Publications

SLAM Publication Highlights

This list contains recent highlight publications from Leiden SLAM groups. It is not exhaustive. Please check the Google Scholar profiles of the PIs out for comprehensive lists.


2025

Exotic mechanical properties enabled by countersnapping instabilities

Paul Ducarme, Bart Weber, Martin van Hecke, and Johannes TB Overvelde

Proceedings of the National Academy of Sciences - (2025)

Mechanical snapping instabilities are leveraged by natural systems, metamaterials, and devices for rapid sensing, actuation, and shape changes, as well as to absorb impact. In all current forms of snapping, shapes deform in the same direction as the exerted forces, even though there is no physical law that dictates this. Here, we realize countersnapping mechanical structures that respond in the opposite way. In contrast to regular snapping, countersnapping manifests itself in a sudden shortening transition under increasing tension or a sudden increase in tensile force under increasing extension. We design these structures by combining basic flexible building blocks that leverage geometric nonlinearities. We demonstrate experimentally that countersnapping can be employed to obtain new exotic properties, such as unidirectional stick–slip motion, switchable stiffness that does not otherwise affect the state of the system, and passive resonance avoidance. Moreover, we demonstrate that combining multiple countersnapping elements allows sequential stiffness switching for elements coupled in parallel, or instantaneous collective switching for elements in series. By expanding the repertoire of realizable elastic instabilities, our work opens routes to principles for mechanical sensing, computation, and actuation.

Exotic mechanical properties enabled by countersnapping instabilities

Paul Ducarme, Bart Weber, Martin van Hecke, and Johannes TB Overvelde

Proceedings of the National Academy of Sciences - (2025)

Mechanical snapping instabilities are leveraged by natural systems, metamaterials, and devices for rapid sensing, actuation, and shape changes, as well as to absorb impact. In all current forms of snapping, shapes deform in the same direction as the exerted forces, even though there is no physical law that dictates this. Here, we realize countersnapping mechanical structures that respond in the opposite way. In contrast to regular snapping, countersnapping manifests itself in a sudden shortening transition under increasing tension or a sudden increase in tensile force under increasing extension. We design these structures by combining basic flexible building blocks that leverage geometric nonlinearities. We demonstrate experimentally that countersnapping can be employed to obtain new exotic properties, such as unidirectional stick–slip motion, switchable stiffness that does not otherwise affect the state of the system, and passive resonance avoidance. Moreover, we demonstrate that combining multiple countersnapping elements allows sequential stiffness switching for elements coupled in parallel, or instantaneous collective switching for elements in series. By expanding the repertoire of realizable elastic instabilities, our work opens routes to principles for mechanical sensing, computation, and actuation.

Geometric control and memory in networks of hysteretic elements

Dor Shohat and Martin van Hecke

Physical Review Letters - (2025) [arXiv] [pdf]

The response of driven frustrated media stems from interacting hysteretic elements. We derive explicit mappings from networks of hysteretic springs to their abstract representation as interacting hysterons. These mappings reveal how the physical network controls the signs, magnitudes, symmetries, and pairwise nature of the hysteron interactions. In addition, strong geometric nonlinearities can produce pathways that require excess hysterons or even break hysteron models. Our results pave the way for metamaterials with geometrically controlled interactions, pathways, and functionalities, and highlight fundamental limitations of abstract hysterons in modeling disordered systems.

Geometric control and memory in networks of hysteretic elements

Dor Shohat and Martin van Hecke

Physical Review Letters - (2025) [arXiv] [pdf]

The response of driven frustrated media stems from interacting hysteretic elements. We derive explicit mappings from networks of hysteretic springs to their abstract representation as interacting hysterons. These mappings reveal how the physical network controls the signs, magnitudes, symmetries, and pairwise nature of the hysteron interactions. In addition, strong geometric nonlinearities can produce pathways that require excess hysterons or even break hysteron models. Our results pave the way for metamaterials with geometrically controlled interactions, pathways, and functionalities, and highlight fundamental limitations of abstract hysterons in modeling disordered systems.

Control of collective activity to crystallize an oscillator gas

Marine Le Blay, Joshua H. K. Saldi, Alexandre Morin

Nature Physics - (2025) [arXiv]

Motility-induced phase separation occurs in assemblies of self-propelled units when activity is coupled negatively to density. By contrast, the consequences of a positive coupling between density and activity on the collective behaviour of active matter remain unexplored. Here we show that collective activity can emerge from such a positive coupling among non-motile building blocks. We perform experiments with self-sustained oscillators powered by contact-charge electrophoresis. Although the oscillators are non-motile by design, they spontaneously form an active gas when confined together. The super-elastic nature of collisions constitutes a positive density–activity coupling and underlies the active gas properties. Elucidating the origin of binary collisions allows us to precisely control the structure of the active gas and its eventual crystallization. Beyond considering the overlooked positive coupling between density and activity, our work suggests that rich collective properties can emerge not only from the symmetry of interactions between active building blocks but also from their adaptable and responsive behaviour.

Control of collective activity to crystallize an oscillator gas

Marine Le Blay, Joshua H. K. Saldi, Alexandre Morin

Nature Physics - (2025) [arXiv]

Motility-induced phase separation occurs in assemblies of self-propelled units when activity is coupled negatively to density. By contrast, the consequences of a positive coupling between density and activity on the collective behaviour of active matter remain unexplored. Here we show that collective activity can emerge from such a positive coupling among non-motile building blocks. We perform experiments with self-sustained oscillators powered by contact-charge electrophoresis. Although the oscillators are non-motile by design, they spontaneously form an active gas when confined together. The super-elastic nature of collisions constitutes a positive density–activity coupling and underlies the active gas properties. Elucidating the origin of binary collisions allows us to precisely control the structure of the active gas and its eventual crystallization. Beyond considering the overlooked positive coupling between density and activity, our work suggests that rich collective properties can emerge not only from the symmetry of interactions between active building blocks but also from their adaptable and responsive behaviour.

2024

Controlled pathways and sequential information processing in serially coupled mechanical hysterons

Jingran Liu, Margot Teunisse, George Korovin, Ivo R Vermaire, Lishuai Jin, Hadrien Bense, and Martin van Hecke

Proceedings of the National Academy of Sciences - (2024)

The complex sequential response of frustrated materials results from the interactions between material bits called hysterons. Hence, a central challenge is to understand and control these interactions, so that materials with targeted pathways and functionalities can be realized. Here, we show that hysterons in serial configurations experience geometrically controllable antiferromagnetic-like interactions. We create hysteron-based metamaterials that leverage these interactions to realize targeted pathways, including those that break the return point memory property, characteristic of independent or weakly interacting hysterons. We uncover that the complex response to sequential driving of such strongly interacting hysteron-based materials can be described by finite state machines. We realize information processing operations such as string parsing in materia, and outline a general framework to uncover and characterize the FSMs for a given physical system. Our work provides a general strategy to understand and control hysteron interactions, and opens a broad avenue toward material-based information processing.

Controlled pathways and sequential information processing in serially coupled mechanical hysterons

Jingran Liu, Margot Teunisse, George Korovin, Ivo R Vermaire, Lishuai Jin, Hadrien Bense, and Martin van Hecke

Proceedings of the National Academy of Sciences - (2024)

The complex sequential response of frustrated materials results from the interactions between material bits called hysterons. Hence, a central challenge is to understand and control these interactions, so that materials with targeted pathways and functionalities can be realized. Here, we show that hysterons in serial configurations experience geometrically controllable antiferromagnetic-like interactions. We create hysteron-based metamaterials that leverage these interactions to realize targeted pathways, including those that break the return point memory property, characteristic of independent or weakly interacting hysterons. We uncover that the complex response to sequential driving of such strongly interacting hysteron-based materials can be described by finite state machines. We realize information processing operations such as string parsing in materia, and outline a general framework to uncover and characterize the FSMs for a given physical system. Our work provides a general strategy to understand and control hysteron interactions, and opens a broad avenue toward material-based information processing.

Soft and Stiff Normal Modes in Floppy Colloidal Square Lattices

Julio Melio, Silke E Henkes, Daniela J Kraft

Physical Review Letters - (2024) [arXiv] [pdf]

Floppy microscale spring networks are widely studied in theory and simulations, but no well-controlled experimental system currently exists. Here, we show that square lattices consisting of colloid-supported lipid bilayers functionalized with DNA linkers act as microscale floppy spring networks. We extract their normal modes by inverting the particle displacement correlation matrix, showing the emergence of a spectrum of soft modes with low effective stiffness in addition to stiff modes that derive from linker interactions. Evaluation of the softest mode, a uniform shear mode, reveals that shear stiffness decreases with lattice size. Experiments match well with Brownian particle simulations, and we develop a theoretical description based on mapping interactions onto a linear response model to describe the modes. Our results reveal the importance of entropic steric effects and can be used for developing reconfigurable materials at the colloidal length scale.

Soft and Stiff Normal Modes in Floppy Colloidal Square Lattices

Julio Melio, Silke E Henkes, Daniela J Kraft

Physical Review Letters - (2024) [arXiv] [pdf]

Floppy microscale spring networks are widely studied in theory and simulations, but no well-controlled experimental system currently exists. Here, we show that square lattices consisting of colloid-supported lipid bilayers functionalized with DNA linkers act as microscale floppy spring networks. We extract their normal modes by inverting the particle displacement correlation matrix, showing the emergence of a spectrum of soft modes with low effective stiffness in addition to stiff modes that derive from linker interactions. Evaluation of the softest mode, a uniform shear mode, reveals that shear stiffness decreases with lattice size. Experiments match well with Brownian particle simulations, and we develop a theoretical description based on mapping interactions onto a linear response model to describe the modes. Our results reveal the importance of entropic steric effects and can be used for developing reconfigurable materials at the colloidal length scale.

Nonadditivity in Many-Body Interactions between Membrane-Deforming Spheres Increases Disorder

Ali Azadbakht, Thomas R Weikl, and Daniela J Kraft

ACS nano - (2024) [arXiv] [pdf]

Membrane-induced interactions play an important role in organizing membrane proteins. Measurements of the interactions between two and three membrane deforming objects have revealed their nonadditive nature. They are thought to lead to complex many-body effects, however, experimental evidence is lacking. We here present an experimental method to measure many-body effects in membrane-mediated interactions using colloidal spheres placed between a deflated giant unilamellar vesicles and a planar substrate. The confined colloidal particles cause a large deformation of the membrane while not being physicochemically attached to it and interact through it. Two particles attract with a maximum force of 0.2 pN. For three particles, compact equilateral triangles were preferred over linear arrangements. We use numerical energy minimization to establish that the attraction stems from a reduction in the membrane-deformation energy caused by the particles. Confining up to 36 particles, we find a preference for hexagonally close packed clusters. However, with increasing number of particles the order of the confined particles decreases, at the same time, diffusivity of the particles increases. Our experiments show that the nonadditive nature of membrane-mediated interactions affects the interactions and arrangements and ultimately leads to spherical aggregates with liquid-like order of potential importance for cellular processes.

Nonadditivity in Many-Body Interactions between Membrane-Deforming Spheres Increases Disorder

Ali Azadbakht, Thomas R Weikl, and Daniela J Kraft

ACS nano - (2024) [arXiv] [pdf]

Membrane-induced interactions play an important role in organizing membrane proteins. Measurements of the interactions between two and three membrane deforming objects have revealed their nonadditive nature. They are thought to lead to complex many-body effects, however, experimental evidence is lacking. We here present an experimental method to measure many-body effects in membrane-mediated interactions using colloidal spheres placed between a deflated giant unilamellar vesicles and a planar substrate. The confined colloidal particles cause a large deformation of the membrane while not being physicochemically attached to it and interact through it. Two particles attract with a maximum force of 0.2 pN. For three particles, compact equilateral triangles were preferred over linear arrangements. We use numerical energy minimization to establish that the attraction stems from a reduction in the membrane-deformation energy caused by the particles. Confining up to 36 particles, we find a preference for hexagonally close packed clusters. However, with increasing number of particles the order of the confined particles decreases, at the same time, diffusivity of the particles increases. Our experiments show that the nonadditive nature of membrane-mediated interactions affects the interactions and arrangements and ultimately leads to spherical aggregates with liquid-like order of potential importance for cellular processes.

2023

Spontaneous Demixing of Binary Colloidal Flocks

Samadarshi Maity and Alexandre Morin

Physical Review Letters - (2023) [arXiv] [pdf]

Population heterogeneity is ubiquitous among active living systems, but little is known about its role in determining their spatial organization and large-scale dynamics. Combining evidence from synthetic active fluids assembled from self-propelled colloidal particles along with theoretical predictions at the continuum scale, we demonstrate the spontaneous demixing of binary polar liquids within circular confinement. Our analysis reveals how both active speed heterogeneity and nonreciprocal repulsive interactions lead to self-sorting behavior. By establishing general principles for the self-organization of binary polar liquids, our findings highlight the specificity of multicomponent active systems.

Spontaneous Demixing of Binary Colloidal Flocks

Samadarshi Maity and Alexandre Morin

Physical Review Letters - (2023) [arXiv] [pdf]

Population heterogeneity is ubiquitous among active living systems, but little is known about its role in determining their spatial organization and large-scale dynamics. Combining evidence from synthetic active fluids assembled from self-propelled colloidal particles along with theoretical predictions at the continuum scale, we demonstrate the spontaneous demixing of binary polar liquids within circular confinement. Our analysis reveals how both active speed heterogeneity and nonreciprocal repulsive interactions lead to self-sorting behavior. By establishing general principles for the self-organization of binary polar liquids, our findings highlight the specificity of multicomponent active systems.

Wrapping Pathways of Anisotropic Dumbbell Particles by Giant Unilamellar Vesicles

Ali Azadbakht, and Billie Meadowcroft, and Thijs Varkevisser, and Anđela Šarić, and Daniela J. Kraft,

Nano Letters - (2023) [arXiv] [pdf]

Endocytosis is a key cellular process involved in the uptake of nutrients, pathogens or the diagnosis and therapy of diseases. Most studies have focused on spherical objects, whereas biologically relevant shapes can be highly anisotropic. In this letter, we use an experimental model system based on Giant Unilamellar Vesicles (GUVs) and dumbbell-shaped colloidal particles to mimic and investigate the first stage of the passive endocytic process: engulfment of an anisotropic object by the membrane. Our model has specific ligand-receptor interactions realized by mobile receptors on the vesicles and immobile ligands on the particles. Through a series of experiments, theory and molecular dynamics simulations, we quantify the wrapping process of anisotropic dumbbells by GUVs and identify distinct stages of the wrapping pathway. We find that the strong curvature variation in the neck of the dumbbell as well as membrane tension are crucial in determining both the speed of wrapping and the final states.

Wrapping Pathways of Anisotropic Dumbbell Particles by Giant Unilamellar Vesicles

Ali Azadbakht, and Billie Meadowcroft, and Thijs Varkevisser, and Anđela Šarić, and Daniela J. Kraft,

Nano Letters - (2023) [arXiv] [pdf]

Endocytosis is a key cellular process involved in the uptake of nutrients, pathogens or the diagnosis and therapy of diseases. Most studies have focused on spherical objects, whereas biologically relevant shapes can be highly anisotropic. In this letter, we use an experimental model system based on Giant Unilamellar Vesicles (GUVs) and dumbbell-shaped colloidal particles to mimic and investigate the first stage of the passive endocytic process: engulfment of an anisotropic object by the membrane. Our model has specific ligand-receptor interactions realized by mobile receptors on the vesicles and immobile ligands on the particles. Through a series of experiments, theory and molecular dynamics simulations, we quantify the wrapping process of anisotropic dumbbells by GUVs and identify distinct stages of the wrapping pathway. We find that the strong curvature variation in the neck of the dumbbell as well as membrane tension are crucial in determining both the speed of wrapping and the final states.

Counting and Sequential Information Processing in Mechanical Metamaterials

Lennard J. Kwakernaak and Martin van Hecke

Physical Review Letters - (2023) [arXiv] [pdf]

Materials with an irreversible response to cyclic driving exhibit an evolving internal state which, in principle, encodes information on the driving history. Here we realize irreversible metamaterials that count mechanical driving cycles and store the result into easily interpretable internal states. We extend these designs to aperiodic metamaterials which are sensitive to the order of different driving magnitudes, and realize 'lock and key' metamaterials that only reach a specific state for a given target driving sequence. Our strategy is robust, scalable and extendable, and opens new routes towards smart sensing, soft robotics and mechanical information processing.

Counting and Sequential Information Processing in Mechanical Metamaterials

Lennard J. Kwakernaak and Martin van Hecke

Physical Review Letters - (2023) [arXiv] [pdf]

Materials with an irreversible response to cyclic driving exhibit an evolving internal state which, in principle, encodes information on the driving history. Here we realize irreversible metamaterials that count mechanical driving cycles and store the result into easily interpretable internal states. We extend these designs to aperiodic metamaterials which are sensitive to the order of different driving magnitudes, and realize 'lock and key' metamaterials that only reach a specific state for a given target driving sequence. Our strategy is robust, scalable and extendable, and opens new routes towards smart sensing, soft robotics and mechanical information processing.

Multistable sheets with rewritable patterns for switchable shape-morphing

AS Meeussen, and M Van Hecke

Nature - (2023)

Flat sheets patterned with folds, cuts or swelling regions can deform into complex three-dimensional shapes under external stimuli. However, current strategies require prepatterning and lack intrinsic shape selection. Moreover, they either rely on permanent deformations, preventing corrections or erasure of a shape, or sustained stimulation, thus yielding shapes that are unstable. Here we show that shape-morphing strategies based on mechanical multistability can overcome these limitations. We focus on undulating metasheets that store memories of mechanical stimuli in patterns of self-stabilizing scars. After removing external stimuli, scars persist and force the sheet to switch to sharply selected curved, curled and twisted shapes. These stable shapes can be erased by appropriate forcing, allowing rewritable patterns and repeated and robust actuation. Our strategy is material agnostic, extendable to other undulation patterns and instabilities, and scale-free, allowing applications from miniature to architectural scales.

Multistable sheets with rewritable patterns for switchable shape-morphing

AS Meeussen, and M Van Hecke

Nature - (2023)

Flat sheets patterned with folds, cuts or swelling regions can deform into complex three-dimensional shapes under external stimuli. However, current strategies require prepatterning and lack intrinsic shape selection. Moreover, they either rely on permanent deformations, preventing corrections or erasure of a shape, or sustained stimulation, thus yielding shapes that are unstable. Here we show that shape-morphing strategies based on mechanical multistability can overcome these limitations. We focus on undulating metasheets that store memories of mechanical stimuli in patterns of self-stabilizing scars. After removing external stimuli, scars persist and force the sheet to switch to sharply selected curved, curled and twisted shapes. These stable shapes can be erased by appropriate forcing, allowing rewritable patterns and repeated and robust actuation. Our strategy is material agnostic, extendable to other undulation patterns and instabilities, and scale-free, allowing applications from miniature to architectural scales.

2022

Repulsive torques alone trigger crystallization of constant speed active particles

Marine Le Blay and Alexandre Morin

Soft Matter - (2022) [arXiv] [pdf]

We investigate the possibility for self-propelled particles to crystallize without reducing their intrinsic speed. We illuminate how, in the absence of any force, the competition between self-propulsion and repulsive torques determine the macroscopic phases of constant-speed active particles. This minimal model expands upon existing approaches for an improved understanding of crystallization of active matter.

Repulsive torques alone trigger crystallization of constant speed active particles

Marine Le Blay and Alexandre Morin

Soft Matter - (2022) [arXiv] [pdf]

We investigate the possibility for self-propelled particles to crystallize without reducing their intrinsic speed. We illuminate how, in the absence of any force, the competition between self-propulsion and repulsive torques determine the macroscopic phases of constant-speed active particles. This minimal model expands upon existing approaches for an improved understanding of crystallization of active matter.

2021

Profusion of transition pathways for interacting hysterons

Martin van Hecke

PRE - (2021) [pdf]

The response, pathways, and memory effects of cyclically driven complex media can be captured by hysteretic elements called hysterons. Here we demonstrate the profound impact of hysteron interactions on pathways and memory. Specifically, while the Preisach model of independent hysterons features a restricted class of pathways which always satisfy return point memory, we show that three interacting hysterons generate more than 15 000 transition graphs, with most violating return point memory and having features completely distinct from the Preisach model. Exploring these opens a route to designer pathways and information processing in complex matter.

Profusion of transition pathways for interacting hysterons

Martin van Hecke

PRE - (2021) [pdf]

The response, pathways, and memory effects of cyclically driven complex media can be captured by hysteretic elements called hysterons. Here we demonstrate the profound impact of hysteron interactions on pathways and memory. Specifically, while the Preisach model of independent hysterons features a restricted class of pathways which always satisfy return point memory, we show that three interacting hysterons generate more than 15 000 transition graphs, with most violating return point memory and having features completely distinct from the Preisach model. Exploring these opens a route to designer pathways and information processing in complex matter.

Complex pathways and memory in compressed corrugated sheets

Hadrien Bense, and Martin van Hecke

PNAS - (2021) [pdf]

The nonlinear response of driven complex materials—disorderedmagnets, amorphous media, and crumpled sheets—features intri-cate transition pathways where the system repeatedly hops be-tween metastable states. Such pathways encode memory effectsand may allow information processing, yet tools are lacking toexperimentally observe and control these pathways, and their fullbreadth has not been explored. Here we introduce compressionof corrugated elastic sheets to precisely observe and manipulatetheir full, multistep pathways, which are reproducible, robust,and controlled by geometry. We show how manipulation of theboundaries allows us to elicit multiple targeted pathways froma single sample. In all cases, each state in the pathway can beencoded by the binary state of material bits called hysterons, andthe strength of their interactions plays a crucial role. In particular,as function of increasing interaction strength, we observe Preisachpathways, expected in systems of independently switching hys-terons; scrambled pathways that evidence hitherto unexploredinteractions between these material bits; and accumulator path-ways which leverage these interactions to perform an elementarycomputation. Our work opens a route to probe, manipulate, andunderstand complex pathways, impacting future applications insoft robotics and information processing in materials.

Complex pathways and memory in compressed corrugated sheets

Hadrien Bense, and Martin van Hecke

PNAS - (2021) [pdf]

The nonlinear response of driven complex materials—disorderedmagnets, amorphous media, and crumpled sheets—features intri-cate transition pathways where the system repeatedly hops be-tween metastable states. Such pathways encode memory effectsand may allow information processing, yet tools are lacking toexperimentally observe and control these pathways, and their fullbreadth has not been explored. Here we introduce compressionof corrugated elastic sheets to precisely observe and manipulatetheir full, multistep pathways, which are reproducible, robust,and controlled by geometry. We show how manipulation of theboundaries allows us to elicit multiple targeted pathways froma single sample. In all cases, each state in the pathway can beencoded by the binary state of material bits called hysterons, andthe strength of their interactions plays a crucial role. In particular,as function of increasing interaction strength, we observe Preisachpathways, expected in systems of independently switching hys-terons; scrambled pathways that evidence hitherto unexploredinteractions between these material bits; and accumulator path-ways which leverage these interactions to perform an elementarycomputation. Our work opens a route to probe, manipulate, andunderstand complex pathways, impacting future applications insoft robotics and information processing in materials.

2020

Jigsaw puzzle design of pluripotent origami

Pieter Dieleman, Niek Vasmel, Scott Waitukaitis and Martin van Hecke

Nature Physics - (2020) [pdf]

Origami is rapidly transforming the design of robots, deployable structures and metamaterials. However, as foldability requires a large number of complex compatibility conditions that are difficult to satisfy, the design of crease patterns is limited to heuristics and computer optimization. Here we introduce a systematic strategy that enables intuitive and effective design of complex crease patterns that are guaranteed to fold. First, we exploit symmetries to construct 140 distinct foldable motifs, and represent these as jigsaw puzzle pieces. We then show that when these pieces are fitted together they encode foldable crease patterns. This maps origami design to solving combinatorial problems, which allows us to systematically create, count and classify a vast number of crease patterns. We show that all of these crease patterns are pluripotent—capable of folding into multiple shapes—and solve exactly for the number of possible shapes for each pattern. Finally, we employ our framework to rationally design a crease pattern that folds into two independently defined target shapes, and fabricate such pluripotent origami. Our results provide physicists, mathematicians and engineers with a powerful new design strategy

Jigsaw puzzle design of pluripotent origami

Pieter Dieleman, Niek Vasmel, Scott Waitukaitis and Martin van Hecke

Nature Physics - (2020) [pdf]

Origami is rapidly transforming the design of robots, deployable structures and metamaterials. However, as foldability requires a large number of complex compatibility conditions that are difficult to satisfy, the design of crease patterns is limited to heuristics and computer optimization. Here we introduce a systematic strategy that enables intuitive and effective design of complex crease patterns that are guaranteed to fold. First, we exploit symmetries to construct 140 distinct foldable motifs, and represent these as jigsaw puzzle pieces. We then show that when these pieces are fitted together they encode foldable crease patterns. This maps origami design to solving combinatorial problems, which allows us to systematically create, count and classify a vast number of crease patterns. We show that all of these crease patterns are pluripotent—capable of folding into multiple shapes—and solve exactly for the number of possible shapes for each pattern. Finally, we employ our framework to rationally design a crease pattern that folds into two independently defined target shapes, and fabricate such pluripotent origami. Our results provide physicists, mathematicians and engineers with a powerful new design strategy

Topological defects produce exotic mechanics in complex metamaterials

Anne Meeussen, Erdal Oguz, Yair Shokef, and Martin van Hecke

Nature physics - (2020) [pdf]

The basic tenet of metamaterials is that the architecture controls the physics. So far, most studies have considered defect-free architectures. However, defects, and particularly topological defects, play a crucial role in natural materials. Here we provide a systematic strategy for introducing such defects in mechanical metamaterials. We first present metamaterials that are a mechanical analogue of spin systems with tunable ferromagnetic and antiferromagnetic interactions, then design an exponential number of frustration-free metamaterials and finally introduce topological defects by rotating a string of building blocks in these metamaterials. We uncover the distinct mechanical signature of topological defects using experiments and simulations, and leverage this to design complex metamaterials in which external forces steer deformations and stresses towards complementary parts of the system. Our work presents a new avenue to systematically including spatial complexity, frustration and topology in mechanical metamaterials.

Topological defects produce exotic mechanics in complex metamaterials

Anne Meeussen, Erdal Oguz, Yair Shokef, and Martin van Hecke

Nature physics - (2020) [pdf]

The basic tenet of metamaterials is that the architecture controls the physics. So far, most studies have considered defect-free architectures. However, defects, and particularly topological defects, play a crucial role in natural materials. Here we provide a systematic strategy for introducing such defects in mechanical metamaterials. We first present metamaterials that are a mechanical analogue of spin systems with tunable ferromagnetic and antiferromagnetic interactions, then design an exponential number of frustration-free metamaterials and finally introduce topological defects by rotating a string of building blocks in these metamaterials. We uncover the distinct mechanical signature of topological defects using experiments and simulations, and leverage this to design complex metamaterials in which external forces steer deformations and stresses towards complementary parts of the system. Our work presents a new avenue to systematically including spatial complexity, frustration and topology in mechanical metamaterials.

2018

A characteristic length scale causes anomalous size effects and boundary programmability in mechanical metamaterials

Bastiaan Florijn, Chris Kettenis, and Martin van Hecke

Nature Physics - (2018) [pdf]

The architecture of mechanical metamaterials is designed to harness geometry, nonlinearity and topology to obtain advanced functionalities such as shape morphing, programmability and one-way propagation. Although a purely geometric framework successfully captures the physics of small systems under idealized conditions, large systems or heterogeneous driving conditions remain essentially unexplored. Here we uncover strong anomalies in the mechanics of a broad class of metamaterials, such as auxetics, shape changers or topological insulators; a non-monotonic variation of their stiffness with system size, and the ability of textured boundaries to completely alter their properties. These striking features stem from the competition between rotation-based deformations—relevant for small systems—and ordinary elasticity, and are controlled by a characteristic length scale which is entirely tunable by the architectural details. Our study provides new vistas for designing, controlling and programming the mechanics of metamaterials.

A characteristic length scale causes anomalous size effects and boundary programmability in mechanical metamaterials

Bastiaan Florijn, Chris Kettenis, and Martin van Hecke

Nature Physics - (2018) [pdf]

The architecture of mechanical metamaterials is designed to harness geometry, nonlinearity and topology to obtain advanced functionalities such as shape morphing, programmability and one-way propagation. Although a purely geometric framework successfully captures the physics of small systems under idealized conditions, large systems or heterogeneous driving conditions remain essentially unexplored. Here we uncover strong anomalies in the mechanics of a broad class of metamaterials, such as auxetics, shape changers or topological insulators; a non-monotonic variation of their stiffness with system size, and the ability of textured boundaries to completely alter their properties. These striking features stem from the competition between rotation-based deformations—relevant for small systems—and ordinary elasticity, and are controlled by a characteristic length scale which is entirely tunable by the architectural details. Our study provides new vistas for designing, controlling and programming the mechanics of metamaterials.

Multi-step self-guided pathways for shape-changing metamaterials

Corentin Coulais, Alberico Sabbadini, Fre Vink and Martin van Hecke

Nature - (2018) [pdf]

Multi-step pathways—which consist of a sequence of reconfigurations of a structure—are central to the functionality of various natural and artificial systems. Such pathways execute autonomously in self-guided processes such as protein folding and self-assembly, but have previously required external control to execute in macroscale mechanical systems, provided by, for example, actuators in robotics or manual folding in origami. Here we demonstrate shape-changing, macroscale mechanical metamaterials that undergo self-guided, multi-step reconfiguration in response to global uniform compression. We avoid the need for external control by using metamaterials that are made purely of passive components. The design of the metamaterials combines nonlinear mechanical elements with a multimodal architecture that enables a sequence of topological reconfigurations caused by the formation of internal self-contacts between the elements of the metamaterial. We realize the metamaterials by using computer-controlled water-jet cutting of flexible materials, and show that the multi-step pathway and final configuration can be controlled by rational design of the nonlinear mechanical elements. We also demonstrate that the self-contacts suppress errors in the pathway. Finally, we create hierarchical architectures to extend the number of distinct reconfiguration steps. Our work establishes general principles for designing mechanical pathways, opening up new avenues for self-folding media pluripotent materials and pliable devices in areas such as stretchable electronics and soft robotics.

Multi-step self-guided pathways for shape-changing metamaterials

Corentin Coulais, Alberico Sabbadini, Fre Vink and Martin van Hecke

Nature - (2018) [pdf]

Multi-step pathways—which consist of a sequence of reconfigurations of a structure—are central to the functionality of various natural and artificial systems. Such pathways execute autonomously in self-guided processes such as protein folding and self-assembly, but have previously required external control to execute in macroscale mechanical systems, provided by, for example, actuators in robotics or manual folding in origami. Here we demonstrate shape-changing, macroscale mechanical metamaterials that undergo self-guided, multi-step reconfiguration in response to global uniform compression. We avoid the need for external control by using metamaterials that are made purely of passive components. The design of the metamaterials combines nonlinear mechanical elements with a multimodal architecture that enables a sequence of topological reconfigurations caused by the formation of internal self-contacts between the elements of the metamaterial. We realize the metamaterials by using computer-controlled water-jet cutting of flexible materials, and show that the multi-step pathway and final configuration can be controlled by rational design of the nonlinear mechanical elements. We also demonstrate that the self-contacts suppress errors in the pathway. Finally, we create hierarchical architectures to extend the number of distinct reconfiguration steps. Our work establishes general principles for designing mechanical pathways, opening up new avenues for self-folding media pluripotent materials and pliable devices in areas such as stretchable electronics and soft robotics.

2017

Flexible Mechanical Metamaterials

Katia Bertoldi, Vincenzo Vitelli, Johan Christensen and Martin van Hecke

Nature Reviews Materials - (2017)

Mechanical metamaterials exhibit properties and functionalities that cannot be realized in conventional materials. Originally, the field focused on achieving unusual (zero or negative) values for familiar mechanical parameters, such as density, Poisson's ratio or compressibility, but more recently, new classes of metamaterials-including shape-morphing, topological and nonlinear metamaterials-have emerged. These materials exhibit exotic functionalities, such as pattern and shape transformations in response to mechanical forces, unidirectional guiding of motion and waves, and reprogrammable stiffness or dissipation. In this Review, we identify the design principles leading to these properties and discuss, in particular, linear and mechanism-based metamaterials (such as origami-based and kirigami-based metamaterials), metamaterials harnessing instabilities and frustration, and topological metamaterials. We conclude by outlining future challenges for the design, creation and conceptualization of advanced mechanical metamaterials.

Flexible Mechanical Metamaterials

Katia Bertoldi, Vincenzo Vitelli, Johan Christensen and Martin van Hecke

Nature Reviews Materials - (2017)

Mechanical metamaterials exhibit properties and functionalities that cannot be realized in conventional materials. Originally, the field focused on achieving unusual (zero or negative) values for familiar mechanical parameters, such as density, Poisson's ratio or compressibility, but more recently, new classes of metamaterials-including shape-morphing, topological and nonlinear metamaterials-have emerged. These materials exhibit exotic functionalities, such as pattern and shape transformations in response to mechanical forces, unidirectional guiding of motion and waves, and reprogrammable stiffness or dissipation. In this Review, we identify the design principles leading to these properties and discuss, in particular, linear and mechanism-based metamaterials (such as origami-based and kirigami-based metamaterials), metamaterials harnessing instabilities and frustration, and topological metamaterials. We conclude by outlining future challenges for the design, creation and conceptualization of advanced mechanical metamaterials.

2016

Combinatorial design of textured mechanical metamaterials

Corentin Coulais, Eial Teomy, Koen de Reus, Yair Shokef and Martin van Hecke

Nature - (2016) [pdf]

We create mechanical metamaterials whose response to uniaxial compression can be programmed by lateral confinement, allowing monotonic, nonmonotonic, and hysteretic behavior. These functionalities arise from a broken rotational symmetry which causes highly nonlinear coupling of deformations along the two primary axes of these metamaterials. We introduce a soft mechanism model which captures the programmable mechanics, and outline a general design strategy for confined mechanical metamaterials. Finally, we show how inhomogeneous confinement can be explored to create multistability and giant hysteresis.

Combinatorial design of textured mechanical metamaterials

Corentin Coulais, Eial Teomy, Koen de Reus, Yair Shokef and Martin van Hecke

Nature - (2016) [pdf]

We create mechanical metamaterials whose response to uniaxial compression can be programmed by lateral confinement, allowing monotonic, nonmonotonic, and hysteretic behavior. These functionalities arise from a broken rotational symmetry which causes highly nonlinear coupling of deformations along the two primary axes of these metamaterials. We introduce a soft mechanism model which captures the programmable mechanics, and outline a general design strategy for confined mechanical metamaterials. Finally, we show how inhomogeneous confinement can be explored to create multistability and giant hysteresis.

2015

Origami Multistability: From Single Vertices to Metasheets

Scott Waitukaitis, Rémi Menaut, Bryan Gin-ge Chen, and Martin van Hecke

PRL - (2015) [pdf]

We show that the simplest building blocks of origami-based materials—rigid, degree-four vertices—are generically multistable. The existence of two distinct branches of folding motion emerging from the flat state suggests at least bistability, but we show how nonlinearities in the folding motions allow generic vertex geometries to have as many as five stable states. In special geometries with collinear folds and symmetry, more branches emerge leading to as many as six stable states. Tuning the fold energy parameters, we show how monostability is also possible. Finally, we show how to program the stability features of a single vertex into a periodic fold tessellation. The resulting metasheets provide a previously unanticipated functionality—tunable and switchable shape and size via multistability.

Origami Multistability: From Single Vertices to Metasheets

Scott Waitukaitis, Rémi Menaut, Bryan Gin-ge Chen, and Martin van Hecke

PRL - (2015) [pdf]

We show that the simplest building blocks of origami-based materials—rigid, degree-four vertices—are generically multistable. The existence of two distinct branches of folding motion emerging from the flat state suggests at least bistability, but we show how nonlinearities in the folding motions allow generic vertex geometries to have as many as five stable states. In special geometries with collinear folds and symmetry, more branches emerge leading to as many as six stable states. Tuning the fold energy parameters, we show how monostability is also possible. Finally, we show how to program the stability features of a single vertex into a periodic fold tessellation. The resulting metasheets provide a previously unanticipated functionality—tunable and switchable shape and size via multistability.

2014

Programmable Mechanical Metamaterials

Bastiaan Florijn, Corentin Coulais, and Martin van Hecke

PRL - (2014) [pdf]

We create mechanical metamaterials whose response to uniaxial compression can be programmed by lateral confinement, allowing monotonic, nonmonotonic, and hysteretic behavior. These functionalities arise from a broken rotational symmetry which causes highly nonlinear coupling of deformations along the two primary axes of these metamaterials. We introduce a soft mechanism model which captures the programmable mechanics, and outline a general design strategy for confined mechanical metamaterials. Finally, we show how inhomogeneous confinement can be explored to create multistability and giant hysteresis.

Programmable Mechanical Metamaterials

Bastiaan Florijn, Corentin Coulais, and Martin van Hecke

PRL - (2014) [pdf]

We create mechanical metamaterials whose response to uniaxial compression can be programmed by lateral confinement, allowing monotonic, nonmonotonic, and hysteretic behavior. These functionalities arise from a broken rotational symmetry which causes highly nonlinear coupling of deformations along the two primary axes of these metamaterials. We introduce a soft mechanism model which captures the programmable mechanics, and outline a general design strategy for confined mechanical metamaterials. Finally, we show how inhomogeneous confinement can be explored to create multistability and giant hysteresis.