arXiv subjects

Martin van Hecke

Publications and source records attributed to Martin van Hecke.

At least 55 records · Page 3Linked to original sources

arXiv2016

Contact Changes of Sheared Systems: Scaling, Correlations, and Mechanisms

We probe the onset and effect of contact changes in 2D soft harmonic particle packings which are sheared quasistatically under controlled strain. First, we show that in the majority of cases, the first contact changes correspond to the creation or breaking of contacts on a single particle, with contact breaking overwhelmingly likely for low pressures and/or small systems, and contact making and breaking equally likely for large pressures and in the thermodynamic limit. The statistics of the corresponding strains are near-Poissonian. The mean characteristic strains exhibit scaling with the number of particles N and pressure P, and reveal the existence of finite size effects akin to those seen for linear response quantities. Second, we show that linear response accurately predicts the strains of the first contact changes, which allows us to study the scaling of the characteristic strains of making and breaking contacts separately. Both of these show finite size scaling, and we formulate scaling arguments that are consistent with the observed behavior. Third, we probe the effect of the first contact change on the shear modulus G, and show in detail how the variation of G remains smooth and bounded in the large system size limit: even though contact changes occur then at vanishingly small strains, their cumulative effect, even at a fixed value of the strain, are limited, so that effectively, linear response remains well-defined. Fourth, we explore multiple contact changes under shear, and find strong and surprising correlations between alternating making and breaking events. Fifth, we show that by making a link with extremal statistics, our data is consistent with a very slow crossover to self averaging with system size, so that the thermodynamic limit is reached much more slowly than expected based on finite size scaling of elastic quantities or contact breaking strains.

cond-mat.soft↗

arXiv2016

Combinatorial Design of Textured Mechanical Metamaterials

The structural complexity of metamaterials is limitless, although in practice, most designs comprise periodic architectures which lead to materials with spatially homogeneous features. More advanced tasks, arising in e.g. soft robotics, prosthetics and wearable tech, involve spatially textured mechanical functionality which require aperiodic architectures. However, a naïve implementation of such structural complexity invariably leads to frustration, which prevents coherent operation and impedes functionality. Here we introduce a combinatorial strategy for the design of aperiodic yet frustration-free mechanical metamaterials, whom we show to exhibit spatially textured functionalities. We implement this strategy using cubic building blocks - voxels - which deform anisotropically, a local stacking rule which allows cooperative shape changes by guaranteeing that deformed building blocks fit as in a 3D jigsaw puzzle, and 3D printing. We show that, first, these aperiodic metamaterials exhibit long-range holographic order, where the 2D pixelated surface texture dictates the 3D interior voxel arrangement. Second, they act as programmable shape shifters, morphing into spatially complex but predictable and designable shapes when uniaxially compressed. Third, their mechanical response to compression by a textured surface reveals their ability to perform sensing and pattern analysis. Combinatorial design thus opens a new avenue towards mechanical metamaterials with unusual order and machine-like functionalities.

cond-mat.soft↗

arXiv2016

Programmable Mechanical Metamaterials: the Role of Geometry

We experimentally and numerically study the precise role of geometry for the mechanics of biholar metamaterials, quasi-2D slabs of rubber patterned by circular holes of two alternating sizes. We recently showed how the response to uniaxial compression of these metamaterials can be programmed by their lateral confinement $^1$. In particular, there is a range of confining strains $\varepsilon_x$ for which the resistance to compression becomes non-trivial - non-monotonic or hysteretic - in a range of compressive strains $\varepsilon_y$. Here we show how the dimensionless geometrical parameters $t$ and $χ$, which characterize the porosity and size ratio of the holes that pattern these metamaterials, can significantly tune these ranges over a wide range. We study the behavior for the limiting cases where $t$ and $χ$ become large, and discuss the new physics that arises there. Away from these extreme limits, the variation of the strain ranges of interest is smooth with porosity, but the variation with size ratio evidences a cross-over at low $χ$ from biholar to monoholar (equal sized holes) behavior, related to the elastic instabilities in purely monoholar metamaterials$^2$. Our study provides precise guidelines for the rational design of programmable biholar metamaterials, tailored to specific applications, and indicates that the widest range of programmability arises for moderate values of both $t$ and $χ$.

cond-mat.soft↗

arXiv2016

Criticality in vibrated frictional flows at finite strain rate

We evidence critical fluctuations in the strain-rate of granular flows that are weakly vibrated. Strikingly, the critical point arises at {\em finite} values of the mean strain rate and vibration strength, far away from the yielding critical point at zero flow rate. We show that the global rheology, as well as the amplitude and correlation time of the fluctuations, are consistent with a mean-field, Landau like description, where strain rate and stress act as conjugated variables. We introduce a general model which captures the observed phenomenology, and argue that this type of critical behavior generically arises when self fluidization competes with friction.

cond-mat.soft↗

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

Origami building blocks: generic and special 4-vertices

Four rigid panels connected by hinges that meet at a point form a 4-vertex, the fundamental building block of origami metamaterials. Here we show how the geometry of 4-vertices, given by the sector angles of each plate, affects their folding behavior. For generic vertices, we distinguish three vertex types and two subtypes. We establish relationships based on the relative sizes of the sector angles to determine which folds can fully close and the possible mountain-valley assignments. Next, we consider what occurs when sector angles or sums thereof are set equal, which results in 16 special vertex types. One of these, flat-foldable vertices, has been studied extensively, but we show that a wide variety of qualitatively different folding motions exist for the other 15 special and 3 generic types. Our work establishes a straightforward set of rules for understanding the folding motion of both generic and special 4-vertices and serves as a roadmap for designing origami metamaterials.

cond-mat.soft↗

arXiv2015

Rigidity Loss in Disordered Systems: Three Scenarios

We reveal significant qualitative differences in the rigidity transition of three types of disordered network materials: randomly diluted spring networks, jammed sphere packings, and stress-relieved networks that are diluted using a protocol that avoids the appearance of floppy regions. The marginal state of jammed and stress-relieved networks are globally isostatic, while marginal randomly diluted networks show both overconstrained and underconstrained regions. When a single bond is added to or removed from these isostatic systems, jammed networks become globally overconstrained or floppy, whereas the effect on stress-relieved networks is more local and limited. These differences are also reflected in the linear elastic properties and point to the highly effective and unusual role of global self-organization in jammed sphere packings.

cond-mat.soft↗

arXiv2015

Heaping, Secondary Flows and Broken Symmetry in Flows of Elongated Granular Particles

In this paper we report experiments where we shear granular rods in split-bottom geometries, and find that a significant heap of height of least 40% of the filling height can form at the particle surface. We show that heaping is caused by a significant secondary flow, absent for spherical particles. Flow reversal transiently reverses the secondary flow, leading to a quick collapse and slower regeneration of the heap. We present a symmetry argument and experimental data that show that the generation of the secondary flow is driven by a misalignment of the mean particle orientation with the streamlines of the flow. This general mechanism is expected to be important in all flows of sufficiently anisometric grains.

cond-mat.soft↗

arXiv2014

Jamming in finite systems: stability, anisotropy, fluctuations and scaling

Athermal packings of soft repulsive spheres exhibit a sharp jamming transition in the thermodynamic limit. Upon further compression, various structural and mechanical properties display clean power-law behavior over many decades in pressure. As with any phase transition, the rounding of such behavior in finite systems close to the transition plays an important role in understanding the nature of the transition itself. The situation for jamming is surprisingly rich: the assumption that jammed packings are isotropic is only strictly true in the large-size limit, and finite-size has a profound effect on the very meaning of jamming. Here, we provide a comprehensive numerical study of finite-size effects in sphere packings above the jamming transition, focusing on stability as well as the scaling of the contact number and the elastic response.

cond-mat.soft↗

arXiv2014

Anisotropy of Weakly Vibrated Granular Flows

We experimentally probe the anisotropy of the fabric of weakly vibrated, flowing granular media. Depending on the driving parameters --- flow rate and vibration strength --- this anisotropy varies significantly. We show how the anisotropy collapses when plotted as function of the driving stresses, uncovering a direct link between stresses and anisotropy. Moreover, our data suggests that for small anisotropies, the shear stresses vanish. Anisotropy of the fabric of granular media thus plays a crucial role in determining the rheology of granular flows.

cond-mat.soft↗

arXiv2014

Origami Multistabilty: From Single Vertices to Metasheets

We explore the surprisingly rich energy landscape of origami-like folding planar structures. We show that the configuration space of rigid-paneled degree-4 vertices, the simplest building blocks of such systems, consists of at least two distinct branches meeting at the flat state. This suggests that generic vertices are at least bistable, but we find that the nonlinear nature of these branches allows for vertices with as many as five distinct stable states. In vertices with collinear folds and/or symmetry, more branches emerge leading to up to six stable states. Finally, we introduce a procedure to tile arbitrary 4-vertices while preserving their stable states, thus allowing the design and creation of multistable origami metasheets.

cond-mat.soft↗

arXiv2014

Contact Changes near Jamming

We probe the onset and effect of contact changes in soft harmonic particle packings which are sheared quasistatically. We find that the first contact changes are the creation or breaking of contacts on a single particle. We characterize the critical strain, statistics of breaking versus making a contact, and ratio of shear modulus before and after such events, and explain their finite size scaling relations. For large systems at finite pressure, the critical strain vanishes but the ratio of shear modulus before and after a contact change approaches one: linear response remains relevant in large systems. For finite systems close to jamming the critical strain also vanishes, but here linear response already breaks down after a single contact change.

cond-mat.soft↗

arXiv2014

Programmable Mechanical Metamaterials

We create mechanical metamaterials whose response to uniaxial compression can be programmed by lateral confinement, allowing monotonic, non-monotonic 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 multi stability and giant hysteresis.

cond-mat.soft↗

arXiv2013

Rheology of Weakly Vibrated Granular Media

We probe the rheology of weakly vibrated granular flows as function of flow rate, vibration strength and pressure by performing experiments in a vertically vibrated split-bottom shear cell. For slow flows, we establish the existence of a novel vibration dominated granular flow regime, where the driving stresses smoothly vanish as the driving rate is diminished. We distinguish three qualitatively different vibration dominated rheologies, most strikingly a regime where the shear stresses no longer are proportional to the pressure.

cond-mat.soft↗

arXiv2013

Nonlocal Granular Rheology: Role of Pressure and Anisotropy

We probe the secondary rheology of granular media, by imposing a main flow and immersing a vane-shaped probe into the slowly flowing granulate. The secondary rheology is then the relation between the exerted torque T and rotation rate ωof our probe. In the absence of any main flow, the probe experiences a clear yield-stress, whereas for any finite flow rate, the yield stress disappears and the secondary rheology takes on the form of a double exponential relation between ωand T. This secondary rheology does not only depend on the magnitude of T, but is anisotropic --- which we show by varying the relative orientation of the probe and main flow. By studying the depth dependence of the three characteristic torques that characterize the secondary rheology, we show that for counter flow, the dominant contribution is frictional like --- i.e., T and pressure are proportional for given ω--- whereas for co flow, the situation is more complex. Our experiments thus reveal the crucial role of anisotropy for the rheology of granular media.

cond-mat.soft↗

arXiv2013

Shock Waves in Weakly Compressed Granular Media

We experimentally probe nonlinear wave propagation in weakly compressed granular media, and observe a crossover from quasi-linear sound waves at low impact, to shock waves at high impact. We show that this crossover grows with the confining pressure $P_0$, whereas the shock wave speed is independent of $P_0$ --- two hallmarks of granular shocks predicted recently. The shocks exhibit powerlaw attenuation, which we model with a logarithmic law implying that local dissipation is weak. We show that elastic and potential energy balance in the leading part of the shocks.

cond-mat.soft↗

arXiv2012

Rheology of sedimenting particle pastes

We study the local and global rheology of non-Brownian suspensions in a solvent that is not density-matched, leading to either creaming or sedimentation of the particles. Both local and global measurements show that the incomplete density matching leads to the appearance of a critical shear rate above which the suspension is homogenized by the flow, and below which sedimentation or creaming happens. We show that the value of the critical shear rate and its dependence on the experimental parameters are governed by a simple competition between the viscous and gravitational forces, and present a simple scaling model that agrees with the experimental results from different types of experiments (local and global) in different setups and systems.

cond-mat.soft↗

arXiv2012

Particle Diffusion in Slow Granular Bulk Flows

We probe the diffusive motion of particles in slowly sheared three dimensional granular suspensions. For sufficiently large strains, the particle dynamics exhibits diffusive Gaussian statistics, with the diffusivity proportional to the local strain rate - consistent with a local, quasi static picture. Surprisingly, the diffusivity is also inversely proportional to the depth of the particles within the flow - at the free surface, diffusivity is thus ill defined. We find that the crossover to Gaussian displacement statistics is governed by the same depth dependence, evidencing a non-trivial strain scale in three dimensional granular flows.

cond-mat.soft↗