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Katia Bertoldi

Publications and source records attributed to Katia Bertoldi.

33 records · Page 2Linked to original sources
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↗
arXiv2022

Ultralight and ultra-stiff nano-cardboard panels: mechanical analysis, characterization, and design principles

We introduce a class of ultra-light and ultra-stiff sandwich panels designed for use in photophoretic levitation applications and investigate their mechanical behavior using both computational analyses and micro-mechanical testing. The sandwich panels consist of two face sheets connected with a core that consists of hollow cylindrical ligaments arranged in a honeycomb-based hexagonal pattern. Computational modeling shows that the panels have superior bending stiffness and buckling resistance compared to similar panels with a basketweave core, and that their behavior is well described by Uflyand-Mindlin plate theory. By optimizing the ratio of the face sheet thickness to the ligament wall thickness, panels maybe obtained that have a bending stiffness that is more than five orders of magnitude larger than that of a solid plate with the same area density. Using a scalable microfabrication process, we demonstrate that panels as large as 3x3 cm^2 with a density of 20 kg/m^3 can be made in a few hours. Micro-mechanical testing of the panels is performed by deflecting microfabricated cantilevered panels using a nanoindenter. The experimentally measured bending stiffness of the cantilevered panels is in very good agreement with the computational results, demonstrating exquisite control over the dimensions, form, and properties of the microfabricated panels.

physics.app-ph↗
arXiv2021

MuA-Ori: Multimodal Actuated Origami

Recently, inflatable elements integrated in robotics systems have enabled complex motions as a result of simple inputs. However, these fluidic actuators typically exhibit unimodal deformation upon inflation. Here, we present a new design concept for modular, fluidic actuators that can switch between deformation modes as a response to an input threshold. Our system comprises bistable origami modules in which snapping breaks rotational symmetry, giving access to a bending deformation. By tuning geometry, the modules can be designed to snap at different pressure thresholds, rotate clockwise or counterclockwise when actuated, and bend in different planes. Due to their ability to assume multiple deformation modes as response to a single pressure input we call our system MuA-Ori, or Multimodal Actuated Origami. MuA-Ori provides an ideal platform to design actuators that can switch between different configurations, reach multiple, pre-defined targets in space, and move along complex trajectories.

cs.RO↗
arXiv2020

Programming nonreciprocity and reversibility in multistable mechanical metamaterials

Nonreciprocity can be passively achieved by harnessing material nonlinearities. In particular, networks of nonlinear bistable elements with asymmetric energy landscapes have recently been shown to support unidirectional transition waves. However, in these systems energy can be transferred only when the elements switch from the higher to the lower energy well, allowing for a one-time signal transmission. Here, we show that in a mechanical metamaterial comprising a 1D array of bistable arches nonreciprocity and reversability can be independently programmed and are not mutually exclusive. By connecting shallow arches with symmetric energy wells and decreasing energy barriers, we design a reversible mechanical diode that can sustain multiple signal transmissions. Further, by alternating arches with symmetric and asymmetric energy landscapes we realize a nonreciprocal chain that enables propagation of different transition waves in opposite directions.

physics.app-ph↗
arXiv2020

Kirigami-inspired inflatables with programmable shapes

Kirigami, the Japanese art of paper cutting, has recently enabled the design of stretchable mechanical metamaterials that can be easily realized by embedding arrays of periodic cuts into an elastic sheet. Here, we exploit kirigami principles to design inflatables that can mimic target shapes upon pressurization. Our system comprises a kirigami sheet embedded into an unstructured elastomeric membrane. First, we show that the inflated shape can be controlled by tuning the geometric parameters of the kirigami pattern. Then, by applying a simple optimization algorithm, we identify the best parameters that enable the kirigami inflatables to transform into a family of target shapes at a given pressure. Furthermore, thanks to the tessellated nature of the kirigami, we show that we can selectively manipulate the parameters of the single units to allow the reproduction of features at different scales and ultimately enable a more accurate mimicking of the target.

cond-mat.soft↗
arXiv2019

Geometric charges and nonlinear elasticity of soft metamaterials

Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and conceptual frameworks are largely lacking. Using an analogy with electrostatics, and building on recent developments in a nonlinear geometric formulation of elasticity, we develop a formalism that maps the elastic problem into that of nonlinear interaction of elastic charges. This approach offers an intuitive conceptual framework, qualitatively explaining the linear response, the onset of mechanical instability and aspects of the post-instability state. Apart from intuition, the formalism also quantitatively reproduces full numeric simulations of several prototypical structures. Possible applications of the tools developed in this work for the study of ordered and disordered porous mechanical metamaterials are discussed.

cond-mat.soft↗
arXiv2019

Propagation of pop ups in kirigami shells

Kirigami-inspired metamaterials are attracting increasing interest because of their ability to achieve extremely large strains and shape changes via out-of-plane buckling. While in flat kirigami sheets the ligaments buckle simultaneously as Euler columns leading to a continuous phase transition, here we demonstrate that kirigami shells can also support discontinuous phase transitions. Specifically, we show via a combination of experiments, numerical simulations and theoretical analysis that in cylindrical kirigami shells the snapping-induced curvature inversion of the initially bent ligaments results in a pop-up process that first localizes near an imperfection and then, as the deformation is increased, progressively spreads through the structure. Notably, we find that the width of the transition zone as well as the stress at which propagation of the instability is triggered can be controlled by carefully selecting the geometry of the cuts and the curvature of the shell. Our study significantly expands the ability of existing kirigami metamaterials and opens avenues for the design of the next generation of responsive surfaces, as demonstrated by the design of a smart skin that significantly enhance the crawling efficiency of a simple linear actuator.

cond-mat.soft↗
arXiv2017

Porous mechanical metamaterials as interacting elastic charges

We present an analytical framework to describe the complex nonlinear response of two-dimensional porous mechanical metamaterials. We adopt a geometric approach to elasticity in which pores are represented by elastic charges, and show that this method captures with high level of accuracy both the shape deformation of individual pores as well as collective deformation patterns resulting from interactions between neighboring pores. Specifically, we show that quadrupoles and hexadecapoles - the two lowest order multipoles available in elasticity - are capable of matching the experimentally observed evolution in shape and relative orientation of the holes in a variety of periodic porous mechanical metamaterials. Our work demonstrates the ability of elastic charges to capture the physics of highly deformable porous solids and paves the way to the development of new theoretical frameworks for the description and rational design of porous mechanical metamaterials.

cond-mat.soft↗
arXiv2017

Buckling-Induced Kirigami

We investigate the mechanical response of thin sheets perforated with a square array of mutually orthogonal cuts, which leaves a network of squares connected by small ligaments. Our combined analytical, experimental and numerical results indicate that under uniaxial tension the ligaments buckle out-of-plane, inducing the formation of 3D patterns whose morphology is controlled by the load direction. We also find that by largely stretching the buckled perforated sheets, plastic strains develop in the ligaments. This gives rise to the formation of kirigami sheets comprising periodic distribution of cuts and permanent folds. As such, the proposed buckling-induced pop-up strategy points to a simple route for manufacturing complex morphable structures out of flat perforated sheets.

cond-mat.soft↗
arXiv2016

Harnessing Geometric Frustration to Form Band Gaps in Acoustic Channel Lattices

We demonstrate both numerically and experimentally that geometric frustration in two-dimensional periodic acoustic networks consisting of arrays of narrow air channels can be harnessed to form band gaps (ranges of frequency in which the waves cannot propagate in any direction through the system). While resonant standing wave modes and interferences are ubiquitous in all the analyzed network geometries, we show that they give rise to band gaps only in the geometrically frustrated ones (i.e. those comprising of triangles and pentagons). Our results not only reveal a new mechanism based on geometric frustration to suppress the propagation of pressure waves in specific frequency ranges, but also opens avenues for the design of a new generation of smart systems that control and manipulate sound and vibrations.

physics.class-ph↗
arXiv2015

Discontinuous Buckling of Wide Beams and Metabeams

We uncover how nonlinearities dramatically alter the buckling of elastic beams. First, we show experimentally that sufficiently wide ordinary elastic beams and specifically designed metabeams ---beams made from a mechanical metamaterial--- exhibit discontinuous buckling, an unstable form of buckling where the post-buckling stiffness is negative. Then we use simulations to uncover the crucial role of nonlinearities, and show that beams made from increasingly nonlinear materials exhibit increasingly negative post-buckling slope. Finally, we demonstrate that for sufficiently strong nonlinearity, we can observe discontinuous buckling for metabeams as slender as $1\%$ numerically and $5\%$ experimentally.

cond-mat.soft↗
arXiv2015

Topological Phononic Crystals with One-Way Elastic Edge Waves

We report a new type of phononic crystals with topologically non-trivial bandgaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves. In our design, gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic analogue of the electronic quantum Hall effect. We investigate the response of both hexagonal and square gyroscopic lattices and observe bulk Chern number of 1 and 2, indicating that these structures support single and multi-mode edge elastic waves immune to back-scattering. These robust one-way phononic waveguides could potentially lead to the design of a novel class of surface wave devices that are widely used in electronics, telecommunication and acoustic imaging.

cond-mat.mes-hall↗
arXiv2014

A comparative analysis of numerical approaches to the mechanics of elastic sheets

Numerically simulating deformations in thin elastic sheets is a challenging problem in computational mechanics due to destabilizing compressive stresses that result in wrinkling. Determining the location, structure, and evolution of wrinkles in these problems have important implications in design and is an area of increasing interest in the fields of physics and engineering. In this work, several numerical approaches previously proposed to model equilibrium deformations in thin elastic sheets are compared. These include standard finite element-based static post-buckling approaches as well as a recently proposed method based on dynamic relaxation, which are applied to the problem of an annular sheet with opposed tractions where wrinkling is a key feature. Numerical solutions are compared to analytic predictions, enabling a quantitative evaluation of the predictive power of the various methods. Results indicate that static finite element approaches are highly sensitive to initial imperfections, relying on \textit{a priori} knowledge of the equilibrium wrinkling pattern to generate optimal results. In contrast, dynamic relaxation is much less sensitive to initial imperfections and can generate solutions for a wide variety of loading conditions without requiring knowledge of the equilibrium solution beforehand.

cond-mat.mtrl-sci↗