Stefano Giordano - Academia.edu (original) (raw)
Papers by Stefano Giordano
This article describes an explicit approach to urnmodels of the balanced generalized Pólya type (... more This article describes an explicit approach to urnmodels of the balanced generalized Pólya type (with two types of balls). The treatment starts by obtaining the difference equations, describing the discrete time behavior of the expected value and of the variance of the selection probability for a given type of ball. The explicit solutions of such difference equations have been found in terms of gamma and psi (digamma) functions. This unified approach is useful in didactics in order to present a general method that leads to the final results without using complicated analytical tools. The more advanced mathematical procedure utilized is the solution of a first-order difference equation. All the theoretical results have been confirmed by a series of Monte Carlo simulations in order to clarify and better explain the behavior of the system.
International Journal of Applied Electromagnetics and Mechanics, 2007
In this paper we analyse the electrical effects of the presence of cracks in solid conductors. We... more In this paper we analyse the electrical effects of the presence of cracks in solid conductors. We have studied such problematic from different points of view. Firstly, we have analytically evaluated the behaviour of the electrical field near a crack in an isotropic solid where a uniform current density is flowing, drawing a comparison with the behaviour of the well known stress and strain tensor fields in the analogue elastic problem. This computation has been made with a slit-crack (two-dimensional field analysis) and with a circular crack (three-dimensional field analysis). So, in order to quantify the spatial fluctuations of the local electric field around the crack we have numerically found the density of states for the field showing that it exhibit sharp peaks and abrupt changes in the slope at certain critical points which are analogous to van Hove singularities in the density of states for phonons and electrons in solids. Finally, we have performed a theoretical analysis of the conductivity of a microcracked solid. The distribution of cracks in the solid follows a given orientational distribution, which modify the conduction properties of the overall material. In particular, we have shown that the conductivity depends exponentially on the cracks density and on the size of each crack embedded in the medium.
Physical Review B, 2008
Interfaces between different media represent the most common structure in composite and complex m... more Interfaces between different media represent the most common structure in composite and complex materials, e.g., with applications in microelectronics and photovoltaics. We analyze the elastic properties of the a-Si/c-Si interface, which involves two completely different atomic structures. We prove that the continuum approach and the atomistic simulation are consistent if atomic-scale elastic fields are properly averaged.
Journal of Physics: Condensed Matter, 2006
The discovery of new materials with peculiar optical properties as well as the prediction of thei... more The discovery of new materials with peculiar optical properties as well as the prediction of their behaviour given the microstructure is a matter of remarkable interest in the community of material scientists. A complete theory allowing such a prediction is not yet available. We have formulated a theory able to analytically predict the effective second-and third-order nonlinear electrical behaviour of a dilute dispersion of randomly oriented anisotropic nonlinear spheres in a linear host. The inclusion medium has non-vanishing second-and third-order nonlinear hypersusceptibilities. As a result, the overall composite material is nonlinear but isotropic because of the random orientation of the inclusions. We derive the expressions for the equivalent permittivity and for the Kerr equivalent hypersusceptibility in terms of the characteristic electric tensors describing the electrical behaviour of the spheres. The complete averaging over inclusion positions and orientations led to general results in the dilute limit. We show that these results are consistent with earlier theories and that they provide null second-order hypersusceptibility as expected in a macroscopically isotropic medium. This theory generalizes the well-known Maxwell-Garnett formula and it can be easily specialized to any of the 32 crystallographic symmetry classes. Despite this study assuming static conditions, it can be generalized to the sinusoidal regime, pointing at an interesting way to engineer optically active materials with desired behaviour.
Journal of Engineering Materials and Technology, 2007
A material composed of a mixture of distinct homogeneous media can be considered as a homogeneous... more A material composed of a mixture of distinct homogeneous media can be considered as a homogeneous one at a sufficiently large observation scale. In this work, the problem of the elastic mixture characterization is solved in the case of linear random mixtures, that is, materials for which the various components are isotropic, linear, and mixed together as an ensemble of particles having completely random shapes and positions. The proposed solution of this problem has been obtained in terms of the elastic properties of each constituent and of the stoichiometric coefficients. In other words, we have explicitly given the features of the micro-macro transition for a random mixture of elastic material. This result, in a large number of limiting cases, reduces to various analytical expressions that appear in earlier literature. Moreover, some comparisons with the similar problem concerning the electric characterization of random mixtures have been drawn. The specific analysis of porous ran...
Journal of Electrostatics, 2005
A multipole theory describing the interactions between dielectric cylinders in a uniform field is... more A multipole theory describing the interactions between dielectric cylinders in a uniform field is developed. We treat the most general case of N parallel cylinders placed in arbitrary positions. The exact theory is obtained by developing the polarisation charge surface density on each cylinder in a Fourier series. The related coefficients, the so-called multipoles, may be obtained from a linear set of equations which is derived and analysed in the paper. For systems of closely spaced cylinders, with high ratio of the dielectric constant of the cylinders compared to that of the homogeneous medium (in the worst case, conductive cylinders in contact with each other) a very large number of multipole terms is required to achieve convergence. In spite of the large number of required terms, the general multipole expansion is rapidly convergent in all other cases and is important from a theoretical point of view. Numerical results are presented for canonical dispositions of cylinders and for more complicated arrangements. Finally, such a multipole expansion has been applied to the dielectric characterisation of composite materials formed by a regular array of parallel cylinders, thereby obtaining the equivalent permittivity using a numerically efficient technique.
European Journal of Mechanics - A/Solids, 2003
The paper deals with the elastic characterisation of dispersions of randomly oriented ellipsoids:... more The paper deals with the elastic characterisation of dispersions of randomly oriented ellipsoids: we start from the theory of strongly diluted mixtures and successively we generalise it with a differential scheme. The micro-mechanical averaging inside the composite material is carried out by means of explicit results which allows us to obtain closed-form expressions for the macroscopic or equivalent elastic moduli of the overall composite materials. This micromechanical technique has been explicitely developed for describing embeddings of randomly oriented not spherical objects. In particular, this study has been applied to characterise media with different shapes of the inclusions (spheres, cylinders and planar inhomogeneities) and for special media involved in the mixture definition (voids or rigid particles): an accurate analysis of all these cases has been studied yielding a set of relations describing several composite materials of great technological interest. The differential effective medium scheme (developed for generally shaped ellipsoids) extends such results to higher values of the volume fraction of the inhomogeneities embedded in the mixture. For instance, the analytical study of the differential scheme for porous materials (with ellipsoidal zero stiffness voids) reveals a universal behaviour of the effective Poisson ratio for high values of the porosity. This means that Poisson ratio at high porosity assumes characteristic values depending only on the shape of the inclusions and not on the elastic response of the matrix.
International Journal of Engineering Science, 2005
The paper deals with the electrical and elastic characterisation of dispersions of pseudo-oriente... more The paper deals with the electrical and elastic characterisation of dispersions of pseudo-oriented ellipsoids of rotation: it means that we are dealing with mixtures of inclusions of different eccentricities and arbitrary non-random orientational distributions. The analysis ranges from parallel spheroidal inclusions to completely random oriented inclusions. A unified theory covers all the orientational distributions between the random and the parallel ones. The electrical and micro-mechanical averaging inside the composite material is carried out by means of explicit results which allows us to obtain closed-form expressions for the macroscopic or equivalent dielectric constants or elastic moduli of the overall composite materials. In particular, this study allows us to affirm that the electrical behaviour of such a dispersion of pseudo-oriented particles is completely defined by one order parameter which depends on the given angular distribution. Moreover, the elastic characterisation of this heterogeneous material depends on two order parameters, which derive from the orientational distribution. The theory may be applied to characterise media with different shapes of the inclusions (i.e. spheres, cylinders or planar inhomogeneities) yielding a set of procedures describing several composite materials of great technological interest.
Physical Review E
Geometric Brownian motion is an exemplary stochastic processes obeying multiplicative noise, with... more Geometric Brownian motion is an exemplary stochastic processes obeying multiplicative noise, with widespread applications in several fields, e.g., in finance, in physics, and biology. The definition of the process depends crucially on the interpretation of the stochastic integrals which involves the discretization parameter α with 0 α 1, giving rise to the well-known special cases α = 0 (Itô), α = 1/2 (Fisk-Stratonovich), and α = 1 (Hänggi-Klimontovich or anti-Itô). In this paper we study the asymptotic limits of the probability distribution functions of geometric Brownian motion and some related generalizations. We establish the conditions for the existence of normalizable asymptotic distributions depending on the discretization parameter α. Using the infinite ergodicity approach, recently applied to stochastic processes with multiplicative noise by E. Barkai and collaborators, we show how meaningful asymptotic results can be formulated in a transparent way.
Physical Review B, 2017
We numerically demonstrate the possibility to manipulate domain walls in magnetoelastic nanostrip... more We numerically demonstrate the possibility to manipulate domain walls in magnetoelastic nanostripes by means of uniform mechanical stresses. The symmetry breaking of the magnetic states in unidimensional ferromagnets allows the control of the domain-wall position or velocity in geometrically tailored nanostripes coupled to piezoelectric substrates. We further predict that this approach yields unusual domain-wall configurations with velocities of the same order of magnitude as that induced by magnetic fields or spin-polarized currents, while the energy consumption is considerably smaller.
The European Physical Journal B, 2016
Magnetic domain walls are fundamental objects arising in ferromagnetic materials, largely investi... more Magnetic domain walls are fundamental objects arising in ferromagnetic materials, largely investigated both through micromagnetic simulations and experiments. While current-and field-based techniques for inducing domain wall propagation have been widely studied for fundamental understanding and application-oriented purposes, the possibility to manipulate domain walls using mechanical stress in magnetoelastic materials has only recently drawn interest. Here, a complete analytical model describing stress-induced transverse domain wall movement in ferromagnetic nanostripe with variable cross-section is presented. This approach yields a nonlinear integro-differential equation describing the magnetization field. Its numerical implementation, based on the nonlinear relaxation method, demonstrates the possibility to precisely control the position of a domain wall through mechanical action.
Physical Review B, 2012
Magneto-electro-elastic and multiferroic materials can be combined in appealing nanostructures ch... more Magneto-electro-elastic and multiferroic materials can be combined in appealing nanostructures characterized by the coexistence and coupling of electric, magnetic, and mechanical phases with potential applications in novel multifunctional devices. Here, we derive a theory for nonvolatile room-temperature memory elements composed of magnetostrictive nanoparticles embedded in a piezoelectric matrix: two stable orthogonal magnetization states are obtained by the competition of anisotropy and external magnetic polarization. The innovative nontoggle switching between the states is modeled by a thorough combination of the nanomechanical Eshelby approach with the nanomagnetic Landau-Lifshitz-Gilbert formalism, yielding a robust picture of the dynamical behavior and allowing the improvement of the energetic efficiency.
Physical Review E
The fracture behavior of brittle and ductile materials can be strongly influenced by thermal fluc... more The fracture behavior of brittle and ductile materials can be strongly influenced by thermal fluctuations, especially in micro-and nano-devices as well as in rubberlike and biological materials. However, temperature effects, in particular on the brittle-to-ductile transition, still require a deeper theoretical investigation. As a step in this direction we propose a theory, based on equilibrium statistical mechanics, able to describe the temperature dependent brittle fracture and brittle-to-ductile transition in prototypical discrete systems consisting in a lattice with breakable elements. Concerning the brittle behavior, we obtain closed form expressions for the temperature-dependent fracture stress and strain, representing a generalized Griffith criterion, ultimately describing the fracture as a genuine phase transition. With regard to the brittle-to-ductile transition, we obtain a complex critical scenario characterized by a threshold temperature between the two fracture regimes (brittle and ductile), an upper and a lower yield strength, and a critical temperature corresponding to the complete breakdown. To show the effectiveness of the proposed models in describing thermal fracture behaviors at small scales, we successfully compare our theoretical results with molecular dynamics simulations of Si and GaN nanowires.
Continuum Mechanics and Thermodynamics
Applied Mechanics
Sacrificial bonds have been observed in several biological materials and structures and can incre... more Sacrificial bonds have been observed in several biological materials and structures and can increase their toughness, i.e., their resistance to fracture. They provide a reversible mechanism for dissipating mechanical energy before the possible system rupture. From a structural point of view, sacrificial bonds consist of short polymer chains that short-circuit parts of a main macromolecular chain (generating hidden lengths) and absorb energy by breaking them instead of the main chain. The toughness increase due to the presence of sacrificial bonds is typically named extra-toughness. Here, we developed a statistical mechanics and thermodynamics-based theory able to estimate the force–extension relation for chains with sacrificial bonds and to calculate the corresponding extra-toughness. The model is useful to better understand the sacrificial bond effects in biomaterials but also to apply the biomimetic paradigm and foster the development of high-performance artificial polymeric mater...
The European Physical Journal Plus
Non-local and non-convex energies represent fundamental interacting effects regulating the comple... more Non-local and non-convex energies represent fundamental interacting effects regulating the complex behavior of many systems in biophysics and materials science. We study one dimensional, prototypical schemes able to represent the behavior of several biomacromolecules and the phase transformation phenomena in solid mechanics. To elucidate the
In this work we analyze the problem of finding the electric behavior of an anisotropic ellipsoid ... more In this work we analyze the problem of finding the electric behavior of an anisotropic ellipsoid (arbitrarily shaped) placed in a dielectric anisotropic environment. We suppose that the whole system is exposed to a uniform electric field remotely applied. In order to find the resulting electric quantities inside the particle and outside it we adopt a technique largely utilized for solving similar problems in elasticity theory. The inhomogeneity problems in elastostatics are solved within the framework of the Eshelby theory, which adopts, as crucial points, the concepts of eigenstrains and inclusions. The generalization and assessment of such an approach for the dielectric inhomogeneity problems is here addressed by means of the introduction of the concepts of eigenfields and inclusions in electrostatics. The advantages of this methodology are mainly two: firstly, we can consider completely arbitrary dielectric anisotropic behavior both for the particle and the host matrix. Secondly,...
Effective permittivity of materials containing graded ellipsoidal inclusions
International Journal of Solids and Structures, 2013
This article appeared in a journal published by Elsevier. The attached copy is furnished to the a... more This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are
Physical Review E, 2021
We study the relation between stochastic thermodynamics and nonequilibrium thermodynamics by eval... more We study the relation between stochastic thermodynamics and nonequilibrium thermodynamics by evaluating the entropy production and the relation between fluxes and forces in a harmonic system with N particles in contact with N different reservoirs. We suppose that the system is in a nonequilibrium stationary state in a first phase and we study the relaxation to equilibrium in a second phase. During this relaxation, we can identify the linear relation between fluxes and forces satisfying the Onsager reciprocity and we obtain a nonlinear expression for the entropy production. Only when forces and fluxes are small does the entropic production turn into a quadratic form in the forces, as predicted by the Onsager theory.
This article describes an explicit approach to urnmodels of the balanced generalized Pólya type (... more This article describes an explicit approach to urnmodels of the balanced generalized Pólya type (with two types of balls). The treatment starts by obtaining the difference equations, describing the discrete time behavior of the expected value and of the variance of the selection probability for a given type of ball. The explicit solutions of such difference equations have been found in terms of gamma and psi (digamma) functions. This unified approach is useful in didactics in order to present a general method that leads to the final results without using complicated analytical tools. The more advanced mathematical procedure utilized is the solution of a first-order difference equation. All the theoretical results have been confirmed by a series of Monte Carlo simulations in order to clarify and better explain the behavior of the system.
International Journal of Applied Electromagnetics and Mechanics, 2007
In this paper we analyse the electrical effects of the presence of cracks in solid conductors. We... more In this paper we analyse the electrical effects of the presence of cracks in solid conductors. We have studied such problematic from different points of view. Firstly, we have analytically evaluated the behaviour of the electrical field near a crack in an isotropic solid where a uniform current density is flowing, drawing a comparison with the behaviour of the well known stress and strain tensor fields in the analogue elastic problem. This computation has been made with a slit-crack (two-dimensional field analysis) and with a circular crack (three-dimensional field analysis). So, in order to quantify the spatial fluctuations of the local electric field around the crack we have numerically found the density of states for the field showing that it exhibit sharp peaks and abrupt changes in the slope at certain critical points which are analogous to van Hove singularities in the density of states for phonons and electrons in solids. Finally, we have performed a theoretical analysis of the conductivity of a microcracked solid. The distribution of cracks in the solid follows a given orientational distribution, which modify the conduction properties of the overall material. In particular, we have shown that the conductivity depends exponentially on the cracks density and on the size of each crack embedded in the medium.
Physical Review B, 2008
Interfaces between different media represent the most common structure in composite and complex m... more Interfaces between different media represent the most common structure in composite and complex materials, e.g., with applications in microelectronics and photovoltaics. We analyze the elastic properties of the a-Si/c-Si interface, which involves two completely different atomic structures. We prove that the continuum approach and the atomistic simulation are consistent if atomic-scale elastic fields are properly averaged.
Journal of Physics: Condensed Matter, 2006
The discovery of new materials with peculiar optical properties as well as the prediction of thei... more The discovery of new materials with peculiar optical properties as well as the prediction of their behaviour given the microstructure is a matter of remarkable interest in the community of material scientists. A complete theory allowing such a prediction is not yet available. We have formulated a theory able to analytically predict the effective second-and third-order nonlinear electrical behaviour of a dilute dispersion of randomly oriented anisotropic nonlinear spheres in a linear host. The inclusion medium has non-vanishing second-and third-order nonlinear hypersusceptibilities. As a result, the overall composite material is nonlinear but isotropic because of the random orientation of the inclusions. We derive the expressions for the equivalent permittivity and for the Kerr equivalent hypersusceptibility in terms of the characteristic electric tensors describing the electrical behaviour of the spheres. The complete averaging over inclusion positions and orientations led to general results in the dilute limit. We show that these results are consistent with earlier theories and that they provide null second-order hypersusceptibility as expected in a macroscopically isotropic medium. This theory generalizes the well-known Maxwell-Garnett formula and it can be easily specialized to any of the 32 crystallographic symmetry classes. Despite this study assuming static conditions, it can be generalized to the sinusoidal regime, pointing at an interesting way to engineer optically active materials with desired behaviour.
Journal of Engineering Materials and Technology, 2007
A material composed of a mixture of distinct homogeneous media can be considered as a homogeneous... more A material composed of a mixture of distinct homogeneous media can be considered as a homogeneous one at a sufficiently large observation scale. In this work, the problem of the elastic mixture characterization is solved in the case of linear random mixtures, that is, materials for which the various components are isotropic, linear, and mixed together as an ensemble of particles having completely random shapes and positions. The proposed solution of this problem has been obtained in terms of the elastic properties of each constituent and of the stoichiometric coefficients. In other words, we have explicitly given the features of the micro-macro transition for a random mixture of elastic material. This result, in a large number of limiting cases, reduces to various analytical expressions that appear in earlier literature. Moreover, some comparisons with the similar problem concerning the electric characterization of random mixtures have been drawn. The specific analysis of porous ran...
Journal of Electrostatics, 2005
A multipole theory describing the interactions between dielectric cylinders in a uniform field is... more A multipole theory describing the interactions between dielectric cylinders in a uniform field is developed. We treat the most general case of N parallel cylinders placed in arbitrary positions. The exact theory is obtained by developing the polarisation charge surface density on each cylinder in a Fourier series. The related coefficients, the so-called multipoles, may be obtained from a linear set of equations which is derived and analysed in the paper. For systems of closely spaced cylinders, with high ratio of the dielectric constant of the cylinders compared to that of the homogeneous medium (in the worst case, conductive cylinders in contact with each other) a very large number of multipole terms is required to achieve convergence. In spite of the large number of required terms, the general multipole expansion is rapidly convergent in all other cases and is important from a theoretical point of view. Numerical results are presented for canonical dispositions of cylinders and for more complicated arrangements. Finally, such a multipole expansion has been applied to the dielectric characterisation of composite materials formed by a regular array of parallel cylinders, thereby obtaining the equivalent permittivity using a numerically efficient technique.
European Journal of Mechanics - A/Solids, 2003
The paper deals with the elastic characterisation of dispersions of randomly oriented ellipsoids:... more The paper deals with the elastic characterisation of dispersions of randomly oriented ellipsoids: we start from the theory of strongly diluted mixtures and successively we generalise it with a differential scheme. The micro-mechanical averaging inside the composite material is carried out by means of explicit results which allows us to obtain closed-form expressions for the macroscopic or equivalent elastic moduli of the overall composite materials. This micromechanical technique has been explicitely developed for describing embeddings of randomly oriented not spherical objects. In particular, this study has been applied to characterise media with different shapes of the inclusions (spheres, cylinders and planar inhomogeneities) and for special media involved in the mixture definition (voids or rigid particles): an accurate analysis of all these cases has been studied yielding a set of relations describing several composite materials of great technological interest. The differential effective medium scheme (developed for generally shaped ellipsoids) extends such results to higher values of the volume fraction of the inhomogeneities embedded in the mixture. For instance, the analytical study of the differential scheme for porous materials (with ellipsoidal zero stiffness voids) reveals a universal behaviour of the effective Poisson ratio for high values of the porosity. This means that Poisson ratio at high porosity assumes characteristic values depending only on the shape of the inclusions and not on the elastic response of the matrix.
International Journal of Engineering Science, 2005
The paper deals with the electrical and elastic characterisation of dispersions of pseudo-oriente... more The paper deals with the electrical and elastic characterisation of dispersions of pseudo-oriented ellipsoids of rotation: it means that we are dealing with mixtures of inclusions of different eccentricities and arbitrary non-random orientational distributions. The analysis ranges from parallel spheroidal inclusions to completely random oriented inclusions. A unified theory covers all the orientational distributions between the random and the parallel ones. The electrical and micro-mechanical averaging inside the composite material is carried out by means of explicit results which allows us to obtain closed-form expressions for the macroscopic or equivalent dielectric constants or elastic moduli of the overall composite materials. In particular, this study allows us to affirm that the electrical behaviour of such a dispersion of pseudo-oriented particles is completely defined by one order parameter which depends on the given angular distribution. Moreover, the elastic characterisation of this heterogeneous material depends on two order parameters, which derive from the orientational distribution. The theory may be applied to characterise media with different shapes of the inclusions (i.e. spheres, cylinders or planar inhomogeneities) yielding a set of procedures describing several composite materials of great technological interest.
Physical Review E
Geometric Brownian motion is an exemplary stochastic processes obeying multiplicative noise, with... more Geometric Brownian motion is an exemplary stochastic processes obeying multiplicative noise, with widespread applications in several fields, e.g., in finance, in physics, and biology. The definition of the process depends crucially on the interpretation of the stochastic integrals which involves the discretization parameter α with 0 α 1, giving rise to the well-known special cases α = 0 (Itô), α = 1/2 (Fisk-Stratonovich), and α = 1 (Hänggi-Klimontovich or anti-Itô). In this paper we study the asymptotic limits of the probability distribution functions of geometric Brownian motion and some related generalizations. We establish the conditions for the existence of normalizable asymptotic distributions depending on the discretization parameter α. Using the infinite ergodicity approach, recently applied to stochastic processes with multiplicative noise by E. Barkai and collaborators, we show how meaningful asymptotic results can be formulated in a transparent way.
Physical Review B, 2017
We numerically demonstrate the possibility to manipulate domain walls in magnetoelastic nanostrip... more We numerically demonstrate the possibility to manipulate domain walls in magnetoelastic nanostripes by means of uniform mechanical stresses. The symmetry breaking of the magnetic states in unidimensional ferromagnets allows the control of the domain-wall position or velocity in geometrically tailored nanostripes coupled to piezoelectric substrates. We further predict that this approach yields unusual domain-wall configurations with velocities of the same order of magnitude as that induced by magnetic fields or spin-polarized currents, while the energy consumption is considerably smaller.
The European Physical Journal B, 2016
Magnetic domain walls are fundamental objects arising in ferromagnetic materials, largely investi... more Magnetic domain walls are fundamental objects arising in ferromagnetic materials, largely investigated both through micromagnetic simulations and experiments. While current-and field-based techniques for inducing domain wall propagation have been widely studied for fundamental understanding and application-oriented purposes, the possibility to manipulate domain walls using mechanical stress in magnetoelastic materials has only recently drawn interest. Here, a complete analytical model describing stress-induced transverse domain wall movement in ferromagnetic nanostripe with variable cross-section is presented. This approach yields a nonlinear integro-differential equation describing the magnetization field. Its numerical implementation, based on the nonlinear relaxation method, demonstrates the possibility to precisely control the position of a domain wall through mechanical action.
Physical Review B, 2012
Magneto-electro-elastic and multiferroic materials can be combined in appealing nanostructures ch... more Magneto-electro-elastic and multiferroic materials can be combined in appealing nanostructures characterized by the coexistence and coupling of electric, magnetic, and mechanical phases with potential applications in novel multifunctional devices. Here, we derive a theory for nonvolatile room-temperature memory elements composed of magnetostrictive nanoparticles embedded in a piezoelectric matrix: two stable orthogonal magnetization states are obtained by the competition of anisotropy and external magnetic polarization. The innovative nontoggle switching between the states is modeled by a thorough combination of the nanomechanical Eshelby approach with the nanomagnetic Landau-Lifshitz-Gilbert formalism, yielding a robust picture of the dynamical behavior and allowing the improvement of the energetic efficiency.
Physical Review E
The fracture behavior of brittle and ductile materials can be strongly influenced by thermal fluc... more The fracture behavior of brittle and ductile materials can be strongly influenced by thermal fluctuations, especially in micro-and nano-devices as well as in rubberlike and biological materials. However, temperature effects, in particular on the brittle-to-ductile transition, still require a deeper theoretical investigation. As a step in this direction we propose a theory, based on equilibrium statistical mechanics, able to describe the temperature dependent brittle fracture and brittle-to-ductile transition in prototypical discrete systems consisting in a lattice with breakable elements. Concerning the brittle behavior, we obtain closed form expressions for the temperature-dependent fracture stress and strain, representing a generalized Griffith criterion, ultimately describing the fracture as a genuine phase transition. With regard to the brittle-to-ductile transition, we obtain a complex critical scenario characterized by a threshold temperature between the two fracture regimes (brittle and ductile), an upper and a lower yield strength, and a critical temperature corresponding to the complete breakdown. To show the effectiveness of the proposed models in describing thermal fracture behaviors at small scales, we successfully compare our theoretical results with molecular dynamics simulations of Si and GaN nanowires.
Continuum Mechanics and Thermodynamics
Applied Mechanics
Sacrificial bonds have been observed in several biological materials and structures and can incre... more Sacrificial bonds have been observed in several biological materials and structures and can increase their toughness, i.e., their resistance to fracture. They provide a reversible mechanism for dissipating mechanical energy before the possible system rupture. From a structural point of view, sacrificial bonds consist of short polymer chains that short-circuit parts of a main macromolecular chain (generating hidden lengths) and absorb energy by breaking them instead of the main chain. The toughness increase due to the presence of sacrificial bonds is typically named extra-toughness. Here, we developed a statistical mechanics and thermodynamics-based theory able to estimate the force–extension relation for chains with sacrificial bonds and to calculate the corresponding extra-toughness. The model is useful to better understand the sacrificial bond effects in biomaterials but also to apply the biomimetic paradigm and foster the development of high-performance artificial polymeric mater...
The European Physical Journal Plus
Non-local and non-convex energies represent fundamental interacting effects regulating the comple... more Non-local and non-convex energies represent fundamental interacting effects regulating the complex behavior of many systems in biophysics and materials science. We study one dimensional, prototypical schemes able to represent the behavior of several biomacromolecules and the phase transformation phenomena in solid mechanics. To elucidate the
In this work we analyze the problem of finding the electric behavior of an anisotropic ellipsoid ... more In this work we analyze the problem of finding the electric behavior of an anisotropic ellipsoid (arbitrarily shaped) placed in a dielectric anisotropic environment. We suppose that the whole system is exposed to a uniform electric field remotely applied. In order to find the resulting electric quantities inside the particle and outside it we adopt a technique largely utilized for solving similar problems in elasticity theory. The inhomogeneity problems in elastostatics are solved within the framework of the Eshelby theory, which adopts, as crucial points, the concepts of eigenstrains and inclusions. The generalization and assessment of such an approach for the dielectric inhomogeneity problems is here addressed by means of the introduction of the concepts of eigenfields and inclusions in electrostatics. The advantages of this methodology are mainly two: firstly, we can consider completely arbitrary dielectric anisotropic behavior both for the particle and the host matrix. Secondly,...
Effective permittivity of materials containing graded ellipsoidal inclusions
International Journal of Solids and Structures, 2013
This article appeared in a journal published by Elsevier. The attached copy is furnished to the a... more This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are
Physical Review E, 2021
We study the relation between stochastic thermodynamics and nonequilibrium thermodynamics by eval... more We study the relation between stochastic thermodynamics and nonequilibrium thermodynamics by evaluating the entropy production and the relation between fluxes and forces in a harmonic system with N particles in contact with N different reservoirs. We suppose that the system is in a nonequilibrium stationary state in a first phase and we study the relaxation to equilibrium in a second phase. During this relaxation, we can identify the linear relation between fluxes and forces satisfying the Onsager reciprocity and we obtain a nonlinear expression for the entropy production. Only when forces and fluxes are small does the entropic production turn into a quadratic form in the forces, as predicted by the Onsager theory.