arXiv subjects

Luuk A. Lubbers

Publications and source records attributed to Luuk A. Lubbers.

5 recordsLinked to original sources

arXiv2019

Excess Floppy Modes and Multi-Branched Mechanisms in Metamaterials with Symmetries

Floppy modes --- deformations that cost zero energy --- are central to the mechanics of a wide class of systems. For disordered systems, such as random networks and particle packings, it is well-understood how the number of floppy modes is controlled by the topology of the connections. Here we uncover that symmetric geometries, present in e.g. mechanical metamaterials, can feature an unlimited number of excess floppy modes that are absent in generic geometries, and in addition can support floppy modes that are multi-branched. We study the number $Δ$ of excess floppy modes by comparing generic and symmetric geometries with identical topologies, and show that $Δ$ is extensive, peaks at intermediate connection densities, and exhibits mean field scaling. We then develop an approximate yet accurate cluster counting algorithm that captures these findings. Finally, we leverage our insights to design metamaterials with multiple folding mechanisms.

cond-mat.soft↗

arXiv2017

Dynamical Theory of the Inverted Cheerios Effect

Recent experiments have shown that liquid drops on highly deformable substrates exhibit mutual interactions. This is similar to the Cheerios effect, the capillary interaction of solid particles at a liquid interface, but now the roles of solid and liquid are reversed. Here we present a dynamical theory for this inverted Cheerios effect, taking into account elasticity, capillarity and the viscoelastic rheology of the substrate. We compute the velocity at which droplets attract, or repel, as a function of their separation. The theory is compared to a simplified model in which the viscoelastic dissipation is treated as a localized force at the contact line. It is found that the two models differ only at small separation between the droplets, and both of them accurately describe experimental observations.

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↗

arXiv2014

Drops on soft solids: Free energy and double transition of contact angles

The equilibrium shape of liquid drops on elastic substrates is determined by minimising elastic and capillary free energies, focusing on thick incompressible substrates. The problem is governed by three length scales: the size of the drop $R$, the molecular size $a$, and the ratio of surface tension to elastic modulus $γ/E$. We show that the contact angles undergo two transitions upon changing the substrates from rigid to soft. The microscopic wetting angles deviate from Young's law when $γ/Ea \gg 1$, while the apparent macroscopic angle only changes in the very soft limit $γ/ER \gg 1$. The elastic deformations are worked out in the simplifying case where the solid surface energy is assumed constant. The total free energy turns out lower on softer substrates, consistent with recent experiments.

physics.flu-dyn↗

arXiv2014

Dense Suspension Splat: Monolayer Spreading and Hole Formation After Impact

We use experiments and minimal numerical models to investigate the rapidly expanding monolayer formed by the impact of a dense suspension drop against a smooth solid surface. The expansion creates a lace-like pattern of particle clusters separated by particle-free regions. Both the expansion and the development of the spatial inhomogeneity are dominated by particle inertia, therefore robust and insensitive to details of the surface wetting, capillarity and viscous drag.

physics.flu-dyn↗