arXiv subjects

Pedro M. Reis

Publications and source records attributed to Pedro M. Reis.

At least 37 records · Page 2Linked to original sources

arXiv2021

A geometrically exact model for thin magneto-elastic shells

We develop a reduced model for hard-magnetic, thin, linear-elastic shells that can be actuated through an external magnetic field, with geometrically exact strain measures. Assuming a reduced kinematics based on the Kirchhoff-Love assumption, we derive a reduced two-dimensional magneto-elastic energy that can be minimized through numerical analysis. In parallel, we simplify the reduced energy by expanding it up to the second-order in the displacement field and provide a physical interpretation. Our theoretical analysis allows us to identify and interpret the two primary mechanisms dictating the magneto-elastic response: a combination of equivalent magnetic pressure and forces at the first order, and distributed magnetic torques at the second order. We contrast our reduced framework against a three-dimensional nonlinear model by investigating three test cases involving the indentation and the pressure buckling of shells under magnetic loading. We find excellent agreement between the two approaches, thereby verifying our reduced model for shells undergoing nonlinear and non-axisymmetric deformations. We believe that our model for magneto-elastic shells will serve as a valuable tool for the rational design of magnetic structures, enriching the set of reduced magnetic models.

cond-mat.soft↗

arXiv2021

Smooth triaxial weaving with naturally curved ribbons

Triaxial weaving is a handicraft technique that has long been used to create curved structures using initially straight and flat ribbons. Weavers typically introduce discrete topological defects to produce nonzero Gaussian curvature, albeit with faceted surfaces. We demonstrate that, by tuning the in-plane curvature of the ribbons, the integrated Gaussian curvature of the weave can be varied continuously, which is not feasible using traditional techniques. Further, we reveal that the shape of the physical unit cells is dictated solely by the in-plane geometry of the ribbons, not elasticity. Finally, we leverage the geometry-driven nature of triaxial weaving to design a set of ribbon profiles to weave smooth spherical, ellipsoidal, and toroidal structures.

cond-mat.soft↗

arXiv2021

A comprehensive framework for hard-magnetic beams: reduced-order theory, 3D simulations, and experiments

Thin beams made of magnetorheological elastomers embedded with hard magnetic particles (hard-MREs) are capable of large deflections under an applied magnetic field. We propose a comprehensive framework, comprising a beam model and 3D finite element modeling (FEM), to describe the behavior of hard-MRE beams under both uniform and constant gradient magnetic fields. First, based on the Helmholtz free energy of bulk (3D) hard-MREs, we perform dimensional reduction to derive a 1D description and obtain the equilibrium equation of the beam through variational methods. In parallel, we extend the existing 3D continuum theory for hard-MREs to the general case of non-uniform fields by incorporating the magnetic body force induced by the field gradient and implementing it in FEM. The beam model and FEM are first validated using experiments and then employed to predict the deflection of a cantilever beam in either a uniform or a constant gradient field. The corresponding parameters governing the magneto-elastic coupling are identified. Then, a set of comparative numerical studies for actuation in different configurations yields additional insight into the beam response. Our study builds on previous work on hard-MRE beams, while providing a more complete framework, both in terms of the methodologies used and the configurations considered, to serve as a valuable predictive toolbox for the rational design of beam-like hard-magnetic structures.

cond-mat.soft↗

arXiv2021

A Kirchhoff-like theory for hard magnetic rods under geometrically nonlinear deformation in three dimensions

Magneto-rheological elastomers (MREs) are functional materials that can be actuated by applying an external magnetic field. MREs comprise a composite of hard magnetic particles dispersed into a nonmagnetic elastomeric matrix. By applying a strong magnetic field, one can magnetize the structure to program its deformation under the subsequent application of an external field. Hard MREs, whose coercivities are large, have been receiving particular attention because the programmed magnetization remains unchanged upon actuation. Hence, once a structure made of a hard MRE is magnetized, it can be regarded as magnetized permanently. Motivated by a new realm of applications, there have been significant theoretical developments in the continuum description of hard MREs. By reducing the 3D description into 1D or 2D via dimensional reduction, several theories of hard magnetic slender structures such as linear beams, elastica, and shells have been recently proposed. In this paper, we derive an effective theory for MRE rods under geometrically nonlinear 3D deformation. Our theory is based on reducing the 3D magneto-elastic energy functional for the hard MREs into a 1D Kirchhoff-like description. Restricting the theory to 2D, we reproduce previous works on planar deformations. For further validation in the general case of 3D deformation, we perform precision experiments with both naturally straight and curved rods under either constant or constant-gradient magnetic fields. Our theoretical predictions are in excellent agreement with both discrete simulations and precision-model experiments. Finally, we discuss some limitations of our framework, as highlighted by the experiments, where long-range dipole interactions, which are neglected in the theory, can play a role.

cond-mat.soft↗

arXiv2021

Magneto-active elastic shells with tunable buckling strength

Shell buckling is central in many biological structures and advanced functional materials, even if, traditionally, this elastic instability has been regarded as a catastrophic phenomenon to be avoided for engineering structures. Either way, predicting critical buckling conditions remains a long-standing challenge. The subcritical nature of shell buckling imparts extreme sensitivity to material and geometric imperfections. Consequently, measured critical loads are inevitably lower than classic theoretical predictions. Here, we present a robust mechanism to dynamically tune the buckling strength of shells, exploiting the coupling between mechanics and magnetism. Our experiments on pressurized spherical shells made of a magnetorheological elastomer demonstrate the tunability of their buckling pressure via magnetic actuation. We develop a theoretical model for thin magnetic elastic shells, which rationalizes the underlying mechanism, in excellent agreement with experiments. A dimensionless magneto-elastic buckling number is recognized as the key governing parameter, combining the geometrical, mechanical, and magnetic properties of the system.

cond-mat.soft↗

arXiv2021

The shapes of physical trefoil knots

We perform a compare-and-contrast investigation between the equilibrium shapes of physical and ideal trefoil knots, both in closed and open configurations. Ideal knots are purely geometric abstractions for the tightest configuration tied in a perfectly flexible, self-avoiding tube with an inextensible centerline and undeformable cross-sections. Here, we construct physical realizations of tight trefoil knots tied in an elastomeric rod, and use X-ray tomography and 3D finite element simulation for detailed characterization. Specifically, we evaluate the role of elasticity in dictating the physical knot's overall shape, self-contact regions, curvature profile, and cross-section deformation. We compare the shape of our elastic knots to prior computations of the corresponding ideal configurations. Our results on tight physical knots exhibit many similarities to their purely geometric counterparts, but also some striking dissimilarities that we examine in detail. These observations raise the hypothesis that regions of localized elastic deformation, not captured by the geometric models, could act as precursors for the weak spots that compromise the strength of knotted filaments.

cond-mat.soft↗

arXiv2020

Technical Brief: Finite Element Modeling of Tight Elastic Knots

We present a methodology to simulate the mechanics of knots in elastic rods using geometrically nonlinear, full three-dimensional (3D) finite element analysis. We focus on the mechanical behavior of knots in tight configurations, for which the full 3D deformation must be taken into account. To set up the topology of our knotted structures, we apply a sequence of prescribed displacement steps to the centerline of an initially straight rod that is meshed with 3D solid elements. Self-contact is enforced with a normal penalty force combined with Coulomb friction. As test cases, we investigate both overhand and figure-of-eight knots. Our simulations are validated with precision model experiments, combining rod fabrication and X-ray tomography. Even if the focus is given to the methods, our results reveal that 3D deformation of tight elastic knots is central to their mechanical response. These findings contrast to a previous analysis of loose knots, for which 1D centerline-based rod theories sufficed for a predictive understanding. Our method serves as a robust framework to access complex mechanical behavior of tightly knotted structures that are not readily available through experiments nor existing reduced-order theories.

cond-mat.soft↗

arXiv2020

Mechanics of two filaments in tight contact: The orthogonal clasp

Networks of flexible filaments often involve regions of tight contact. Predictively understanding the equilibrium configurations of these systems is challenging due to intricate couplings between topology, geometry, large nonlinear deformations, and friction. Here, we perform an in-depth study of a simple yet canonical problem that captures the essence of contact between filaments. In the orthogonal clasp, two filaments are brought into contact, with each centerline lying in one of a pair of orthogonal planes. Our data from X-ray tomography (micro-CT) and mechanical testing experiments are in excellent agreement with the finite element method (FEM) simulations. Despite the apparent simplicity of the physical system, the data exhibits strikingly unintuitive behavior, even when the contact is frictionless. Specifically, we observe a curvilinear diamond-shaped ridge in the contact pressure field between the two filaments, sometimes with an inner gap. When a relative displacement is imposed between the filaments, friction is activated, and a highly asymmetric pressure field develops. These findings contrast to the classic capstan analysis of a single filament wrapped around a rigid body. Both the micro-CT and the FEM data indicate that the cross-sections of the filaments can deform significantly. Nonetheless, an idealized geometrical theory assuming undeformable tube cross-sections and neglecting elasticity rationalizes our observations qualitatively and highlights the central role of the small but finite tube radius of the filaments. We believe that our orthogonal clasp analysis provides a building block for future modeling efforts in frictional contact mechanics of more complex filamentary structures.

cond-mat.soft↗

arXiv2015

Curvature-controlled defect localization in crystalline wrinkling patterns

We investigate the influence of curvature and topology on crystalline wrinkling patterns in generic elastic bilayers. Our numerical analysis predicts that the total number of defects created by adiabatic compression exhibits universal quadratic scaling for spherical, ellipsoidal and toroidal surfaces over a wide range of system sizes. However, both the localization of individual defects and the orientation of defect chains depend strongly on the local Gaussian curvature and its gradients across a surface. Our results imply that curvature and topology can be utilized to pattern defects in elastic materials, thus promising improved control over hierarchical bending, buckling or folding processes. Generally, this study suggests that bilayer systems provide an inexpensive yet valuable experimental test-bed for exploring the effects of geometrically induced forces on assemblies of topological charges.

cond-mat.soft↗

arXiv2011

Wrinkling hierarchy in constrained thin sheets from suspended graphene to curtains

We show that thin sheets under boundary confinement spontaneously generate a universal self-similar hierarchy of wrinkles. From simple geometry arguments and energy scalings, we develop a formalism based on wrinklons, the transition zone in the merging of two wrinkles, as building-blocks of the global pattern. Contrary to the case of crumple paper where elastic energy is focused, this transition is described as smooth in agreement with a recent numerical work. This formalism is validated from hundreds of nm for graphene sheets to meters for ordinary curtains, which shows the universality of our description. We finally describe the effect of an external tension to the distribution of the wrinkles.

cond-mat.mtrl-sci↗

arXiv2010

Tearing Graphene Sheets From Adhesive Substrates Produces Tapered Nanoribbons

Graphene is a truly two-dimensional atomic crystal with exceptional electronic and mechanical properties. Whereas conventional bulk and thin-film materials have been studied extensively, the key mechanical properties of graphene, such as tearing and cracking, remain unknown, partly due to its two-dimensional nature and ultimate single-atom-layer thickness, which result in the breakdown of conventional material models. By combining first-principles ReaxFF molecular dynamics and experimental studies, a bottom-up investigation of the tearing of graphene sheets from adhesive substrates is reported, including the observation of the formation of tapered graphene nanoribbons. Through a careful analysis of the underlying molecular rupture mechanisms, it is shown that the resulting nanoribbon geometry is controlled by both the graphene-substrate adhesion energy and by the number of torn graphene layers. By considering graphene as a model material for a broader class of two-dimensional atomic crystals, these results provide fundamental insights into the tearing and cracking mechanisms of highly confined nanomaterials.

cond-mat.mtrl-sci↗

arXiv2008

The Clapping Book

A steady horizontal air stream flows across a book clamped at its downstream end. Pages lift off to form a growing bent stack whose shape is determined by the torques associated with aerodynamic forces, weight and elastic resistance to bending. As more pages lift off to join the bent stack, the increasing importance of bending rigidity to dynamic pressure eventually causes the book to clap shut. The process restarts, and self-sustained oscillations emerge. [Fluid dynamics video]

physics.flu-dyn↗

arXiv2006

Universal velocity distributions in an experimental granular fluid

We present experimental results on the velocity statistics of a uniformly heated granular fluid, in a quasi-2D configuration. We find the base state, as measured by the single particle velocity distribution $f(c)$, to be universal over a wide range of filling fractions and only weakly dependent on all other system parameters. There is a consistent overpopulation in the distribution's tails, which scale as $f\propto\exp(\mathrm{const.}\times c^{-3/2})$. More importantly, the high probability central region of $f(c)$, at low velocities, deviates from a Maxwell-Boltzmann by a second order Sonine polynomial with a single adjustable parameter, in agreement with recent theoretical analysis of inelastic hard spheres driven by a stochastic thermostat. To our knowledge, this is the first time that Sonine deviations have been measured in an experimental system.

cond-mat.soft↗

arXiv2006

Caging dynamics in a granular fluid

We report an experimental investigation of the caging motion in a uniformly heated granular fluid, for a wide range of filling fractions, $ϕ$. At low $ϕ$ the classic diffusive behavior of a fluid is observed. However, as $ϕ$ is increased, temporary cages develop and particles become increasingly trapped by their neighbors. We statistically analyze particle trajectories and observe a number of robust features typically associated with dense molecular liquids and colloids. Even though our monodisperse and quasi-2D system is known to not exhibit a glass transition, we still observe many of the precursors usually associated with glassy dynamics. We speculate that this is due to a process of structural arrest provided, in our case, by the presence of crystallization.

cond-mat.soft↗

arXiv2006

Phases of granular segregation in a binary mixture

We present results from an extensive experimental investigation into granular segregation of a shallow binary mixture in which particles are driven by frictional interactions with the surface of a vibrating horizontal tray. Three distinct phases of the mixture are established viz; binary gas (unsegregated), segregation liquid and segregation crystal. Their ranges of existence are mapped out as a function of the system's primary control parameters using a number of measures based on Voronoi tessellation. We study the associated transitions and show that segregation can be suppressed is the total filling fraction of the granular layer, $C$, is decreased below a critical value, $C_{c}$, or if the dimensionless acceleration of the driving, $γ$, is increased above a value $γ_{c}$.

cond-mat.soft↗

arXiv2006

Crystallization of a quasi-two-dimensional granular fluid

We experimentally investigate the crystallization of a uniformly heated quasi-2D granular fluid as a function of filling fraction. Our experimental results for the Lindemann melting criterion, the radial distribution function, the bond order parameter and the statistics of topological changes at the particle level are the same as those found in simulations of equilibrium hard disks. This direct mapping suggests that the study of equilibrium systems can be effectively applied to study non-equilibrium steady states like those found in our driven and dissipative granular system.

cond-mat.soft↗

arXiv2004

Segregation Mechanisms in a Model of an Experimental Binary Granular Mixture

A simple phenomenological model of a binary granular mixture is developed and investigated numerically. We attempt to model the experimental system of [1,2] where a horizontally vibrated binary monolayer was found to exhibit a transition from a mixed to a segregated state as the filling fraction of the mixture was increased. This model is found to reproduce much of the experimentally observed behaviour, most importantly the transition from the mixed to the segregated state. We use the model to investigate granular segregation mechanisms and explain the experimentally observed behaviour.

cond-mat.stat-mech↗

arXiv2003

Oscillatory fracture path in thin elastic sheet

We report a novel mode of oscillatory crack propagation when a cutting tip is driven through a thin brittle polymer film. The phenomenon is so robust that it can easily be reproduced at hand (using CD packaging material for example). Careful experiments show that the amplitude and wavelength of the oscillatory crack path scale lineraly with the width of the cutting tip over a wide range of lenghtscales but are independant of the width of thje sheet and the cutting speed. A simple geometric model is presented, which provides a simple but thorough interpretation of the oscillations.

cond-mat↗