arXiv subjects

Francesco Dal Corso

Publications and source records attributed to Francesco Dal Corso.

At least 19 recordsLinked to original sources

arXiv2024

A simple yet effective ALE-FE method for the nonlinear planar dynamics of variable-length flexible rods

With recent advances in variable-length structures for use in soft actuation, energy harvesting, energy dissipation and metamaterials, the mathematical modelling and numerical simulation of physical systems with time-varying domains is becoming increasingly important. The planar nonlinear dynamics of one-dimensional elastic structures with variable domain is formulated from a Lagrangian approach by using a non-material reference frame. An Arbitrary Lagrangian-Eulerian (ALE) scheme is proposed where the domain is reparametrized based on a priori unknown configuration parameters. Based on this formulation, a Finite Element (FE) method is developed for theoretically predicting the evolution of a rod constrained at its ends by one or two sliding-sleeves, whose position and inclination can be varied in time, and under external loadings. Finally, case studies and instability problems are investigated to assess the reliability of the proposed formulation against others available and to demonstrate its effectiveness. With respect to previously developed methods for this type of structural problems, the present ALE-FE approach shows a strong theoretical and implementation simplicity, maintaining an efficient and fast convergence according to the cases analyzed. An open source code realized for the present ALE-FE model is made available for solving the nonlinear dynamics of planar systems constrained by one or two independent sliding sleeves. The present research paves the way for further extensions to easily implement solvers for the three-dimensional dynamics of flexible one- and two-dimensional structural systems with moving boundary conditions.

cond-mat.soft↗

arXiv2024

The elastica sling

The nonlinear mechanics of a flexible elastic rod constrained at its edges by a pair of sliding sleeves is analyzed. The planar equilibrium configurations of this variable-length elastica are found to have shape defined only by the inclination of the two constraints, while their distance is responsible only for scaling the size. By extending the theoretical stability criterion available for systems under isoperimetric constraints to the case of variable domains, the existence of no more than one stable equilibrium solution is revealed. The set of sliding sleeves' inclination pairs for which the stability is lost are identified. Such critical conditions allow the indefinite ejection of the flexible rod from the sliding sleeves, thus realizing an elastica sling. Finally, the theoretical findings are validated by experiments on a physical prototype. The present results lead to a novel actuation principle that may find application as a mechanism in energy harvesting, wave mitigation devices, and soft robotic locomotion.

cond-mat.soft↗

arXiv2024

Elastic solids under frictionless rigid contact and configurational force

A homogeneous elastic solid, bounded by a flat surface in its unstressed configuration, undergoes a finite strain when in frictionless contact against a rigid and rectilinear constraint, ending with a rounded or sharp corner, in a two-dimensional formulation. With a strong analogy to fracture mechanics, it is shown that (i.) a path-independent $J$--integral can be defined for frictionless contact problems, (ii.) which is equal to the energy release rate $G$ associated with an infinitesimal growth in the size of the frictionless constraint, and thus gives the value of the configurational force component along the sliding direction. Furthermore, it is found that (iii.) such a configurational sliding force is the Newtonian force component exerted by the elastic solid on the constraint at the frictionless contact. Assuming the kinematics of an Euler-Bernoulli rod for an elastic body of rectangular shape, the results (i.)--(iii.) lead to a new interpretation from a nonlinear solid mechanics perspective of the configurational forces recently disclosed for one-dimensional structures of variable length. Finally, approximate but closed-form solutions (validated with finite element simulations) are exploited to provide further insight into the effect of configurational forces. In particular, two applications are presented which show that a transverse compression can lead to Eulerian buckling or to longitudinal dynamic motion, both realizing novel examples of soft actuation mechanisms. As an application to biology, our results may provide a mechanical explanation for the observed phenomenon of negative durotaxis, where cells migrate from stiffer to softer environments.

cond-mat.soft↗

arXiv2024

Flutter instability in solids and structures, with a view on biomechanics and metamaterials

The phenomenon of oscillatory instability called \lq flutter' was observed in aeroelasticity and rotor dynamics about a century ago. Driven by a series of applications involving nonconservative elasticity theory at different physical scales, ranging from nanomechanics to the mechanics of large space structures and including biomechanical problems of motility and growth, research on flutter is experiencing a new renaissance. A review is presented of the most notable applications and recent advances in fundamentals, both theoretical and experimental aspects, of flutter instability and Hopf bifurcation. Open problems, research gaps, and new perspectives for investigations are indicated.

physics.class-ph↗

arXiv2024

Non-holonomic constraints inducing flutter insability in structures under conservative loadings

Non-conservative loads of the follower type are usually believed to be the source of dynamic instabilities such as flutter and divergence. It is shown that these instabilities (including Hopf bifurcation, flutter, divergence, and destabilizing effects connected to dissipation phenomena) can be obtained in structural systems loaded by conservative forces, as a consequence of the application of non-holonomic constraints. These constraints may be realized through a `perfect skate' (or a non-sliding wheel), or, more in general, through the slipless contact between two circular rigid cylinders, one of which is free of rotating about its axis. The motion of the structure produced by these dynamic instabilities may reach a limit cycle, a feature that can be exploited for soft robotics applications, especially for the realization of limbless locomotion.

physics.class-ph↗

arXiv2023

Stabilization against gravity and self-tuning of an elastic variable-length rod through an oscillating sliding sleeve

An elastic rod, straight in its undeformed state, has a mass attached at one end and a variable length, due to a constraint at the other end by a frictionless sliding sleeve. The constraint is arranged with the sliding direction parallel to a gravity field, in a way that the rod can freely slip inside of the sleeve, when the latter is not moving. In this case, the free fall of the mass continues until the rod is completely injected into the constraint. However, when the sliding sleeve is subject to a harmonic transverse vibration, it is shown that the fall of the mass and the rod injection are hindered by the presence of a configurational force developing at the sliding sleeve and acting oppositely to gravity. During the dynamic motion, such a configurational force is varying in time because it is associated with the variable bending moment at the sleeve entrance. It is (experimentally, analytically, and numerically) demonstrated that, in addition to the states of complete injection or ejection of the elastic rod (for which the mass falls down or is thrown out), a stable sustained oscillation around a finite height can be realized. This 'suspended motion' is the signature of a new attractor, that arises by the constraint oscillation. This behaviour shares similarities with parametric oscillators, as for instance the Kapitza inverted pendulum. However, differently from the classical parametric oscillators, the 'suspended' configuration of the rod violates equilibrium and the stabilization occurs through a transverse mechanical input, instead of a longitudinal one. By varying the sliding sleeve oscillation amplitude and frequency within specific sets of values, the system spontaneously adjusts the sustained motion through a self-tuning of the rod's external length. This self-tuning property opens the way to the design of vibration-based devices with extended frequency range.

physics.class-ph↗

arXiv2022

Non-smooth dynamics of buckling based metainterfaces: rocking-like motion and bifurcations

The non-smooth dynamics is investigated for an elastic planar metainterface composed by two layers of buckling elements, each one allowing motion on one side only. Through the analogy between buckling and unilateral contact and by assuming no-bouncing at impact, the motion of the relevant two degrees of freedom system is reduced to that of a single degree governed by a piecewise-smooth differential equation. The metainterface dynamics has strong similarities with the rocking motion of rigid blocks and displays several types of dynamic bifurcations in the presence of oscillatory forces, including period doubling, branch point cycle, grazing, as well as quasi-periodic and chaotic responses. Moreover, the multistable response is found to be broaden to conditions representative of monostable states within a quasi-static setting, disclosing a multistability anticipation by dynamics. The wide landscape of the dynamic response for the buckling based metainterface provides a novel theoretical framework to be exploited in the design of mechanical devices for vibration attenuation and for energy harvesting.

physics.class-ph↗

arXiv2022

Configurational forces on elastic structures

The discovery of configurational forces acting on elastic structures and its initial applications are reviewed. Configurational forces are related to the possibility that an elastic structure can change its configuration, thus inducing a variation in the potential energy. This concept has already led to several applications (the elastica arm scale, the dripping of an elastic rod, and the torsional actuator), has been shown to strongly affect stability, and to be related to limbless locomotion. It is believed that these results will open a new research territory in mechanics.

cond-mat.soft↗

arXiv2022

Configurational Forces in Penetration Processes

With a loose reference to problems of penetration in biomechanics (for instance, a nanoparticle penetrating through a cell's membrane or a cell sucked with a pipette), the role of configurational forces is investigated during the process in which a compliant intruder is inserted into an elastic structure. For insertion into a rigid constraint, a configurational force proportional to the square of the strain needed to deform the body, which is penetrating, is found. This force has a more complex structure when the compliance of the constraint is kept into account, but in all cases, it tends to expel the penetrating body.

cond-mat.soft↗

arXiv2022

Double restabilization and design of force-displacement response of the extensible elastica with movable constraints

A highly deformable rod, modelled as the extensible elastica, is connected to a movable clamp at one end and to a pin sliding along a frictionless curved profile at the other. Bifurcation analysis shows that axial compliance provides a stabilizing effect in compression, but unstabilizing in tension. Moreover, with varying the constraint's curvature at the origin and the axial vs bending rod's stiffness, in addition to possible buckling in tension, the structure displays none, two, or even four bifurcation loads, the last two associated only to the first buckling mode in compression. Therefore, the straight configuration may lose and recover stability one or two times, thus evidencing single and double restabilization, a feature never observed before. By means of the closed-form solution for the extensible elastica, the quasi-static behaviour of the structure is analytically described under large rotations and axial strain. The presented solution is exploited, together with an {\it ad hoc} developed optimization algorithm, to design the shape of the constraint's profile necessary to obtain a desired force-displacement curve, so to realize a force-limiter or a mechanical device capable of delivering a complex force response upon application of a continuous displacement in both positive and negative direction.

physics.class-ph↗

arXiv2022

Buckling vs unilateral constraint for a multistable metamaterial element

A structural element is designed and investigated, forming the basis for the development of an elastic multistable metamaterial. The leitmotif of the structural design is the implementation of a strut characterized by a bifurcation occurring at either vanishing tensile or compressive load. It is shown that buckling at null load leads to a mechanical equivalence with a unilateral constraint formulation, introducing shocks in dynamics. Towards a future analysis of the latter, the nonlinear quasi-static response is investigated, showing the multistable character of the structure, which may appear as bistable or tetrastable.

physics.class-ph↗

arXiv2021

Flutter instability and Ziegler destabilization paradox for elastic rods subject to non-holonomic constraints

Two types of non-holonomic constraints (imposing a prescription on velocity) are analyzed, connected to an end of a (visco)elastic rod, straight in its undeformed configuration. The equations governing the nonlinear dynamics are obtained and then linearized near the trivial equilibrium configuration. The two constraints are shown to lead to the same equations governing the linearized dynamics of the Beck (or Pfluger) column in one case and of the Reut column in the other. Therefore, although the structural systems are fully conservative (when viscosity is set to zero), they exhibit flutter and divergence instability. In addition, the Ziegler's destabilization paradox is found when dissipation sources are introduced. It follows that these features are proven to be not only a consequence of 'unrealistic non-conservative loads' (as often stated in the literature), rather, the models proposed by Beck, Reut, and Ziegler can exactly describe the linearized dynamics of structures subject to non-holonomic constraints, which are made now fully accessible to experiments.

physics.class-ph↗

arXiv2020

Elastica catastrophe machine: theory, design and experiments

The theory, the design and the experimental validation of a catastrophe machine based on a flexible element are addressed for the first time. A general theoretical framework is developed by extending that of the classical catastrophe machines made up of discrete elastic systems. The new formulation, based on the nonlinear solution of the elastica, is enhanced by considering the concept of the universal snap surface. Among the infinite set of elastica catastrophe machines, two families are proposed and investigated to explicitly assess their features. The related catastrophe locus is disclosed in a large variety of shapes, very different from those generated by the classical counterpart. Substantial changes in the catastrophe locus properties, such as convexity and number of bifurcation points, are achievable by tuning the design parameters of the proposed machines towards the design of very efficient snapping devices. Experiments performed on the physical realization of the elastica catastrophe machine fully validate the present theoretical approach. The developed model can find applications in mechanics at different scales, for instance, in the design of new devices involving actuation or hysteresis loop mechanisms to achieve energy harvesting, locomotion, and wave mitigation.

nlin.CD↗

arXiv2019

Configurational forces and nonlinear structural dynamics

Configurational, or Eshelby-like, forces are shown to strongly influence the nonlinear dynamics of an elastic rod constrained with a frictionless sliding sleeve at one end and with an attached mass at the other end. The configurational force, generated at the sliding sleeve constraint and proportional to the square of the bending moment realized there, has been so far investigated only under quasi-static setting and is now confirmed (through a variational argument) to be present within a dynamic framework. The deep influence of configurational forces on the dynamics is shown both theoretically (through the development of a dynamic nonlinear model in which the rod is treated as a nonlinear spring, obeying the Euler elastica, with negligible inertia) and experimentally (through a specifically designed experimental set-up). During the nonlinear dynamics, the elastic rod may slip alternatively in and out from the sliding sleeve, becoming a sort of nonlinear oscillator displaying a motion eventually ending with the rod completely injected into or completely ejected from the sleeve. The present results may find applications in the dynamics of compliant and extensible devices, for instance, to guide the movement of a retractable and flexible robot arm.

physics.class-ph↗

arXiv2019

Nested Bloch waves in elastic structures with configurational forces

Small axial and flexural oscillations are analyzed for a periodic and infinite structure, constrained by sliding sleeves and composed of elastic beams. A nested Bloch-Floquet technique is introduced to treat the non-linear coupling between longitudinal and transverse displacements induced by the configurational forces generated at the sliding sleeve ends. The action of configurational forces is shown to play an important role from two perspectives. First, the band gap structure for purely longitudinal vibration is broken so that axial propagation may occur at frequencies that are forbidden in the absence of a transverse oscillation and, second, a flexural oscillation may induce axial resonance, a situation in which the longitudinal vibrations tend to become unbounded. The presented results disclose the possibility of exploiting configurational forces in the design of mechanical devices towards longitudinal actuation from flexural vibrations of small amplitude at given frequency.

physics.class-ph↗

arXiv2019

Torsion of elastic solids with sparse voids parallel to the twist axis

With the purpose of investigating a linear elastic solid containing a dilute distribution of cylindrical and prismatic holes parallel to the torsion axis, the full-field solution for an infinite elastic plane containing a single void and subject to torsion is derived. The obtained solution is exploited to derive the analytic expressions for the Stress Concentration Factor (SCF) related to the presence of an elliptical hole, for the Stress Intensity Factor (SIF) for hypocycloidal-shaped hole and star-shaped cracks, and for the Notch Stress Intensity Factor (NSIF) for star-shaped polygons. Special sets of the void location are obtained for which peculiar mechanical behaviours are displayed, such as the stress annihilation at some points along the boundary of elliptical voids and the stress singularity removal at the cusps/points of hypocycloidal shaped/isotoxal star-shaped polygonal voids. By means of finite element simulations it is finally shown that the presented closed-form expressions for the stress intensification provide reliable predictions even for finite domain realizations and, in particular, the infinite-plane solution remains highly accurate when the size of smooth and non-smooth external boundary is greater than twice and five times the void dimension, respectively. Under these geometrical conditions, the derived analytical expressions represent a valid 'guide tool' in mechanical design.

physics.class-ph↗

arXiv2019

Snapping of elastic strips with controlled ends

Snapping mechanisms are investigated for an elastic strip with ends imposed to move and rotate in time. Attacking the problem analytically via Euler's elastica and the second variation of the total potential energy, the number of stable equilibrium configurations is disclosed by varying the kinematics of the strip ends. This result leads to the definition of a `universal snap surface', collecting the sets of critical boundary conditions for which the system snaps. The elastic energy release at snapping is also investigated, providing useful insights for the optimization of impulsive motion. The theoretical predictions are finally validated through comparisons with experimental results and finite element simulations, both fully confirming the reliability of the introduced universal surface. The presented analysis may find applications in a wide range of technological fields, as for instance energy harvesting and jumping robots.

cond-mat.soft↗

arXiv2017

Hypocycloidal Inclusions in Nonuniform Out-of-Plane Elasticity: Stress Singularity vs. Stress Reduction

Stress field solutions and Stress Intensity Factors (SIFs) are found for $n$-cusped hypocycloidal shaped voids and rigid inclusions in an infinite linear elastic plane subject to nonuniform remote antiplane loading, using complex potential and conformal mapping. It is shown that a void with hypocycloidal shape can lead to a higher SIF than that induced by a corresponding star-shaped crack; this is counter intuitive as the latter usually produces a more severe stress field in the material. Moreover, it is observed that when the order $m$ of the polynomial governing the remote loading grows, the stress fields generated by the hypocycloidal-shaped void and the star-shaped crack tend to coincide, so that they become equivalent from the point of view of a failure analysis. Finally, special geometries and loading conditions are discovered for which there is no stress singularity at the inclusion cusps and where the stress is even reduced with respect to the case of the absence of the inclusion. The concept of Stress Reduction Factor (SRF) in the presence of a sharp wedge is therefore introduced, contrasting with the well-known definition of Stress Concentration Factor (SCF) in the presence of inclusions with smooth boundary. The results presented in this paper provide criteria that will help in the design of ultra strong composite materials, where stress singularities always promote failure. Furthermore, they will facilitate finding the special conditions where resistance can be optimized in the presence of inclusions with non-smooth boundary.

cond-mat.soft↗