Francesco Dell'Isola

Generalized Hooke's law for isotropic second gradient materials

In the spirit of Germain the most general objective stored elastic energy for a second gradient material is deduced using a literature result of Fortuné & Vallée. Linear isotropic constitutive relations for stress and hyperstress in terms of strain and strain-gradient are then obtained proving that these materials are characterized by seven elastic moduli and generalizing previous studies by Toupin, Mindlin and Sokolowski. Using a suitable decomposition of the strain-gradient, it is found a necessary and sufficient condition, to be verified by the elastic moduli, assuring positive definiteness of the stored elastic energy. The problem of warping in linear torsion of a prismatic second gradient cylinder is formulated, thus obtaining a possible measurement procedure for one of the second gradient elastic moduli.

Edge Contact Forces and Quasi-Balanced Power

We consider continuous media in which contact edge forces are present. Introducing thenotion of quasi-balanced contact force distribution, we are able to prove the conjectures by Noll andVirga [1] concerning the representation of contact edge forces. We generalize the Hamel--Nolltheorem on the Cauchy postulate. Then we adapt the celebrated tetrahedron construction of Cauchy in orderto obtain a representation theorem for stress states. In fact, we show that two stress tensors of order twoand three are necessary for such a representation. Moreover we find the relationship between the notionof interstitial working introduced by Dunn and Serrin [2] and the notion of contact edge force.

Passive damping of beam vibrations through distributed electric networks and piezoelectric transducers: prototype design and experimental validation

The aim of this work is two-fold: to design devices for passive electric damping of structural vibrations by distributed piezoelectric transducers and electric networks, and to experimentally validate the effectiveness of such a damping concept. Two different electric networks are employed, namely a purely resistive network and an inductive–resistive one. The presented devices can be considered as distributed versions of the well-known resistive and resonant shunt of a single piezoelectric transducer. The technical feasibility and damping effectiveness of the proposed novel devices are assessed through the construction of an experimental prototype. Experimental results are shown to be in very good agreement with theoretical predictions. It is proved that the presented technique allows for a substantial reduction in the inductances used when compared with those required by the single resonant shunted transducer. In particular, it is shown that the required inductance decreases when the number of piezoelectric elements is increased. The electric networks are optimized in order to reduce forced vibrations close to the first resonance frequency. Nevertheless, the damping effectiveness for higher modes is experimentally proved. As well as specific results, fundamental theoretical and experimental considerations for passive distributed vibration control are provided.

Comparison of piezoelectronic networks acting as distributed vibration absorbers

Abstract Electric vibration absorbers made of distributed piezoelectric devices for the control of beam vibrations are studied. The absorbers are obtained by interconnecting an array of piezoelectric transducers uniformly distributed on a beam with different modular electric networks. Five different topologies are considered and their damping performance is analysed and compared. Their optimal parameters are found by adopting a criterion for critical damping of k-waves: the parameters are suitably chosen to have the quickest temporal vibration decay for a single wave number k. The analysis is based on homogenized models of the modular piezo-electromechanical systems, i.e. they are regarded as continuous systems by assuming that the number of modules per unit length is high enough with respect to the considered wave numbers. Calling k -absorbers the corresponding optimal absorbers, we show that: (i) k-waves are damped in k-absorbers with an optimal decay time which is independent of the absorber interconnecting topology, while it depends only on the piezoelectric coupling coefficient; (ii) the efficiency of k-absorbers depends significantly on the absorber interconnecting topology for k different from k; (iii) one of the proposed absorbers (which is made of a fourth-order electric transmission line with a second-order electric dissipation) equally performs for all the wave numbers and accomplishes an effective multi-modal damping for the mechanically forced response; (iv) the optimal values of the electric parameters differently depend on the number n of used circuit modules for different interconnecting topologies and, in particular, the optimal inductance per module needed in a fourth-order electric transmission line is proportional 1/ n 3 .

Synthesis of Fibrous Complex Structures: Designing Microstructure to Deliver Targeted Macroscale Response

In Mechanics, material properties are most often regarded as being given, and based on this, many technical solutions are usually conceived and constructed. However, nowadays manufacturing processes have advanced to the point that metamaterials having selected properties can be designed and fabricated. Three-dimensional printing, electrospinning, self-assembly, and many other advanced manufacturing techniques are raising a number of scientific questions which must be addressed if the potential of these new technologies is to be fully realized. In this work, we report on the status of modeling and analysis of metamaterials exhibiting a rich and varied macroscopic response conferred by complex microstructures and particularly focus on strongly interacting inextensible or nearly inextensible fibers. The principal aim is to furnish a framework in which the mechanics of 3D rapid prototyping of microstructured lattices and fabrics can be clearly understood and exploited. Moreover, several-related open questions will be identified and discussed, and some methodological considerations of general interest are provided.

On the derivation of thermomechanical balance equations for continuous systems with a nonmaterial interface

Abstract The integral balance laws of continuous systems with an interface are obtained as a limit of balance law relative to suitable three-dimensional continuum. This approach supplies a physical interpretation of the quantities appearing in the balance laws and dodges around the not invariance under Galilean transformations of angular momentum balance.

Vibration control in plates by uniformly distributed PZT actuators interconnected via electric networks

In this paper a novel device aimed at controlling the mechanical vibrations of plates by means of a set of electrically-interconnected piezoelectric actuators is described. The actuators are embedded uniformly in the plate wherein they connect every node of an electric network to ground, thus playing the two-fold role of capacitive element in the electric network and of couple suppliers. A mathematical model is introduced to describe the propagation of electro-mechanical waves in the device; its validity is restricted to the case of wave-forms with wave-length greater than the dimension of the piezoelectric actuators used. A self-resonance criterion is established which assures the possibility of electro-mechanical energy exchange. Finally the problem of vibration control in simply supported and clamped plates is addressed; the optimal net-impedance is determined. The results indicate that the proposed device can improve the performances of piezoelectric actuation.

A micro-structured continuum modelling compacting fluid-saturated grounds: the effects of pore-size scale parameter

SummaryThe effect of a “pore-size” length-scale parameterl on compaction of grounds with fluid inclusions is studied. They are modelled as continua endowed with micro-structure by means of the macro-modelling procedure proposed in [2]. We show the dependence of field evolution equations on the micro-structure parameterl and compare our model with the homogenized asymptotic ones. The consideration of the pore sizel allows us to forecast the onset ofmicro-displacement waves as a consequence of a ground settling and to suggest a possible description of the genesis of certain microerthquakes [5] [6].

Modal coupling in one-dimensional electromechanical structured continua

SummaryA passive continuously distributed control of mechanical vibrations is proposed. The piezoelectric actuators are interconnected by a linear electric transmission line. We introduce coupling and internal resonance criteria to determine the optimal choices for electric parameters. These criteria can be found decomposing the differential operator appearing in the linear evolutions according to a partition of the state vector into mechanical and electrical parts. The results we find allow for the design of an experimental set up.

A phenomenological approach to phase transition in classical field theory

In this paper we propose some surface constitutive equations when added to the balance laws and jump conditions allow us to formulate in principle a boundary value problem for phase transitions modelled as a continuum with an interface.