arXiv subjects

Marcelo A. Dias

Publications and source records attributed to Marcelo A. Dias.

26 records · Page 2Linked to original sources

arXiv2017

Analytic analysis of auxetic metamaterials through analogy with rigid link systems

Recent progress in advanced additive manufacturing techniques has stimulated the growth of the field of mechanical metamaterials. One area particular interest in this subject is the creation of auxetic material properties through elastic instability. This paper focuses on a novel methodology in the analysis of auxetic metamaterials through analogy with rigid link lattice systems. Our analytic methodology gives extremely good agreement with finite element simulations for both the onset of elastic instability and post-buckling behaviour including Poisson's ratio. The insight into the relationships between mechanisms within lattices and their mechanical behaviour has the potential to guide the rational design of lattice based metamaterials.

cond-mat.soft↗

arXiv2016

Designing recipes for auxetic behaviour of 2-d lattices

We present an analytical model to investigate the mechanics of 2-dimensional lattices composed of elastic beams of non-uniform cross-section. Our approach is based on reducing a lattice to a single beam subject to the action of a set of linear and torsional springs, thus allowing the problem to be solved through a transfer matrix method. We show a non-trivial region of design space that yields materials with auxetic properties for strains greater than that required to trigger elastic instability. The critical loading required to make this transition from positive to negative Poisson's ratio is calculated. Furthermore, we present lattice parameters that provide direction-dependent deformation modes offering great tailorability of the mechanical properties of finite size lattices. Not only is our analytical formulation in good agreement with the finite element simulation results, but it provides an insight into the role of the interplay between structure and elastic instability, and gives an efficient methodology to pursue questions of rational design in the field of mechanical metamaterials.

cond-mat.soft↗

arXiv2015

Minimal model for transient swimming in a liquid crystal

When a microorganism begins swimming from rest in a Newtonian fluid such as water, it rapidly attains its steady-state swimming speed since changes in the velocity field spread quickly when the Reynolds number is small. However, swimming microorganisms are commonly found or studied in complex fluids. Because these fluids have long relaxation times, the time to attain the steady- state swimming speed can also be long. In this article we study the swimming startup problem in the simplest liquid crystalline fluid: a two-dimensional hexatic liquid crystal film. We study the dependence of startup time on anchoring strength and Ericksen number, which is the ratio of viscous to elastic stresses. For strong anchoring, the fluid flow starts up immediately but the liquid crystal field and swimming velocity attain their sinusoidal steady-state values after a time proportional to the relaxation time of the liquid crystal. When the Ericksen number is high, the behavior is the same as in the strong anchoring case for any anchoring strength. We also find that the startup time increases with the ratio of the rotational viscosity to the shear viscosity, and then ultimately saturates once the rotational viscosity is much greater than the shear viscosity.

physics.flu-dyn↗

arXiv2014

"Wunderlich, meet Kirchhoff": A general and unified description of elastic ribbons and thin rods

The equations for the equilibrium of a thin elastic ribbon are derived by adapting the classical theory of thin elastic rods. Previously established ribbon models are extended to handle geodesic curvature, natural out-of-plane curvature, and a variable width. Both the case of a finite width (Wunderlich's model) and the limit of small width (Sadowksky's model) are recovered. The ribbon is assumed to remain developable as it deforms, and the direction of the generatrices is used as an internal variable. Internal constraints expressing inextensibility are identified. The equilibrium of the ribbon is found to be governed by an equation of equilibrium for the internal variable involving its second-gradient, by the classical Kirchhoff equations for thin rods, and by specific, thin-rod-like constitutive laws; this extends the results of Starostin and van der Heijden (2007) to a general ribbon model. Our equations are applicable in particular to ribbons having geodesic curvature, such as an annulus cut out in a piece of paper. Other examples of application are discussed. By making use of a material frame rather than the Frénet-Serret's frame, the present work unifies the description of thin ribbons and thin rods.

cond-mat.soft↗

arXiv2013

Swimming near Deformable Membranes at Low Reynolds Number

Microorganisms are rarely found in Nature swimming freely in an unbounded fluid. Instead, they typically encounter other organisms, hard walls, or deformable boundaries such as free interfaces or membranes. Hydrodynamic interactions between the swimmer and nearby objects lead to many interesting phenomena, such as changes in swimming speed, tendencies to accumulate or turn, and coordinated flagellar beating. Inspired by this class of problems, we investigate locomotion of microorganisms near deformable boundaries. We calculate the speed of an infinitely long swimmer close to a flexible surface separating two fluids; we also calculate the deformation and swimming speed of the flexible surface. When the viscosities on either side of the flexible interface differ, we find that fluid is pumped along or against the swimming direction, depending on which viscosity is greater.

physics.flu-dyn↗

arXiv2013

A non-linear rod model for folded elastic strips

We consider the equilibrium shapes of a thin, annular strip cut out in an elastic sheet. When a central fold is formed by creasing beyond the elastic limit, the strip has been observed to buckle out-of-plane. Starting from the theory of elastic plates, we derive a Kirchhoff rod model for the folded strip. A non-linear effective constitutive law incorporating the underlying geometrical constraints is derived, in which the angle the ridge appears as an internal degree of freedom. By contrast with traditional thin- walled beam models, this constitutive law captures large, non-rigid deformations of the cross-sections, including finite variations of the dihedral angle at the ridge. Using this effective rod theory, we identify a buckling instability that produces the out-of-plane configurations of the folded strip, and show that the strip behaves as an elastic ring having one frozen mode of curvature. In addition, we point out two novel buckling patterns: one where the centerline remains planar and the ridge angle is modulated; another one where the bending deformation is localized. These patterns are observed experimentally, explained based on stability analyses, and reproduced in simulations of the post-buckled configurations.

cond-mat.soft↗

arXiv2012

The shape and mechanics of curved fold origami structures

We develop recursion equations to describe the three-dimensional shape of a sheet upon which a series of concentric curved folds have been inscribed. In the case of no stretching outside the fold, the three-dimensional shape of a single fold prescribes the shape of the entire origami structure. To better explore these structures, we derive continuum equations, valid in the limit of vanishing spacing between folds, to describe the smooth surface intersecting all the mountain folds. We find that this surface has negative Gaussian curvature with magnitude equal to the square of the fold's torsion. A series of open folds with constant fold angle generate a helicoid.

cond-mat.soft↗

arXiv2012

Geometric Mechanics of Curved Crease Origami

Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is folded along a central circular curve to form a three-dimensional buckled structure driven by geometrical frustration. We quantify this shape in terms of the radius of the circle, the dihedral angle of the fold and the mechanical properties of the sheet of paper and the fold itself. When the sheet is isometrically deformed everywhere except along the fold itself, stiff folds result in creases with constant curvature and oscillatory torsion. However, relatively softer folds inherit the broken symmetry of the buckled shape with oscillatory curvature and torsion. Our asymptotic analysis of the isometrically deformed state is corroborated by numerical simulations which allow us to generalize our analysis to study multiply folded structures.

cond-mat.soft↗