arXiv subjects

Katia Bertoldi

Publications and source records attributed to Katia Bertoldi.

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

Folding-Driven Auxetic Weft Knit Textiles with Integrated Capacitive Sensing

Machine knitting provides a scalable platform for manufacturing multifunctional textiles in which geometry, mechanics, and embedded functionality can be programmed at the stitch level. However, predictive design tools capable of linking knit architecture to large-deformation mechanical response remain limited. Here, we develop a reduced-order spring-network model that captures the relaxation, unfolding, and deformation of knitted fabrics composed of checkerboard arrangements of rib and garter patches. The model accurately predicts the corrugated relaxed configuration of the knits and the evolution of local deformations under tensile loading using only linear extensional and torsional springs. Combining simulations with experiments, we show that the programmed unfolding of the corrugations generates tunable auxetic behavior, with both the magnitude of the negative Poisson's ratio and the strain at which it occurs governed by the unit-cell geometry. We further integrate capacitive strain sensing directly during fabrication through partial plating of conductive yarns, eliminating post-processing. The resulting knitted capacitors exhibit programmable tradeoffs between strain sensitivity and sensing range, enabling either highly sensitive sensors over narrow deformation windows or lower-sensitivity sensors capable of measuring larger strains. Together, our modeling framework and fabrication strategy provide a route toward the rational design of mechanically programmable, sensorized knits with tailored shape-morphing and sensing functionalities.

cond-mat.soft↗

arXiv2026

Shape optimization of pneumatic soft actuators

Soft actuators, characterized by their compliance and flexibility, have tremendous potential for diverse applications, ranging from medical devices to submarine operations. However, significant challenges remain in the design of these actuators, specifically in maintaining precise control over their mechanical behavior and motion. To date, heuristic methods have been commonly used to design soft actuators, which are potentially incapable of producing designs that achieve specific target behaviors. We propose a gradient-based inverse design framework to synthesize three dimensional soft actuators with tailored mechanical responses. Our design framework utilizes gradient information that captures the inherent geometrical and material nonlinearities of the soft actuator to morph its shape. We exemplify the capabilities of the proposed framework by designing soft actuators with bespoke deformation patterns, making use of sophisticated deformation mechanisms to realize the target behavior. The capabilities of the proposed framework are validated via experimental testing of cast designs, which confirms a strong correlation between measurements and numerical simulations.

cs.CE↗

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

Knitting Multistability

Curved elastic shells can be fabricated through molding or by harnessing residual stresses. These shells often exhibit snap-through behavior and multistability when loaded. We present a unique way of fabricating curved elastic shells that exhibit multistability and snap-through behavior, weft-knitting. The knitting process introduces internal stresses into the textile sheet, which leads to complex 3D curvatures. We explore the relationship between the geometry and the mechanical response, identifying a parameter space where the textiles are multistable. We harness the snapping behavior and shape change through multistability to design soft conductive switches with built-in haptic feedback, and incorporate these textile switches into wearable devices. This work will allow us to harness the nonlinear mechanical behavior of textiles to create functional, soft, and seamless wearable devices. This includes but is not limited to the devices for additional cycling visibility and safety that we envision.

cond-mat.soft↗

arXiv2025

Harnessing Oscillatory Dynamics for Reprogrammable Mechanical Functionality

A long-standing goal in the field of "mechanical computing" is the creation of truly reprogrammable mechanical structures, where the function of each unit can be dynamically defined, modified, and accessed on demand, much like rewriting data on a hard drive. Prior efforts have largely focused on bistable building blocks, which mimic binary states, but robust and efficient methods for programming large arrays of such units remain limited. In this study, we introduce a new approach for defining and reconfiguring the state of mechanical bits. Specifically, we investigate arrays of pendula whose boundary conditions break symmetry, effectively transforming them into mechanical bits. When actuation times are short compared to the natural oscillation periods, the state of each pendulum can be controlled solely by adjusting the timing of global boundary conditions. This mechanism enables rapid reprogramming, arbitrary information writing, and even the construction of a "mechanical piano" capable of generating user-defined note and chord sequences within only a few oscillation cycles. Because it integrates seamlessly with diverse functionalities, our strategy establishes a scalable framework for reprogrammable mechanical systems and can be readily generalized to other oscillatory systems like membranes or beams.

physics.class-ph↗

arXiv2025

Wave-number lock-in in buckled elastic structures: an analogue to parametric instabilities

Parametric instabilities are a known feature of periodically driven dynamic systems; at particular frequencies and amplitudes of the driving modulation, the system's quasi-periodic response undergoes a frequency lock-in, leading to a periodically unstable response. Here, we demonstrate an analogous phenomenon in a purely static context. We show that the buckling patterns of an elastic beam resting on a modulated Winkler foundation display the same kind of frequency lock-in observed in dynamic systems. Through simulations and experiments, we reveal that compressed elastic strips with modulated height alternate between predictable quasi-periodic and periodic buckling modes. Our findings uncover previously unexplored analogies between structural and dynamic instabilities, highlighting how even simple elastic structures can give rise to rich and intriguing behaviors.

math-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

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

Origami crawlers: exploring a single origami vertex for complex path navigation

The ancient art of origami, traditionally used to transform simple sheets into intricate objects, also holds potential for diverse engineering applications, such as shape morphing and robotics. In this study, we demonstrate that one of the most basic origami structures (i.e., a rigid, foldable degree-four vertex) can be engineered to create a crawler capable of navigating complex paths using only a single input. Through a combination of experimental studies and modeling, we show that modifying the geometry of a degree four vertex enables sheets to move either in a straight line or turn. Furthermore, we illustrate how leveraging the nonlinearities in folding allows the design of crawlers that can switch between moving straight and turning. Remarkably, these crawling modes can be controlled by adjusting the range of the actuation folding angle. Our study opens avenues for simple machines that can follow intricate trajectories with minimal actuation.

cs.RO↗

arXiv2024

Designing Mechanical Meta-Materials by Learning Equivariant Flows

Mechanical meta-materials are solids whose geometric structure results in exotic nonlinear behaviors that are not typically achievable via homogeneous materials. We show how to drastically expand the design space of a class of mechanical meta-materials known as cellular solids, by generalizing beyond translational symmetry. This is made possible by transforming a reference geometry according to a divergence free flow that is parameterized by a neural network and equivariant under the relevant symmetry group. We show how to construct flows equivariant to the space groups, despite the fact that these groups are not compact. Coupling this flow with a differentiable nonlinear mechanics simulator allows us to represent a much richer set of cellular solids than was previously possible. These materials can be optimized to exhibit desirable mechanical properties such as negative Poisson's ratios or to match target stress-strain curves. We validate these new designs in simulation and by fabricating real-world prototypes. We find that designs with higher-order symmetries can exhibit a wider range of behaviors.

cs.CE↗

arXiv2024

Reprogrammable sequencing for physically intelligent under-actuated robots

Programming physical intelligence into mechanisms holds great promise for machines that can accomplish tasks such as navigation of unstructured environments while utilizing a minimal amount of computational resources and electronic components. In this study, we introduce a novel design approach for physically intelligent under-actuated mechanisms capable of autonomously adjusting their motion in response to environmental interactions. Specifically, multistability is harnessed to sequence the motion of different degrees of freedom in a programmed order. A key aspect of this approach is that these sequences can be passively reprogrammed through mechanical stimuli that arise from interactions with the environment. To showcase our approach, we construct a four degree of freedom robot capable of autonomously navigating mazes and moving away from obstacles. Remarkably, this robot operates without relying on traditional computational architectures and utilizes only a single linear actuator.

cs.RO↗

arXiv2024

Unravelling the Mechanics of Knitted Fabrics Through Hierarchical Geometric Representation

Knitting interloops one-dimensional yarns into three-dimensional fabrics that exhibit behaviours beyond their constitutive materials. How extensibility and anisotropy emerge from the hierarchical organisation of yarns into knitted fabrics has long been unresolved. We sought to unravel the mechanical roles of tensile mechanics, assembly and dynamics arising from the yarn level on fabric nonlinearity by developing a yarn-based dynamical model. This physically validated model captures the fundamental mechanical response of knitted fabrics, analogous to flexible metamaterials and biological fiber networks due to geometric nonlinearity within such hierarchical systems. Fabric anisotropy originates from observed yarn-yarn rearrangements during alignment dynamics and is topology-dependent. This yarn-based model also provides a design space of knitted fabrics to embed functionalities by varying geometric configuration and material property in instructed procedures compatible to machine manufacturing. Our hierarchical approach to build up a knitted fabrics computationally modernizes an ancient craft and represents a first step towards mechanical programmability of knitted fabrics in wide engineering applications.

cond-mat.soft↗

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

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↗