arXiv subjects

Martin van Hecke

Publications and source records attributed to Martin van Hecke.

At least 19 recordsLinked to original sources

arXiv2026

Vectorial driving of multistable materials: singularities, pt-graphs, and non-generic paths

Describing and predicting the response of multistable materials to external driving is central to memory formation, programmable metamaterials, soft robotics, and in-materia computing. While scalar driving is captured by transition graphs (t-graphs), vectorial driving produces path-dependent responses that require the recently introduced path-transition graphs (pt-graphs). In both cases, transitions are governed by singularities in the energy landscape: for scalar driving these correspond to saddle-node bifurcations, but for vectorial driving, higher-order singularities become important. Combining experiments on chain-like metamaterials with a minimal spring model, we investigate how higher-order singularities shape pt-graphs and the resulting path-dependent responses. We moreover discuss the role of non-generic driving paths through higher-order singularities, where the response is governed by spontaneous symmetry breaking. Finally, we demonstrate how t-graphs emerge as the one-dimensional limit of pt-graphs, unifying scalar and vectorial driving within a common graph-based framework. These results establish a singularity-based approach to path-dependent responses and provide a foundation for designing multistable materials with programmable sequential functionality for smart sensing, soft robotics, and in-materia computation.

cond-mat.soft↗

arXiv2026

Path-dependency and emergent computing under vectorial driving

The sequential response of frustrated materials-ranging from crumpled sheets and amorphous media to metamaterials-reveals their memory effects and emergent computational potential. Despite their spatial extension, most studies rely on a single global stimulus, such as compression, effectively reducing the problem to scalar driving. Here, we introduce vectorial driving of frustrated materials by applying multiple spatially localized stimuli to explore path-dependent, sequential responses. We uncover a wealth of phenomena absent in scalar driving, including non-Abelian responses, mixed-mode behavior, and chiral loop transients. We show that fold singularities connect three states -- ancestor, descendant, and sibling. This recurring pattern serves as the elementary building block of all sequential paths. We then introduce three levels of description of sequential, path-dependent responses. At the most fundamental level, path-dependent transition graphs (pt-graphs) and strain maps capture the response under arbitrary vectorial driving and connect pathways to the underlying singularities. They provide a complete description analogous to transition graphs (t-graphs) for scalar driving. However, as pt-graphs and strain maps become unwieldy for high-dimensional driving, we introduce b-graphs -- graphs whose nodes and transitions encode the systems response to binarized vectorial driving. These present a less complete but much simpler second-level description by restricting attention to binary input and their induced transitions. Finally, we introduce graph-based motifs that enable a systematic analysis of b-graphs. As statistical measures of pathway complexity, these motifs can be obtained in systems of any size or complexity. Our work paves the way for strategies to explore, harness, and understand complex materials and memory, while advancing embodied intelligence and in-materia computing.

cond-mat.soft↗

arXiv2025

Interacting Hysterons with Asymptotically Small or Large Spans

Models of interacting hysteretic elements, called hysterons, capture the sequential response and complex memory effects in a wide range of complex systems and can guide the design of intelligent metamaterials. However, even simple models with few hysterons feature a bewildering number and variety of behaviors. Here we study the hysteron model in two physically relevant limits, where {the} response {of a hysteron system} is easier to understand. First, when the hysteron span - the gap between its two hysteretic transitions - dominates all other scales, the range of pathways encoded in transition graphs (t-graphs) becomes limited because many avalanches {are} absent. Second, when the hysteron span becomes vanishingly small, hysterons behave as interacting binary spins, {which require avalanches in order to} exhibit nontrivial pathways. Finally we show that hysterons can be mimicked by pairs of strongly interacting spins, {such} that collections of $n$ interacting hysterons can be mapped to $2n$ interacting spins, albeit {via} highly specific interactions. {Altogether,} our work provides a deeper understanding of the role of the hysteron parameters on their collective behavior, and points to connections and differences between spin- and hysteron-based models of complex matter.

cond-mat.dis-nn↗

arXiv2025

Multimodal motion and behavior switching of multistable ciliary walkers

The collective motion of arrays of cilia - tiny, hairlike protrusions - drives the locomotion of numerous microorganisms, enabling multimodal motion and autonomous switching between gaits to navigate complex environments. To endow minimalist centimeter-scale robots with similarly rich dynamics, we introduce millimeter-scale flexible cilia that buckle under the robots weight, coupling multistability and actuation within a single physical mechanism. When placed on a vibrating surface, these ciliary walkers select their propulsion direction through the buckled states of their cilia, allowing multimodal motion and switching between modes in response to perturbations. We first show that bimodal walkers with left-right symmetric cilia can autonomously reverse direction upon encountering obstacles. Next, we demonstrate that walkers with isotropic cilia exhibit both translational and rotational motion and switch between them in response to environmental interactions. At increasing densities, swarms of such walkers collectively transition from predominantly spinning to translational motion. Finally, we show that the shape, placement and number of cilia controls the modes of motion of the walkers. Our results establish a rational, physically grounded strategy for designing minimalist soft robots where complex behaviors emerge from feedback between internal mechanical states and environmental interactions, laying the foundation for autonomous robotic collectives without the need for centralized control.

cond-mat.soft↗

arXiv2025

Transition Graphs of Interacting Hysterons: Structure, Design, Organization and Statistics

Transition graphs capture the memory and sequential response of multistable media, by specifying their evolution under external driving. Microscopically, collections of bistable elements, or hysterons, provide a powerful model for these materials, with recent work highlighting the crucial role of hysteron interactions. Here, we introduce a general framework that links transition graphs and the microscopic parameters of interacting hysterons. We first introduce a systematic framework, based on so-called scaffolds, which structures the space of transition graphs and provides tools to deal with their combinatorial explosion. We then connect the topology of transition graphs to partial orders of the microscopic parameters. This allows us to understand the statistical properties of transition graphs, as well as determine whether a given graph is realizable, i.e. compatible with the hysteron framework. Our approach paves the way for a deeper theoretical understanding of memory effects in complex media and opens a route to rationally design pathways and memory effects in materials.

cond-mat.soft↗

arXiv2025

Dynamic Avalanches: Rate-Controlled Switching and Race Conditions

Avalanches are rapid cascades of rearrangements driven by cooperative flipping of hysteretic local elements. Here we show that flipping dynamics and race conditions -- where multiple elements become unstable simultaneously -- give rise to dynamic avalanches that cannot be captured by static models of interacting elements. We realize dynamic avalanches in metamaterials with controlled flipping times and demonstrate how this allows us to modify, promote, and direct avalanche behavior. Our work elucidates the crucial role of internal dynamics in complex materials and introduces dynamic design principles for materializing targeted pathways and sequential functionalities.

cond-mat.soft↗

arXiv2025

Flexel ecosystem: simulating mechanical systems from entities with arbitrarily complex mechanical responses

Nonlinearities and instabilities in mechanical structures have shown great promise for embedding advanced functionalities. However, simulating structures subject to nonlinearities can be challenging due to the complexity of their behavior, such as large shape changes, effect of pre-tension, negative stiffness and instabilities. While traditional finite element analysis is capable of simulating a specific nonlinear structure quantitatively, it can be costly and cumbersome to use due to the high number of degrees of freedom involved. We propose a framework to facilitate the exploration of highly nonlinear structures under quasistatic conditions. In our framework, models are simplified by introducing `flexels', elements capable of intrinsically representing the complex mechanical responses of compound structures. By extending the concept of nonlinear springs, flexels can be characterized by multi-valued response curves, and model various mechanical deformations, interactions and stimuli, e.g., stretching, bending, contact, pneumatic actuation, and cable-driven actuation. We demonstrate that the versatility of the formulation allows to model and simulate, with just a few elements, complex mechanical systems such as pre-stressed tensegrities, tape spring mechanisms, interaction of buckled beams and pneumatic soft gripper actuated using a metafluid. With the implementation of the framework in an easy-to-use Python library, we believe that the flexel formulation will provide a useful modeling approach for understanding and designing nonlinear mechanical structures.

cond-mat.soft↗

arXiv2025

Dynamic self-loops in networks of passive and active binary elements

Models of coupled binary elements capture memory effects in complex dissipative materials, such as transient responses or sequential computing, when their interactions are chosen appropriately. However, for random interactions, self-loops - cyclic transition sequences incompatible with dissipative dynamics - dominate the response and undermine statistical approaches. Here we reveal that self-loops originate from energy injection and limit cycles in the underlying physical system. We furthermore introduce interaction ensembles that strongly suppress or completely eliminate self-loops, allowing statistical studies of memory in large dissipative systems. Our work opens a route towards a unified description of passive and active multistable materials using hysteron models.

cond-mat.soft↗

arXiv2025

Slit-snapping and multistability in buckled beams with partial cuts

Elastic instabilities such as buckling and snapping have evolved into a powerful design principle, enabling memory, sequential shape morphing, and computing in metamaterials and devices. Modifying the post-buckling configurations or their snapping transitions would greatly expand design possibilities, yet general principles for controlling elastic instabilities are lacking. Here, we show that adding a partial cut, or slit, to a flexible beam enables precise control of post-buckling behavior: under compression, slit-beams first buckle, then snap, leading to trista-bility within the hysteretic regime. A truss model explains these phenomena by uncovering the interplay of geometric and slit induced nonlinearities. Leveraging these insights, we realize multi-slit beams with programmable behavior, unlocking a vast design space featuring giant hysteresis, quadstability, multi-step snapping, tristability at zero compression, and compression-induced snapping between left and right-buckled states. Our strategy is general, simple to design and implement, and enables mechanical metamaterials and devices with advanced memory and sequential behavior.

cond-mat.soft↗

arXiv2025

Aging of amorphous materials under cyclic strain

Amorphous materials driven away from equilibrium display a diverse repertoire of complex, history-dependent behaviors. One striking feature is a failure to return to equilibrium after an abrupt change in otherwise static external conditions. Instead, amorphous materials often exhibit physical aging: an ever-slowing, nonexponential relaxation that can span a huge range of timescales. Here we examine the aging behavior of three different amorphous materials subjected to slow periodic driving. The results reveal a generic aging phenomenon characterized by a logarithmic decay of dissipation per cycle. This observation is evaluated against several mesoscopic models of amorphous matter that successfully capture aging under static conditions: (i) a collection of noninteracting relaxation processes (ii) a noisy hysteron model with random pairwise interactions, and (iii) a structural model consisting of a random network of bi-stable elastic bonds. We find that only the latter model reproduces all experimental findings and relate its success to its persistent, slow exploration of a complex energy landscape with clear signatures of replica symmetry breaking. Thus, cyclic driving emerges as a simple yet powerful protocol to characterize amorphous materials, probe their complex energy landscapes, and distinguish between different models.

cond-mat.soft↗

arXiv2025

Accelerated snapping of slender beams under lateral forcing

The hysteretic snapping under lateral forcing of a compressed, buckled beam is fundamental for many devices and mechanical metamaterials. For a single-tip lateral pusher, an important limitation is that snapping requires the pusher to cross the centerline of the beam. Here, we show that dual-tip pushers allow accelerated snapping, where the beam snaps before the pusher reaches the centerline. As a consequence, we show that when a buckled beam under increased compression comes in contact with a dual-tip pusher, it can snap to the opposite direction -- this is impossible with a single-tip pusher. Additionally, we reveal a novel two-step snapping regime, in which the beam sequentially loses contact with the two tips of the dual-tip pusher. To characterize this class of snapping instabilities, we employ a systematic modal expansion of the beam shape. This expansion allows us to capture and analyze the transition from one-step to two-step snapping geometrically. Finally we demonstrate how to maximize the distance between the pusher and the beam's centerline at the moment of snapping. Together, our work opens up a new avenue for quantitatively and qualitatively controlling and modifying the snapping of buckled beams, with potential applications in mechanical sensors, actuators, and metamaterials.

cond-mat.soft↗

arXiv2025

Transients and multiperiodic responses: a hierarchy of material bits

When cyclically driven, certain disordered materials exhibit transient and multiperiodic responses that are difficult to reproduce in synthetic materials. Here, we show that elementary multiperiodic elements with period T=2, togglerons, can serve as building blocks for such responses. We experimentally realize metamaterials composed of togglerons with tunable transients and periodic responses - including odd periods. Our approach suggests a hierarchy of increasingly complex elements in frustrated media, and opens a new strategy for rational design of sequential metamaterials.

cond-mat.soft↗

arXiv2025

Geometric control and memory in networks of hysteretic elements

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 maps reveal how the physical network controls the signs, magnitudes, symmetries, and pair-wise 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.

cond-mat.soft↗

arXiv2025

Colloidal Pivots Enable Brownian Metamaterials and Machines

Biological machines harness targeted deformations that can be actuated by Brownian fluctuations. However, while synthetic micromachines can similarly leverage targeted deformations they are too stiff to be driven by thermal fluctuations and thus require strong forcing. Furthermore, systems that are able to change their conformation by thermal fluctuations do so uncontrollably or require external control. Here we leverage DNA-based sliding contacts to create colloidal pivots, rigid anisotropic objects that freely fluctuate around their pivot point, and use a hierarchical strategy to assemble these into Brownian metamaterials and machines with targeted deformation modes. We realize the archetypical rotating diamond and rotating triangle, or Kagome, geometries, and quantitatively show how thermal fluctuations drive their predicted auxetic deformations. Finally, we implement magnetic particles into the colloidal pivots to achieve an elementary Brownian machine with easily actuatable deformations that can harness Brownian fluctuations. Together, our work introduces a strategy for creating thermal mechanical metamaterials and leverages them for functional Brownian devices, paving the way to materialize flexible, actuatable structures for micro-robots, smart materials, and nano-medicine.

cond-mat.soft↗

arXiv2024

Roadmap for Animate Matter

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

cond-mat.mtrl-sci↗

arXiv2024

Prospecting for Pluripotency in Metamaterial Design

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

cond-mat.soft↗

arXiv2024

The Collective Snapping of a Pair of Bumping Buckled Beams

When a pair of parallel buckling beams of unequal width make lateral contact under increasing compression, eventually either the thin or the thick beam will snap, leading to collective motion of the beam pair. Using experiments and FEM simulations, we find that the distance $D$ between the beams selects which beam snaps first, and that the critical distance $D^*$ scales linear with the combined width of the two beams. To understand this behavior, we show that the collective motion of the beams is governed by a pitchfork bifurcation that occurs at strains just below snapping. Specifically, we use a model of two coupled Bellini trusses to find a closed form expression for the location of this pitchfork bifurcation that captures the linear scaling of $D^*$ with beam width. Our work uncovers a novel elastic instability that combines buckling, snapping and contact nonlinearities. This instability underlies the packing of parallel confined beams, and can be leveraged in advanced metamaterials.

cond-mat.soft↗

arXiv2023

Emergent Nonlocal Combinatorial Design Rules for Multimodal Metamaterials

Combinatorial mechanical metamaterials feature spatially textured soft modes that yield exotic and useful mechanical properties. While a single soft mode often can be rationally designed by following a set of tiling rules for the building blocks of the metamaterial, it is an open question what design rules are required to realize multiple soft modes. Multimodal metamaterials would allow for advanced mechanical functionalities that can be selected on the fly. Here we introduce a transfer matrix-like framework to design multiple soft modes in combinatorial metamaterials composed of aperiodic tilings of building blocks. We use this framework to derive rules for multimodal designs for a specific family of building blocks. We show that such designs require a large number of degeneracies between constraints, and find precise rules on the real space configuration that allow such degeneracies. These rules are significantly more complex than the simple tiling rules that emerge for single-mode metamaterials. For the specific example studied here, they can be expressed as local rules for tiles composed of pairs of building blocks in combination with a nonlocal rule in the form of a global constraint on the type of tiles that are allowed to appear together anywhere in the configuration. This nonlocal rule is exclusive to multimodal metamaterials and exemplifies the complexity of rational design of multimode metamaterials. Our framework is a first step towards a systematic design strategy of multimodal metamaterials with spatially textured soft modes.

cond-mat.soft↗