Giovanni Noselli

Structures buckling under tensile dead load

Some 250 years after the systematic experiments by Musschenbroek and their rationalization by Euler, for the first time we show that it is possible to design structures (i.e. mechanical systems whose elements are governed by the equation of the elastica) exhibiting bifurcation and instability (‘buckling’) under tensile load of constant direction and point of application (‘dead’). We show both theoretically and experimentally that the behaviour is possible in elementary structures with a single degree of freedom and in more complex mechanical systems, as related to the presence of a structural junction, called ‘slider’, allowing only relative transversal displacement between the connected elements. In continuous systems where the slider connects two elastic thin rods, bifurcation occurs both in tension and in compression, and is governed by the equation of the elastica, employed here for tensile loading, so that the deformed rods take the form of the capillary curve in a liquid, which is in fact governed by the equation of the elastica under tension. Since axial load in structural elements deeply influences dynamics, our results may provide application to innovative actuators for mechanical wave control; moreover, they open a new perspective in the understanding of failure within structural elements.

Liquid crystal elastomer strips as soft crawlers

Abstract In this paper, we speculate on a possible application of Liquid Crystal Elastomers to the field of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a flat solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change). The presence of frictional forces that are sensitive to the direction of sliding transforms reciprocal, ‘breathing-like’ deformations into directed forward motion. We derive formulas quantifying this motion in the case of distributed friction, by solving a differential inclusion for the displacement field. The simpler case of concentrated frictional interactions at the two ends of the strip is also solved, in order to provide a benchmark to compare the continuously distributed case with a finite-dimensional benchmark. We also provide explicit formulas for the axial force along the crawler body.

Crawling on directional surfaces

Abstract In this paper we study crawling locomotion based on directional frictional interactions, namely, frictional forces that are sensitive to the sign of the sliding velocity. Surface interactions of this type are common in biology, where they arise from the presence of inclined hairs or scales at the crawler/substrate interface, leading to low resistance when sliding ‘along the grain’, and high resistance when sliding ‘against the grain’. This asymmetry can be exploited for locomotion, in a way analogous to what is done in cross-country skiing (classic style, diagonal stride). We focus on a model system, namely, a continuous one-dimensional crawler and provide a detailed study of the motion resulting from several strategies of shape change. In particular, we provide explicit formulae for the displacements attainable with reciprocal extensions and contractions (breathing), or through the propagation of extension or contraction waves. We believe that our results will prove particularly helpful for the study of biological crawling motility and for the design of bio-mimetic crawling robots.

A robotic crawler exploiting directional frictional interactions: experiments, numerics and derivation of a reduced model

We present experimental and numerical results for a model crawler which is able to extract net positional changes from reciprocal shape changes, i.e. ‘breathing-like’ deformations, thanks to directional, frictional interactions with a textured solid substrate, mediated by flexible inclined feet. We also present a simple reduced model that captures the essential features of the kinematics and energetics of the gait, and compare its predictions with the results from experiments and from numerical simulations.

Poroelastic toughening in polymer gels: A theoretical and numerical study

Abstract We explore the Mode I fracture toughness of a polymer gel containing a semi-infinite, growing crack. First, an expression is derived for the energy release rate within the linearized, small-strain setting. This expression reveals a crack tip velocity-independent toughening that stems from the poroelastic nature of polymer gels. Then, we establish a poroelastic cohesive zone model that allows us to describe the micromechanics of fracture in gels by identifying the role of solvent pressure in promoting poroelastic toughening. We evaluate the enhancement in the effective fracture toughness through asymptotic analysis. We confirm our theoretical findings by means of numerical simulations concerning the case of a steadily propagating crack. In broad terms, our results explain the role of poroelasticity and of the processes occurring in the fracturing region in promoting toughening of polymer gels.

Effects of the constraint's curvature on structural instability: tensile buckling and multiple bifurcations

Bifurcation of an elastic structure crucially depends on the curvature of the constraints against which the ends of the structure are prescribed to move, an effect that deserves more attention than it has received so far. In fact, we show theoretically and provide definitive experimental verification that an appropriate curvature of the constraint over which the end of a structure has to slide strongly affects buckling loads and can induce: (i) tensile buckling; (ii) decreasing- (softening), increasing- (hardening) or constant-load (null stiffness) postcritical behaviour; and (iii) multiple bifurcations, determining for instance two bifurcation loads (one tensile and one compressive) in a single-degree-of-freedom elastic system. We show how to design a constraint profile to obtain a desired postcritical behaviour and we provide the solution for the elastica constrained to slide along a circle on one end, representing the first example of an inflexional elastica developed from a buckling in tension. These results have important practical implications in the design of compliant mechanisms and may find applications in devices operating in quasi-static or dynamic conditions, even at the nanoscale.

An analysis of competing toughening mechanisms in layered and particulate solids

The relative potency of common toughening mechanisms is explored for layered solids and particulate solids, with an emphasis on crack multiplication and plasticity. First, the enhancement in toughness due to a parallel array of cracks in an elastic solid is explored, and the stability of co-operative cracking is quantified. Second, the degree of synergistic toughening is determined for combined crack penetration and crack kinking at the tip of a macroscopic, mode I crack; specifically, the asymptotic problem of self-similar crack advance (penetration mode) versus

New phenomena in nonlinear elastic structures: from tensile buckling to configurational forces

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