arXiv subjects

Vincent Tournat

Publications and source records attributed to Vincent Tournat.

At least 19 recordsLinked to original sources

arXiv2026

Wave-based reading of mechanical memory in multistable mass-in-mass metamaterials

Mechanical metamaterials with integrated bistable elements have emerged as promising platforms for mechanical information storage, where transitions between stable states encode information as mechanical bits. While it has been shown that information can be written into such metamaterials by applying global inputs, existing readout strategies rely predominantly on visual inspection. Here, we experimentally demonstrate a mass-in-mass bistable metamaterial with state-dependent stiffness that enables both writing and reading of mechanical information using only boundary-applied dynamic excitations. We further show that such metamaterial architecture functions as both a mechanical sensor of input amplitude and a reconfigurable wave-control device. Together, these results highlight the versatility of bistable metamaterials as multifunctional platforms that integrate mechanical memory, sensing, and adaptive wave manipulation.

physics.app-ph↗

arXiv2026

Conformal Elastodynamics in 2D Dilational Metamaterials

Flexible mechanical structures can undergo large deformations under small loads, enabling large, complex, and nonlinear wave responses under finite-frequency driving. Here, we study a dynamically driven canonical flexible mechanical metamaterial composed of rigid squares connected at their corners by flexible hinges. This metamaterial supports a uniform dilational mechanism and, in the limit of ideal joints, exhibits a Poisson ratio of -1. The presence of this dilational mode of deformation gives rise to a conformal symmetry, in which the dynamics are approximately invariant under a wide class of physical transformations -- conformal maps. We find that the low-frequency response of the system is dominated by conformal deformations consisting of spatially varying rotations and dilations concentrated at the boundary. Even at high frequencies, each conformal map implies a conserved spatially complex momentum. We explore how experimental parameters such as material stiffnesses and the geometry and number of unit cells allow experimental conformal momenta to approach this conservation, varying slowly compared to the non-conformal momenta of same order. These results constitute a new framework opening fundamental avenues for the study of conformal wave phenomena in dilational metamaterials as well as potential strategies for controlling nonlinear waves and vibrations.

cond-mat.soft↗

arXiv2026

Transition Waves in Mechanical Metamaterials with Neighbor-Programmable Energy Landscapes

Transition waves in mechanical metamaterials manifest themselves as propagating interfaces between different stable states in lattices composed of arrays of coupled, intrinsically bistable elements. Here, we show experimentally and numerically that arrays of elastic unit cells that are individually monostable, yet whose energy landscapes can be programmed through interactions with neighboring units, provide a rich and largely unexplored platform for transition wave propagation. We implement this concept by designing a unit cell comprising a von Mises truss supported by two vertical elastic beams. In one-dimensional arrays of such units, we demonstrate that each cell's energy landscape can change from monostable to bistable depending on the state of its neighbors. This neighbor-programmable energy landscape enables the controlled initiation and propagation of transition waves, giving rise to highly discrete, directionally unbiased, domino-like wave propagation. Experiments and numerical simulations show that the existence and speed of the waves are governed by geometric design and mass distribution. Our results establish neighboring effects as a distinct mechanism for transition wave propagation, expanding the design space of mechanical metamaterials beyond architectures that rely on intrinsically multistable building blocks.

physics.app-ph↗

arXiv2026

Phonon controlled mechanical memory via pinning and depinning of transition waves

Multistable mechanical metamaterials enable programmable transitions between discrete stable states through propagating kink transition waves (TWs). Yet controlling these kinks typically requires local actuation or high-energy deformation, limiting scalability. Here we demonstrate a universal strategy for pinning and depinning TWs using local defects and boundary phonon excitations. Inspired by phonon-dislocation interactions in crystalline solids, we use pairs of phonons that form a beating envelope resonant with the pinned kink's translational mode, which lies within a phononic band gap. This resonant coupling efficiently transfers energy to the kink, allowing it to overcome defect barriers and propagate across impurities. The proposed mechanism enables application of these systems as information processing units in mechanical computing, namely as scalable and more robust mechanical memory.

physics.app-ph↗

arXiv2025

Effect of discreteness on domain wall stability in a plate coupled to a foundation of bistable elements

Surfaces and structures capable of multiple stable configurations have attracted growing interest for on-demand shape morphing. In this work, we consider an elastic compliant plate coupled to a two-dimensional foundation comprising an array of bistable elements, a system that can form and retain complex continuous morphologies without sustained actuation via creation of stable domain walls separating regions in different stable states. These domain walls exhibit three distinct behaviors: expansion, shrinking, and metastable pinning. These arise from two limits of foundation discreteness. In the continuum limit, where bistable units are strongly coupled, domain walls undergo global phase transitions analogous to first-order phase transitions. In the anti-continuum limit, discreteness introduces Peierls-Nabarro-type energy modulations that lead to metastable pinning. To quantify these behaviors and the transition between the two limits, we develop a reduced-order model that captures the total potential energy of configurations with domain walls and validate it using finite element analysis (FEA). For axisymmetric domain walls, the model yields phase diagrams identifying the regimes of expansion, shrinking, and pinning as functions of bistable-potential asymmetry, relative foundation discreteness, and domain-wall size. We then extend the analysis to non-axisymmetric geometries and establish local geometric criteria that predict the stability of convex and concave polygonal domain walls, confirmed by simulations. Together, these results clarify how discreteness enables stability through energy-landscape modulation, provide predictive design rules for multistable reconfigurable surfaces, and offer insights into domain-wall stability more generally in elastically coupled multistable metamaterials.

physics.app-ph↗

arXiv2025

Vibrational Transportation of Deformable Axisymmetric Particles

A particle on a substrate supporting a surface acoustic wave can experience horizontal drift excited by the dry friction force. The effect is referred to as vibrational transportation, or as a surface acoustic wave motor. A traditional theory of vibrational transportation considers a particle as a material point moving on a rigid substrate. A more realistic representation is a contact model based on Cattaneo-Mindlin (also called Hertz-Mindlin) mechanics applicable to an axisymmetric deformable particle. A recent semi-analytical extension of the Cattaneo-Mindlin solution called the Method of Memory Diagrams allows one to compute the hysteretic friction force for an arbitrary loading history in terms of contact displacements, and, subsequently, to numerically solve the equations of motion. Depending on the materials' and excitation parameters, the particle can stay in permanent contact with the substrate or experience multiple jumps. In the former case, the particle can slide along the surface, during each wave period, advancing and receding with different efficiencies, which finally results in a drift. The drift can occur both in the wave propagation direction and against it. In the regime of multiple jumps, directed horizontal motion is also possible. It is based on synchronization between the wave period and rebounding events. A rebound occurs once per period and consistently at the same phase. At the beginning of the process, the particle moves with an acceleration that decreases and finally disappears. Exactly the same type of motion against the wave has been observed in our preliminary experiments. We demonstrate that a point mass behaves differently: in a regime of permanent contact, negative and positive sliding are equilibrated, which produces no drift, whereas multiple rebounds of a point mass are always chaotic, at least for fully conservative collisions.

physics.app-ph↗

arXiv2025

Experimental study of the acoustic frequency-up conversion effect by nonlinear thin plates

Classical methods of sound absorption present fundamental limits that can be overcome by using nonlinear effects. Thin clamped plates have been identified as strongly nonlinear elements, capable of transferring the acoustic power of an incident air-borne wave towards higher frequencies. Here, we experimentally show that these plates exhibit different vibrational nonlinear behaviors depending on the amplitude and frequency of the excitation signal. The lowest excitation levels achieved lead to harmonic generation in a weakly nonlinear regime, while higher levels produce quasi-periodic and chaotic regimes. Since these nonlinear vibration regimes govern the acoustic frequency-up conversion process, we investigate the influence of relevant physical and geometrical parameters on the emergence of these nonlinear regimes. A parametric study on plates of different thicknesses reveals that the frequency-up conversion effect is mostly guided by the resonance of the plate at its first eigenfrequency, which depends not only on its thickness but also on a static tension introduced by the clamping. Finally, a design proposition involving multiple plates with different properties is presented in order to reach a broadband frequency-up conversion.

physics.app-ph↗

arXiv2025

Nonlinear mechanical metamaterial cloaks

The concept of cloaking -- hiding objects from external detection -- has seen wide success in linear systems. Yet, translating these advancements to nonlinear mechanical systems remains an open challenge. Here, we present a new approach to nonlinear mechanical cloaking that frames cloaking as an optimization problem aimed at replicating a target mechanical response. We solve this problem using a differentiable simulation framework coupled with gradient-based optimization. We implement this approach in a class of mechanical metamaterials constructed from rigid units with elastic couplings that support large deformation and contact interactions. Using both numerical simulations and physical experiments, we design optimal cloak structures that effectively mask internal inhomogeneities and shield against external mechanical disturbances both in static and dynamic regimes. This approach provides a versatile design paradigm for creating mechanical systems with integrated cloaking functionality across a broad range of loading scenarios.

physics.app-ph↗

arXiv2025

Arbitrary mechanical memory encoding via nonlinear waves in bistable metamaterials

Mechanical metamaterials composed of bistable elements have recently emerged as promising platforms for mechanical memory. Traditional approaches to writing information in these systems typically rely on localized actuation or predefined coupling schemes, which are often labor-intensive or lack adaptability. In this work, we introduce a one-dimensional metamaterial consisting of mass-in-mass bistable units that are statically decoupled yet dynamically switchable, allowing arbitrary mechanical information to be encoded through nonlinear waves applied at the boundary of the system. Through a combination of experiments and simulations, we demonstrate that tailored input signals can selectively trigger state transitions deep within the structure, enabling remote and programmable bit writing. This approach opens a new avenue for mechanical memory, harnessing the robustness of bistable elements and the tunability of nonlinear wave-driven actuation.

physics.app-ph↗

arXiv2025

Gradient catastrophe and Peregrine soliton in nonlinear flexible mechanical metamaterials

We explore the generation of extreme wave events in mechanical metamaterials using the regularization of the gradient catastrophe theory developed by A. Tovbis and M. Bertola for the nonlinear Schr\"odinger equation. According to this theory, Peregrine solitons can locally emerge in the semiclassical limit of the nonlinear Schr\"odinger equation. Our objective is to determine whether the phenomenon of gradient catastrophe can occur in a class of architected structures designated as flexible mechanical metamaterials, both with and without losses. We demonstrate theoretically and numerically that this phenomenon can occur in a canonical example of such flexible mechanical metamaterial, a chain of rotating units, studied earlier for its ability to support robust nonlinear waves such as elastic vector solitons. We find that in the presence of weak losses, the gradient catastrophe persists although the amplitude of extreme generated events is smaller and their onset is delayed compared to the lossless configuration.

nlin.PS↗

arXiv2024

A theoretical framework for physically-realizable kagome metamaterials and its implications on dualities and topological edge modes

Since the discovery of topological modes in idealized ball-and-spring kagome lattices, significant efforts have been devoted to realizing mechanical analogues of these ideal lattices via practical fabrication techniques. While numerical and experimental characterizations of these mechanical analogues have been reported, theoretical modeling that accounts for realistic structural effects (e.g., the bending behavior of thin ligaments-a departure from ideal hinges allowing free rotation) has been lacking. Here we propose a theoretical framework to investigate the dynamic properties of physically-realizable kagome metamaterials consisting of solid triangles and ligaments, in which triangles and ligaments are modeled as rigid bodies and elastic springs, respectively. By applying the framework, validated through finite element analysis, to twisted and deformed kagome metamaterials, we theoretically show the required conditions for achieving certain unique dynamic properties, including dispersion dualities and topological edge modes. The presented study unequivocally reveals the effects of structural components on these properties, which could enable new design strategies for wave propagation manipulation in kagome-based metamaterials.

physics.app-ph↗

arXiv2024

Optically-Controlled Nano-Transducers Based on Cleaved Superlattices for Monitoring Gigahertz Surface Acoustic Vibrations

Surface acoustic waves (SAWs) convey energy at subwavelength depths along surfaces. Using interdigital transducers (IDTs) and opto-acousto-optic transducers (OAOTs), researchers have harnessed coherent SAWs with nanosecond periods and micrometer localization depth for various applications. However, the utilization of cutting-edge OAOTs produced through surface nanopatterning techniques has set the upper limit for coherent SAW frequencies below 100 GHz, constrained by factors such as the quality and pitch of the surface nanopattern, not to mention the electronic bandwidth limitations of the IDTs. In this context, unconventional optically-controlled nano-transducers based on cleaved superlattices (SLs) are here presented as an alternative solution. To demonstrate their viability, we conducted proof-of-concept experiments using ultrafast lasers in a pump-probe configuration on SLs made of alternating AlxGa1-xAs and AlyGa1-yAs layers with approximately 70 nm periodicity and cleaved along their growth direction to produce a periodic nanostructured surface. The acoustic vibrations, generated and detected by laser beams incident on the cleaved surface, span a range from 40 GHz to 70 GHz, corresponding to the generalized surface Rayleigh mode and bulk modes within the dispersion relation. This exploration shows that, in addition to SAWs, cleaved SLs offer the potential to observe surface-skimming longitudinal and transverse acoustic waves at GHz frequencies. This proof-of-concept demonstration below 100 GHz in nanoacoustics using such an unconventional platform offers opportunities for realizing sub-THz to THz coherent surface acoustic vibrations in the future, as SLs can be epitaxially grown with atomic-scale layer width and quality.

physics.optics↗

arXiv2024

Envelope vector solitons in nonlinear flexible mechanical metamaterials

In this paper, we employ a combination of analytical and numerical techniques to investigate the dynamics of lattice envelope vector soliton solutions propagating within a one-dimensional chain of flexible mechanical metamaterial. To model the system, we formulate discrete equations that describe the longitudinal and rotational displacements of each individual rigid unit mass using a lump element approach. By applying the multiple-scales method in the context of a semi-discrete approximation, we derive an effective nonlinear Schr\"odinger equation that characterizes the evolution of rotational and slowly varying envelope waves from the aforementioned discrete motion equations. We thus show that this flexible mechanical metamaterial chain supports envelope vector solitons where the rotational component has the form of either a bright or a dark soliton. In addition, due to nonlinear coupling, the longitudinal displacement displays kink-like profiles thus forming the 2-components vector soliton. These findings, which include specific vector envelope solutions, enrich our knowledge on the nonlinear wave solutions supported by flexible mechanical metamaterials and open new possibilities for the control of nonlinear waves and vibrations.

nlin.PS↗

arXiv2024

Automated discovery of reprogrammable nonlinear dynamic metamaterials

Harnessing the rich nonlinear dynamics of highly-deformable materials has the potential to unlock the next generation of functional smart materials and devices. However, unlocking such potential requires effective strategies to spatially design optimal material architectures for desired nonlinear dynamic responses such as guiding of nonlinear elastic waves, energy focusing, and cloaking. Here, we introduce an inverse-design framework for the discovery of flexible mechanical metamaterials with a target nonlinear dynamic response. The desired dynamic task is encoded via optimal tuning of the full-scale metamaterial geometry through an inverse-design approach powered by a custom-developed fully-differentiable simulation environment. By deploying such strategy, we design mechanical metamaterials tailored for energy focusing, energy splitting, dynamic protection, and nonlinear motion conversion. Furthermore, we illustrate that our design framework can be expanded to automatically discover reprogrammable architectures capable of switching between different dynamic tasks. For instance, we encode two strongly competing tasks -- energy focusing and dynamic protection -- within a single architecture, utilizing static pre-compression to switch between these behaviors. The discovered designs are physically realized and experimentally tested, demonstrating the robustness of the engineered tasks. All together, our approach opens an untapped avenue towards designer materials with tailored robotic-like reprogrammable functionalities.

physics.app-ph↗

arXiv2023

Nucleation of transition waves via collisions of elastic vector solitons

In this work, we show that collisions of one type of nonlinear wave can lead to generation of a different kind of nonlinear wave. Specifically, we demonstrate the formation of topological solitons (or transition waves) via collisions of elastic vector solitons, another type of nonlinear wave, in a multi-stable mechanical system with coupling between translational and rotational degrees of freedom. We experimentally observe the nucleation of a phase transformation arising from colliding waves, and we numerically investigate head-on and overtaking collisions of solitary waves with vectorial properties (i.e., elastic vector solitons). Unlike KdV-type solitons, which maintain their shape despite collisions, our system shows that collisions of two vector solitons can cause nucleation of a new phase via annihilation of the vector soltions, triggering the propagation of transition waves. The propagation of these depends both on the amount of energy carried by the vector solitons and on their respective rotational directions. The observation of the initiation of transition waves with collisions of vector solitons in multistable mechanical systems serves as an example of new fundamental nonlinear wave interactions, and could also prove useful in applications involving reconfigurable structures.

physics.app-ph↗

arXiv2023

Phase transitions in 2D multistable mechanical metamaterials via collisions of soliton-like pulses

In this work, we report observations of phase transitions in 2D multistable mechanical metamaterials that are initiated by collisions of soliton-like pulses in the metamaterial. Analogous to first-order phase transitions in crystalline solids, we experimentally and numerically observe that the multistable metamaterials support phase transitions if the new phase meets or exceeds a critical nucleus size. If this criterion is met, the new phase subsequently propagates in the form of transition waves, converting the rest of the metamaterial to the new phase. More interestingly, we observe that the critical nucleus can be formed via collisions of soliton-like pulses. Moreover, the rich direction-dependent behavior of the nonlinear pulses enables control of the location of nucleation and the spatio-temporal shape of the growing phase.

nlin.PS↗

arXiv2023

Nonlinear waves in flexible mechanical metamaterials

Flexible mechanical metamaterials are compliant structures engineered to achieve unique properties via the large deformation of their components. While their static character has been studied extensively, the study of their dynamic properties is still at an early stage, especially in the nonlinear regime induced by their high deformability. Nevertheless, recent studies show that these systems provide new opportunities for the control of large amplitude elastic waves. Here, we summarize the recent results on the propagation of nonlinear waves in flexible elastic metamaterials, and highlight possible new research directions.

physics.app-ph↗

arXiv2022

Nonlinear waves at the free surface of flexible mechanical metamaterials

In this letter we investigate the propagation of nonlinear pulses along the free surface of flexible metamaterials based on the rotating squares mechanism. While these metamaterials have previously been shown to support the propagation of elastic vector solitons through their bulk, here we demonstrate that they can also support the stable propagation of nonlinear pulses along their free surface. Further, we show that the stability of these surface pulses is higher when they minimally interact with the linear dispersive surface modes. Finally, we provide guidelines to select geometries that minimize such interactions.

physics.app-ph↗