled by bending

In many scenarios -- when we bite food or during a crash -- fracture is inevitable. Finding solutions to steer fracture to mitigate its impact or turn it into a purposeful functionality, is therefore crucial. Strategies using composites, changes in chemical composition or crystal orientation, have proven to be very efficient, but the crack path control remains limited and has not been achieved in load-bearing structures. Here, we introduce fracture metamaterials consisting of slender elements whose bending enables large elastic deformation as fracture propagates. This interplay between bending and fracture enables tunable energy dissipation and the design of on-demand crack paths of arbitrary complexity. To this end, we use topology optimisation to create unit cells with anisotropic fracture energy, which we then tile up to realize fracture metamaterials with uniform density that we 3D-print. The thin ligaments that constitute the unit cells confer them a strikingly distinct response in tension and shear, and we show that by controlling the orientation and layout of the unit cells the sequential progress of the crack can be controlled, making the fracture path arbitrarily tortuous. This tortuosity increases the energy dissipation of the metamaterial without changing its stiffness. Using bespoke arrangements of unit cells, metamaterials can have on-demand fracture paths of arbitrary complexity. Our findings bring a new perspective on inelastic deformations in mechanical metamaterials, with potential applications in areas as diverse as the food industry, structural design, and for shock and impact damping.

cond-mat.soft↗

arXiv2024

Active Solids Model: Rigid Body Motion and Shape-changing Mechanisms

Active solids such as cell collectives, colloidal clusters, and active metamaterials exhibit diverse collective phenomena, ranging from rigid body motion to shape-changing mechanisms. The nonlinear dynamics of such active materials remains however poorly understood when they host zero-energy deformation modes and when noise is present. Here, we show that stress propagation in a model of active solids induces the spontaneous actuation of multiple soft floppy modes, even without exciting vibrational modes. By introducing an adiabatic approximation, we map the dynamics onto an effective Landau free energy, predicting mode selection and the onset of collective dynamics. These results open new ways to study and design living and robotic materials with multiple modes of locomotion and shape-change.

cond-mat.soft↗