RICERCA
Latest results
A morphing aileron having two stable equilibrium branches depending on the aerodynamic load (Italian Patent: N. 102018000006527)
Instability of the curved configuration
increasing the speed at around 30 m/s
Instability of the flat configuration
decreasing the speed at around 17 m/s
Regular and chaotic dynamics of a shell with zero-stiffness
Chaotic motion
Constant-speed precession of the curvature axis
The rotation is only apparent since the shell is actually clamped.
A low-order mixed variational principle for the generalized Marguerre–von Kármán equations
A vanishing stiffness shell is actuated by three sets of PZT patches obtaining a gear-less motor.
A neutrally stable shell in a Stokes flow: a rotational Taylor's sheet
Click on the image to get the video
A shell which is bistable once clamped (in cooperation with Aviorec)
We are also patenting a shell which is has two different solution branches depending on the applied load
Multistable structures
Morphing structures are capable to change their configuration during their operating life in response to external inputs. From the mathematical point of view these structures possess two or more stable equilibria and are therefore characterized by multiwell energy functionals.
We started investigating in 2007 if completely stable transitions are possible between the two stable equilibria of a buckled beam; this is indeed the case if at least two independent actuation arameters are used.
Later we have turned our attention to multistable shells: playing with their initial curvature and their material anisotropy, one can indeed obtain a very complex multistable scenario where the shell can be monostable, bistable or tristable. Using a 3dofs nonlinear model, we did predict the existence of doubly-curved shells tristability in 2008; this was therefore experimentally confirmed in 2013.
Currently we are working on reduction methods to deduce, from the shell PDEs, simplified discrete nonlinear models which can account for the boundary conditions. This would open the field to the design and to the shape optimization of shells which remains multistable under the imposition of real boundary conditions.
Maurini, Pouget, Vidoli. European J Mechanics A/Solids 26 (2007)
Vidoli, Maurini. Proceed ings Royal Society A 464 (2008)
Fernades, Maurini, Vidoli. Int J Solids and Structures 47 (2010)
Coburn, Pierrera, Weaver, Vidoli. Composites Structures 96 (2013)
Vidoli. Int J Solids and Structures 50 (2013)
Brunetti, Vincenti, Vidoli, Int J Solids and Structures 2015
Hamouche, Maurini, Vincenti, Vidoli, Meccanica 2016
Seffen, Vidoli, Smart Materials and Structures 2016
Gradient damage models coupled with plasticity
Since the seminal work of (Francfort, Marigo, JMPS 1998), gradient damage models have been successfully used to describe the behavior of brittle and quasi-brittle materials. With the aim of modelling the behavior of ductile materials we consider an energy functional accounting not only for the damage field but also for dissipations due to plastic deformations. Suitable constitutive choices on how the plastic yield stress decreases with damage, allows us to obtain a rich variety of coupled responses.
For the mono-dimensional case, i.e. a traction test on a 1D bar, one can actually compute in closed form the localization of the plastic deformation field and the formation of a cohesive crack (see the figure below on the left).
The two-dimensional case calls for suitable numerical codes to minimize the energy functional: the minimum point is a field of displacement, a field of plastic deformation and a field of damage (see the figure above on the right).
Alessi, Marigo, Vidoli. Mechanics of Materials (2014)
Alessi, Marigo, Vidoli, Arch Rat Mech Analysis (2014)
Alessi, Marigo, Maurini, Vidoli, Int J Mech Sciences (2017)
Fracture mechanics in strain-gradient elasticity
In strain-gradient elasticity, an isotropic elastic solid is characterized not only by the standard Lamè constants but also by 5 additional material parameters (the so-called characteristic lengths). The role of these lengths is to penalize, with five different weights, the gradients of the strain field.
It is well known that a similar theory is well suited to study the stress and strain localization phenomena near singular points (say, for instance, near the apices of cracks).
As the ratio between the characteristic lengths are varied the actual mode of deformation changes. Indeed it can be shown that the strain-gradient effect is equivalent to a distribution of elastic cohesive forces near the crack tip.
We have recently prooved that using strain-gradient elasticity to regularize softening models of damage mechanics is a quite difficult task. With quadratic costs on the strain-gradient terms, it seems impossible to create a crack and associate to its nuclation a well-defined material toughness (Griffith theory).
Sciarra, Vidoli. Mathematics and Mechanics of Solids 17-3, (2011)
Sciarra, Vidoli. J Elasticity 113 (2013)
Le, Maurini, Marigo, Vidoli, CMAME (2018)
Viscoelasticity of rubber and soft materials
Few years ago we had a scientific cooperation with the Bridgestone Research Center in Aprilia near Rome. The goal was to efficiently characterize the energy dissipation in the low-frequency deformations of rubber-like materials. It turns out that the Prony Series, one of the most used rheological models, is not the best candidate to this aim. Indeed we have proved that every rheological model characterized by an exponential decay of the material memory does not have the necessary resolution to describe the low frequency behavior of many soft materials (not so slow but not so fast). Thus the identification of the storage and loss moduli of rubbers and soft materials necessarily require the use of fractional kernels.
Ciambella, Paolone, Vidoli. Mechanics of Materials 42 (2010)
Ciambella, Paolone, Vidoli. Rheologica Acta 50 (2011)
Ciambella, Paolone, Vidoli. Journal Mechanical Behavior of Biomedical Materials (2014)
High-order shear and normal deformable plate theories
During my permanence at Virginia Tech with Prof. Batra, we investigated the use of mixed variational principles, à la Hellinger–Reissner, to systematically derive, from the three-dimensional Cauchy theory, the balance equations and constitutive relations of a plate.
We found a systematic and algorithmic way to construct a Transverse-Shear and Normal-Deformable plate Theory (TSNDT) of arbitrary order in the thickness direction without the need of any correction factor.
Similar high-order plate theories could be characterized by a relevant number of degrees of freedom in each point. However after studying the decaying properties of plane waves travelling in such high-order plates we were able to formulate a rigorous ordering of the relative importance of the kinematical descriptors.
Vidoli, Batra. J Elasticity 59 (2000)
Batra, Vidoli. AIAA Journal 40 (2002)
Batra, Vestroni, Vidoli. Journal of Sound and Vibration 257 (2002)
Actuators networks for effective multi-modal structural control
Since the beginning of my PhD thesis in 1998, we have been working for several years, to an effective and truly multi-modal method for structural vibration control.
Once a distributed set of actuators (for instance a set of piezoelectric patches) is glued to the structure, the idea was to suitably design the electric network interconnecting them. In particular if the interconnecting network is designed to be analog of the underlying structure, one is able to trigger an internal resonance between the structural and electric modes: a very efficient way to transfer the energy from mechanical to electric form.
The problem is therefore transformed in finding the analog circuits of the main structural members (Euler beam, torsional shaft, Kirchhoff plate ...). After some time we found that already in the 40's the seminal works of Gabriel Kron were dedicated to this aim.
The figures below show two experimental validations of the concept.
