arXiv subjects

Gabriele Barbagallo

Publications and source records attributed to Gabriele Barbagallo.

18 recordsLinked to original sources

arXiv2026

Derivation of the Smarr formula from the Komar charge in Einstein-nonlinear electrodynamics theories and applications to regular black holes

We construct the generalized Komar charge of generic, non-linear theories of electrodynamics (NLED) in 4 dimensions coupled to Einstein gravity. The contribution of the dimensionful coupling constant present in all these theories is obtained by promoting it to a dynamical field which is forced to be constant on-shell by a Lagrange multiplier. We use this charge to derive a Smarr formula for asymptotically-flat black-hole and soliton solutions of these theories that includes the contribution of the coupling constant. Previously, this contribution had been found using homogeneity arguments. We test our results on a broad class of Einstein--NLED theories and analyze in detail the thermodynamics of the regular Bardeen black hole using the conservation of the generalized Komar charge to understand the regularity of regular black holes inside the event horizon.

gr-qc↗

arXiv2025

Higher-form symmetries in supergravity, scalar charges and black-hole thermodynamics

Minimal 5-dimensional supergravity compactified on a circle gives the T$^{3}$ model of $\mathcal{N}=2,d=4$ supergravity, whose duality group is SL$(2,\mathbb{R})$. We study exhaustively the relations between all the local and global symmetries of both theories and between the corresponding conserved currents and charges, including the on-shell closed generalized Komar charges associated to isometries. We find that the 2-dimensional subgroup of SL$(2,\mathbb{R})$ that does not include electric-magnetic transformations is realized as a higher-form symmetry group that acts on the 5-dimensional metric and vector field. Using the generalized Komar charges we compute the Smarr formulas for black holes, showing that they are identical once the relations between all the 5- and 4-dimensional thermodynamical quantities are taken into account, which is only possible if certain constraints on the fields are satisfied. We notice that on-shell closed 5-dimensional 3-form charges give, upon dimensional reduction, on-shell closed 3-form currents and 2-form charges. The dimensional reduction of the 5-dimensional generalized Komar 3-form charge associated to a Killing vector gives a new 4-dimensional on-shell closed 3-form current which must be associated to a new global symmetry of the theory when it admits that Killing vector. Some of the results that we have derived are valid for theories of Einstein--Maxwell-like theories of $(p+1)$-forms with Chern--Simons terms, which includes 11-dimensional supergravity as a particular example.

hep-th↗

arXiv2025

A note on the calculation of the Komar integral in the Lorentzian Taub-NUT spacetime

It has recently been shown that one can derive consistent thermodynamical expressions in the Lorentzian Taub--NUT spacetime keeping the Misner-string singularities and taking into account their contributions in the Komar integrals. We show how the same results are obtained when the Mister-string singularities are removed by using Misner's procedure because, even though the complete spacetime has no such singularities anymore, they are unavoidable in all spacelike hypersurfaces which are used in the Komar integrals. Different choices of hypersurfaces may contain different strings and lead to different physics, though.

gr-qc↗

arXiv2024

Sen's Mechanism for Self-Dual Super Maxwell theory

In several elementary particle scenarios, self-dual fields emerge as fundamental degrees of freedom. Some examples are the $D = 2$ chiral boson, $D = 10$ Type IIB supergravity, and $D = 6$ chiral tensor multiplet theory. For those models, a novel variational principle has been proposed in the work of Ashoke Sen. The coupling to supergravity of self-dual models in that new framework is rather peculiar to guarantee the decoupling of unphysical degrees of freedom. We generalize this technique to the self-dual super Maxwell gauge theory in $D = 4$ Euclidean spacetime both in the component formalism and the superspace. We use the geometric tools of rheonomy and integral forms since they are very powerful geometrical techniques for the extension to supergravity. We show the equivalence between the two formulations by choosing a different integral form defined using a Picture Changing Operator. That leads to a meaningful action functional for the variational equations. In addition, we couple the model to a non-dynamical gravitino to extend the analysis slightly beyond the free case. A full-fledged self-dual supergravity analysis will be presented elsewhere.

hep-th↗

arXiv2019

Effective description of anisotropic wave dispersion in mechanical band-gap metamaterials via the relaxed micromorphic model

In this paper the relaxed micromorphic material model for anisotropic elasticity is used to describe the dynamical behavior of a band-gap metamaterial with tetragonal symmetry. Unlike other continuum models (Cauchy, Cosserat, second gradient, classical Mindlin-Eringen micromorphic etc.), the relaxed micromorphic model is endowed to capture the main microscopic and macroscopic characteristics of the targeted metamaterial, namely, stiffness, anisotropy, dispersion and band-gaps. The simple structure of our material model, which simultaneously lives on a micro-, a meso- and a macroscopic scale, requires only the identification of a limited number of frequency-independent and thus truly constitutive parameters, valid for both static and wave-propagation analyses in the plane. The static macro- and micro- parameters are identified by numerical homogenization in static tests on the unit-cell level in [30]. The remaining inertia parameters for dynamical analyses are calibrated on the dispersion curves of the same metamaterial as obtained by a classical Bloch-Floquet analysis for two wave directions. We demonstrate via polar plots that the obtained material parameters describe very well the response of the structural material for all wave directions in the plane, thus covering the complete panorama of anisotropy of the targeted metamaterial.

physics.app-ph↗

arXiv2018

Relaxed micromorphic model of transient wave propagation in anisotropic band-gap metastructures

In this paper, we show that the transient waveforms arising from several localised pulses in a micro-structured material can be reproduced by a corresponding generalised continuum of the relaxed micromorphic type. Specifically, we compare the dynamic response of a bounded micro-structured material to that of bounded continua with special kinematic properties: (i) the relaxed micromorphic continuum and (ii) an equivalent Cauchy linear elastic continuum. We show that, while the Cauchy theory is able to describe the overall behaviour of the metastructure only at low frequencies, the relaxed micromorphic model goes far beyond by giving a correct description of the pulse propagation in the frequency band-gap and at frequencies intersecting the optical branches. In addition, we observe a computational time reduction associated with the use of the relaxed micromorphic continuum, compared to the sensible computational time needed to perform a transient computation in a micro-structured domain.

physics.class-ph↗

arXiv2018

Low-and high-frequency Stoneley waves, reflection and transmission at a Cauchy/relaxed micromorphic interface

In this paper we study the reflective properties of a 2D interface separating a homogeneous solid from a band-gap metamaterial by modeling it as an interface between a classical Cauchy continuum and a relaxed micromorphic medium. We show that the proposed model is able to predict the onset of Stoneley interface waves at the considered interface both at low and high-frequency regimes. More precisely, critical angles for the incident wave can be identified, beyond which classical Stoneley waves, as well as microstructure-related Stoneley waves appear. We show that this onset of Stoneley waves, both at low and high frequencies, strongly depends on the relative mechanical properties of the two media. We suggest that a suitable tailoring of the relative stiffnesses of the two media can be used to conceive 'smart interfaces' giving rise to wide frequency bounds where total reflection or total transmission may occur.

physics.class-ph↗

arXiv2017

Relaxed micromorphic modeling of the interface between a homogeneous solid and a band-gap metamaterial: new perspectives towards meta-structural design

In the present paper, the material parameters of the isotropic relaxed micromorphic model derived for a specific metamaterial in a previous contribution are used to model its transmission properties. Specifically, the reflection and transmission coefficients at an interface between a homogeneous solid and the chosen metamaterial are analyzed by using both the relaxed micromorphic model and a direct FEM implementation of the detailed microstructure. The obtained results show an excellent agreement between the transmission spectra derived via our enriched continuum model and those issued by the direct FEM simulation. Such excellent agreement validates the indirect measure of the material parameters and opens the way towards an efficient meta-structural design.

cond-mat.mtrl-sci↗

arXiv2017

Transparent anisotropy for the relaxed micromorphic model: macroscopic consistency conditions and long wave length asymptotics

In this paper, we study the anisotropy classes of the fourth order elastic tensors of the relaxed micromorphic model, also introducing their second order counterpart by using a Voigt-type vector notation. In strong contrast with the usual micromorphic theories, in our relaxed micromorphic model only classical elasticity-tensors with at most 21 independent components are studied together with rotational coupling tensors with at most 6 independent components. We show that in the limit case $L_c\rightarrow 0$ (which corresponds to considering very large specimens of a microstructured metamaterial the meso- and micro-coefficients of the relaxed model can be put in direct relation with the macroscopic stiffness of the medium via a fundamental homogenization formula. We also show that a similar homogenization formula is not possible in the case of the standard Mindlin-Eringen-format of the anisotropic micromorphic model. Our results allow us to forecast the successful short term application of the relaxed micromorphic model to the characterization of anisotropic mechanical metamaterials.

math-ph↗

arXiv2016

A panorama of dispersion curves for the weighted isotropic relaxed micromorphic model

We consider the weighted isotropic relaxed micromorphic model and provide an in depth investigation of the characteristic dispersion curves when the constitutive parameters of the model are varied. The weighted relaxed micromorphic model generalizes the classical relaxed micromorphic model previously introduced by the authors, since it features the Cartan-Lie decomposition of the tensors $P_{,t}$ and Curl $P$ in their dev, dev sym, skew and spheric part. It is shown that the split of the tensor $P_{,t}$ in the micro-inertia provide an independent control of the cut-offs of the optic benches. This is crucial for the future calibration of the relaxed micromorphic model on real band-gap metamaterials. Even if the physical interest of the introduction of the split of the tensor Curl $P$ is less evident than in the previous case, we discuss in detail which is its effect on the dispersion curves. Finally, we also provide a complete parametric study involving all the constitutive parameters of the introduced model, so giving rise to an exhaustive panorama of dispersion curves for the relaxed micromorphic model.

math-ph↗

arXiv2016

A review on wave propagation modeling in band-gap metamaterials via enriched continuum models

In the present contribution we show that the relaxed micromorphic model is the only non-local continuum model which is able to account for the description of band-gaps in metamaterials for which the kinetic energy accounts separately for micro and macro-motions without considering a micro-macro coupling. Moreover, we show that when adding a gradient inertia term which indeed allows for the description of the coupling of the vibrations of the microstructure to the macroscopic motion of the unit cell, other enriched continuum models of the micromorphic type may allow the description of the onset of band-gaps. Nevertheless, the relaxed micromorphic model proves to be yet the most effective enriched continuum model which is able to describe multiple band-gaps in non-local metamaterials.

math-ph↗

arXiv2016

On the role of micro-inertia in enriched continuum mechanics

In this paper the role of gradient micro-inertia terms $\barη\lVert\nabla u_{,t}\rVert^{2}$ and free micro-inertia terms $η\lVert p_{,t}\rVert^{2}$ is investigated to unveil their respective effect on the dynamical behavior of band-gap metamaterials. We show that the term $\barη\lVert\nabla u_{,t}\rVert^{2}$ alone is only able to disclose relatively simplified dispersive behaviors. On the other hand, the term $η\lVert p_{,t}\rVert^{2}$ is in charge of the description of the full complex behavior of band-gap metamaterials. A suitable mixing of the two micro-inertia terms allows to describe a new feature of the relaxed-micromorphic model, i.e. the description of a second band-gap occurring for higher frequencies. We also show that a split of the gradient micro-inertia $\barη\lVert\nabla u_{,t}\rVert^{2}$, in the sense of Cartan-Lie decomposition of matrices, allows to flatten separately longitudinal and transverse optic branches thus giving the possibility of a second band-gap. Finally, we investigate the effect of the gradient inertia $\barη\lVert\nabla u_{,t}\rVert^{2}$ on more classical enriched models as the Mindlin-Eringen and the internal variable ones. We find that the addition of such gradient micro-inertia allows for the onset of one band-gap in the Mindlin-Eringen model and of three band-gaps in the internal variable model. In this last case, however, non-local effects cannot be accounted for which is a too drastic simplification for most metamaterials. We conclude that, even when adding gradient micro-inertia terms, the relaxed micromorphic model remains the most performing one, among the considered enriched model, for the description of non-local band-gap metamaterials.

physics.class-ph↗

arXiv2016

Modeling the deep drawing of a 3D woven fabric with a second gradient model

Experimental testing on dry woven fabrics exhibits a complex set of evidences that are difficult to be completely described using classical continuum models. The aim of this paper is to show how the introduction of energy terms related to the micro-deformation mechanisms of the fabric, in particular to the bending stiffness of the yarns, helps in the modeling of the mechanical behavior of this kind of materials. To this aim, a second gradient, hyperelastic, initially orthotropic continuum theory is proposed to model fibrous composite interlocks at finite strains. In particular, the present work explores the relationship between the onset of wrinkling appearing during the simulation of the deep drawing of a woven fabric and the use of a second gradient model. It is shown that the introduction of second gradient terms accounting for the description of in-plane and out-of-plane bending rigidities, decreases the onset of wrinkles during the simulation of deep-drawing. In this work, a quadratic energy, roughly proportional to the square of the curvature of the fibers, is presented and implemented in the simulations. This simple constitutive assumption allows to clearly show the effects of the second gradient energy on both the wrinkling description and the numerical stability of the model. The results obtained in second gradient simulations are descriptive of the experimental evidence of deep drawing whose description is targeted in this work. The present paper provides additional evidence of the fact that first gradient continuum theories alone cannot be considered fully descriptive of the behavior of dry woven composite reinforcements. On the other hand, the proposed second gradient model for fibrous composite reinforcements opens the way both to the more accurate simulation of complex forming processes and to the possibility of controlling the onset of wrinkles.

cond-mat.soft↗

arXiv2016

Real wave propagation in the isotropic relaxed micromorphic model

For the recently introduced isotropic relaxed micromorphic generalized continuum model, we show that under the assumption of positive definite energy, planar harmonic waves have real velocity. We also obtain a necessary and sufficient condition for real wave velocity which is weaker than positive-definiteness of the energy. Connections to isotropic linear elasticity and micropolar elasticity are established. Notably, we show that strong ellipticity does not imply real wave velocity in micropolar elasticity, while it does in isotropic linear elasticity.

math-ph↗

arXiv2016

First evidence of non-locality in real band-gap metamaterials: determining parameters in the relaxed micromorphic model

In this paper we propose the first estimate of some elastic parameters of the relaxed micromorphic model on the basis of real experiments of transmission of longitudinal plane waves across an interface separating a classical Cauchy material (steel plate) and a phononic crystal (steel plate with fluid-filled holes). A procedure is set up in order to identify the parameters of our model by superimposing the experimentally-based profile of the reflection coefficient (plotted as function of the frequency of the traveling waves) with the analogous profile obtained via simulations based upon the relaxed micromorphic model. We end up with the determination of 5 out of 6 constitutive parameters which are featured by the relaxed micromorphic model in the isotropic case, plus the determination of the micro-inertia parameter. The sixth elastic parameter, namely the Cosserat couple modulus $μ_{c}$, still remains undetermined, since experimental data concerning the transmission properties of the considered interface for transverse incident waves are not yet available. A fundamental result of the present paper is the estimate of the non-locality intrinsically associated to the underlying microstructure of the metamaterial. As a matter of fact, we appraise that the characteristic length $L_{c}$ measuring the non-locality of the considered phononic crystal is of the order of $1/3$ of the diameter of the considered fluid-filled holes.

cond-mat.mtrl-sci↗

arXiv2016

Bias extension test on an unbalanced woven composite reinforcement: Experiments and modeling via a second-gradient continuum approach

The classical continuum models used for the woven fabrics do not fully describe the whole set of phenomena that occur during the testing of those materials. This incompleteness is partially due to the absence of energy terms related to some micro-structural properties of the fabric and, in particular, to the bending stiffness of the yarns. To account for the most fundamental microstructure-related deformation mechanisms occurring in unbalanced interlocks, a second-gradient, hyperelastic, initially orthotropic continuum model is proposed. A constitutive expression for the strain energy density is introduced to account for i) in-plane shear deformations, ii) highly different bending stiffnesses in the warp and weft directions and iii) fictive elongations in the warp and weft directions which eventually describe the relative sliding of the yarns. Numerical simulations which are able to reproduce the experimental behavior of unbalanced carbon interlocks subjected to a Bias Extension Test are presented. In particular, the proposed model captures the macroscopic asymmetric S-shaped deformation of the specimen, as well as the main features of the associated deformation patterns of the yarns at the mesoscopic scale.

cond-mat.soft↗

arXiv2016

Continuum and discrete models for unbalanced woven fabrics

The classical models used for describing the behavior of woven fabrics do not fully account for the whole set of phenomena that occur during the testing of such materials. This lack of precision is mainly due to the absence of energy terms related to the microstructural properties of the fabric and, in particular, to the bending stiffness of the yarns. In this paper it is shown that in the unbalanced fabrics the different bending stiffnesses of the warp and weft yarns produce macroscopic effects that are extremely visible as, for example, the asymmetric S-shape during a Bias Extension Test (BET). We propose to introduce a constrained micromorphic model and a discrete model that are able to account for i) the angle variation between warp and weft tows, ii) the unbalance in the bending stiffness of the yarns and iii) the relative slipping of the tows. The constrained micromorphic model is framed in the spirit of the Principle of Virtual Powers for the equilibrium of continuum bodies. A suitable constraint is introduced by means of Lagrange multipliers in the strain energydens ity and the resulting constrained model tends a particular second gradientone. The main advantage of using such constrained micromorphic model is that the kinematical and traction boundary conditions that can be imposed on the boundary of the considered body take a natural and unique meaning. The discrete model is set up by opportunely interconnecting Euler-Bernoulli beams with different bending stiffnesses in the two directions by means of rotational and translational elastic springs. The main advantage of such discrete model is that the slipping of the tows is described in a rather realistic way. Suitable numerical simulations are presented for both the continuum and the discrete models and a comparison between the simulations and the experimental results is made showing a definitely good agreement.

cond-mat.soft↗

arXiv2016

Complete band gaps including non-local effects occur only in the relaxed micromorphic model

In this paper we substantiate the claim implicitly made in previous works that the relaxed micromorphic model is the only linear, isotropic, reversibly elastic, nonlocal generalized continuum model able to describe complete band-gaps on a phenomenological level. To this end, we recapitulate the response of the standard Mindlin-Eringen micromorphic model with the full micro-distortion gradient of P, the relaxed micromorphic model depending only on the Curl P of the micro-distortion P, and a variant of the standard micromorphic model in which the curvature depends only on the divergence Div P of the micro distortion. The Div-model has size-effects but the dispersion analysis for plane waves shows the incapability of that model to even produce a partial band gap. Combining the curvature to depend quadratically on Div P and Curl P shows that such a model is similar to the standard Mindlin-Eringen model which can eventually show only a partial band gap.

math-ph↗