The Experts below are selected from a list of 198 Experts worldwide ranked by ideXlab platform
Raffaele Barretta - One of the best experts on this subject based on the ideXlab platform.
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constitutive boundary conditions for nonlocal strain gradient elastic nano beams
International Journal of Engineering Science, 2018Co-Authors: Raffaele Barretta, Francesco Marotti De SciarraAbstract:Abstract Nonlocal strain gradient integral model of elasticity, extension of the fully nonlocal integral law, is widely adopted to assess size effects in nano-beams. The bending moment is sum of convolutions of elastic curvature and of its derivative with a Smoothing Kernel. For nanomechanical problems on unbounded domains, such as in wave propagation, the nonlocal strain gradient integral relation is equivalent to a differential law with constitutive conditions of vanishing at infinity. For bounded nano-beams, the constitutive boundary conditions (CBC) must be added to close the constitutive model. The formulation of these CBC is an original contribution of the paper. Equivalence between nonlocal strain gradient integral model of elasticity and the differential problem with CBC is proven. It is shown that the CBC do not conflict with equilibrium and provide a viable approach to study size-dependent phenomena in nano-beams of applicative interest. Theoretical outcomes are illustrated by examining the static scheme of a nano-actuator modelled by a nano-cantilever inflected by an end-point load. The relevance of a proper formulation of boundary conditions is elucidated by comparing the numerical results with previous attempts in literature.
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stress driven versus strain driven nonlocal integral model for elastic nano beams
Composites Part B-engineering, 2017Co-Authors: Giovanni Romano, Raffaele BarrettaAbstract:Abstract In the strain-driven model of nonlocal elasticity proposed by Eringen , the elastic strain is defined by a Fredholm integral equation in which the stress is the output of a convolution between the local response to an elastic strain and a Smoothing Kernel dependent on a nonlocal parameter. In the wake of this proposal, size effects in nano-beams were investigated in literature by adopting a differential formulation considered to be equivalent to the integral one. Recent improvements have however revealed that equivalence requires also the fulfilment of constitutive boundary conditions. Moreover, this strain-driven nonlocal elastic problem has been shown to be ill-posed, being conflicting with equilibrium requirements. A stress-driven integral constitutive law provides the natural way to get well-posed nonlocal elastic problems for application to nano-structures. The new integral constitutive law is formulated with explicit reference to plane and straight nano-beams according to the standard Bernoulli - Euler structural model. The solution procedure based on the stress-driven nonlocal law is described and adopted for the solution of a simple statically indeterminate scheme, thus showing effectiveness of the new model for the structural design of nano-devices.
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constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams
International Journal of Mechanical Sciences, 2017Co-Authors: Giovanni Romano, Raffaele Barretta, Marina Diaco, Francesco Marotti De SciarraAbstract:Abstract A debated issue, in applications of Eringen 's nonlocal model of elasticity to nanobeams, is the paradox concerning the solution of simple beam problems, such as the cantilever under end-point loading. In the adopted nonlocal model, the bending field is expressed as convolution of elastic curvature with a Smoothing Kernel. The inversion of the nonlocal elastic law leads to solution of a Fredholm integral equation of the first kind. It is here shown that this problem admits a unique solution or no solution at all, depending on whether the bending field fulfils constitutive boundary conditions or not. Paradoxical results found in solving nonlocal elastostatic problems of simple beams are shown to stem from incompatibility between the constitutive boundary conditions and equilibrium conditions imposed on the bending field. The conclusion is that existence of a solution of nonlocal beam elastostatic problems is an exception, the rule being non-existence for problems of applicative interest. Numerical evaluations reported in the literature hide or shadow this conclusion since nodal forces expressing the elastic response are not checked against equilibrium under the prescribed data. The cantilever problem is investigated as case study and analytically solved to exemplify the matter.
Giovanni Romano - One of the best experts on this subject based on the ideXlab platform.
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stress driven versus strain driven nonlocal integral model for elastic nano beams
Composites Part B-engineering, 2017Co-Authors: Giovanni Romano, Raffaele BarrettaAbstract:Abstract In the strain-driven model of nonlocal elasticity proposed by Eringen , the elastic strain is defined by a Fredholm integral equation in which the stress is the output of a convolution between the local response to an elastic strain and a Smoothing Kernel dependent on a nonlocal parameter. In the wake of this proposal, size effects in nano-beams were investigated in literature by adopting a differential formulation considered to be equivalent to the integral one. Recent improvements have however revealed that equivalence requires also the fulfilment of constitutive boundary conditions. Moreover, this strain-driven nonlocal elastic problem has been shown to be ill-posed, being conflicting with equilibrium requirements. A stress-driven integral constitutive law provides the natural way to get well-posed nonlocal elastic problems for application to nano-structures. The new integral constitutive law is formulated with explicit reference to plane and straight nano-beams according to the standard Bernoulli - Euler structural model. The solution procedure based on the stress-driven nonlocal law is described and adopted for the solution of a simple statically indeterminate scheme, thus showing effectiveness of the new model for the structural design of nano-devices.
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constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams
International Journal of Mechanical Sciences, 2017Co-Authors: Giovanni Romano, Raffaele Barretta, Marina Diaco, Francesco Marotti De SciarraAbstract:Abstract A debated issue, in applications of Eringen 's nonlocal model of elasticity to nanobeams, is the paradox concerning the solution of simple beam problems, such as the cantilever under end-point loading. In the adopted nonlocal model, the bending field is expressed as convolution of elastic curvature with a Smoothing Kernel. The inversion of the nonlocal elastic law leads to solution of a Fredholm integral equation of the first kind. It is here shown that this problem admits a unique solution or no solution at all, depending on whether the bending field fulfils constitutive boundary conditions or not. Paradoxical results found in solving nonlocal elastostatic problems of simple beams are shown to stem from incompatibility between the constitutive boundary conditions and equilibrium conditions imposed on the bending field. The conclusion is that existence of a solution of nonlocal beam elastostatic problems is an exception, the rule being non-existence for problems of applicative interest. Numerical evaluations reported in the literature hide or shadow this conclusion since nodal forces expressing the elastic response are not checked against equilibrium under the prescribed data. The cantilever problem is investigated as case study and analytically solved to exemplify the matter.
Francesco Marotti De Sciarra - One of the best experts on this subject based on the ideXlab platform.
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constitutive boundary conditions for nonlocal strain gradient elastic nano beams
International Journal of Engineering Science, 2018Co-Authors: Raffaele Barretta, Francesco Marotti De SciarraAbstract:Abstract Nonlocal strain gradient integral model of elasticity, extension of the fully nonlocal integral law, is widely adopted to assess size effects in nano-beams. The bending moment is sum of convolutions of elastic curvature and of its derivative with a Smoothing Kernel. For nanomechanical problems on unbounded domains, such as in wave propagation, the nonlocal strain gradient integral relation is equivalent to a differential law with constitutive conditions of vanishing at infinity. For bounded nano-beams, the constitutive boundary conditions (CBC) must be added to close the constitutive model. The formulation of these CBC is an original contribution of the paper. Equivalence between nonlocal strain gradient integral model of elasticity and the differential problem with CBC is proven. It is shown that the CBC do not conflict with equilibrium and provide a viable approach to study size-dependent phenomena in nano-beams of applicative interest. Theoretical outcomes are illustrated by examining the static scheme of a nano-actuator modelled by a nano-cantilever inflected by an end-point load. The relevance of a proper formulation of boundary conditions is elucidated by comparing the numerical results with previous attempts in literature.
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constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams
International Journal of Mechanical Sciences, 2017Co-Authors: Giovanni Romano, Raffaele Barretta, Marina Diaco, Francesco Marotti De SciarraAbstract:Abstract A debated issue, in applications of Eringen 's nonlocal model of elasticity to nanobeams, is the paradox concerning the solution of simple beam problems, such as the cantilever under end-point loading. In the adopted nonlocal model, the bending field is expressed as convolution of elastic curvature with a Smoothing Kernel. The inversion of the nonlocal elastic law leads to solution of a Fredholm integral equation of the first kind. It is here shown that this problem admits a unique solution or no solution at all, depending on whether the bending field fulfils constitutive boundary conditions or not. Paradoxical results found in solving nonlocal elastostatic problems of simple beams are shown to stem from incompatibility between the constitutive boundary conditions and equilibrium conditions imposed on the bending field. The conclusion is that existence of a solution of nonlocal beam elastostatic problems is an exception, the rule being non-existence for problems of applicative interest. Numerical evaluations reported in the literature hide or shadow this conclusion since nodal forces expressing the elastic response are not checked against equilibrium under the prescribed data. The cantilever problem is investigated as case study and analytically solved to exemplify the matter.
M Powalka - One of the best experts on this subject based on the ideXlab platform.
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deciphering the radio star formation correlation on kpc scales i adaptive Kernel Smoothing experiments
Astronomy and Astrophysics, 2020Co-Authors: B Vollmer, M Soida, R Beck, M PowalkaAbstract:One of the tightest correlations in astronomy is the relation between the integrated radio continuum and the far-infrared (FIR) emission. Within nearby galaxies, variations in the radio-FIR correlation have been observed, mainly because the cosmic ray electrons migrate before they lose their energy via synchrotron emission or escape. The major cosmic-ray electron transport mechanisms within the plane of galactic disks are diffusion, and streaming. A predicted radio continuum map can be obtained by convolving the map of cosmic-ray electron sources, represented by that of the star formation, with adaptive Gaussian and exponential Kernels. The ratio between the Smoothing lengthscales at 6 cm and 20 cm can be used to determine, between diffusion and streaming, which is the dominant transport mechanism. The dependence of the Smoothing lengthscale on the star formation rate bears information on the dependence of the magnetic field strength, or the ratio between the ordered and turbulent magnetic field strengths on star formation. Star formation maps of eight rather face-on local and Virgo cluster spiral galaxies were constructed from Spitzer and Herschel infrared and GALEX UV observations. These maps were convolved with adaptive Gaussian and exponential Smoothing Kernels to obtain model radio continuum emission maps. It was found that in asymmetric ridges of polarized radio continuum emission, the total power emission is enhanced with respect to the star formation rate. At a characteristic star formation rate ofΣ * = 8 × 10 −3 M yr −1 kpc −2 , the typical lengthscale for the transport of cosmic-ray electrons is l = 0.9 ± 0.3 kpc at 6 cm, and l = 1.8 ± 0.5 kpc at 20 cm. Perturbed spiral galaxies tend to have smaller lengthscales. This is a natural consequence of the enhancement of the magnetic field caused by the interaction. The discrimination between the two cosmic-ray electron transport mechanisms, diffusion, and streaming is based on (i) the convolution Kernel (Gaussian or exponential); (ii) the dependence of the Smoothing Kernel on the local magnetic field, and thus on the local star formation rate; (iii) the ratio between the two Smoothing lengthscales via the frequency dependence of the Smoothing Kernel, and (iv) the dependence of the Smoothing Kernel on the ratio between the ordered and the turbulent magnetic field. Based on our empirical results, methods (i) and (ii) cannot be used to determine the cosmic ray transport mechanism. Important asymmetric large-scale residuals and a local dependence of the Smoothing length on B ord /B turb are most probably responsible for the failure of methods (i) and (ii), respectively. On the other hand, the classifications based on l 6 cm /l 20 cm (method iii) and B ord /B turb (method iv), are well consistent and complementary. We argue that in the six Virgo spiral galaxies, the turbulent magnetic field is globally enhanced in the disk. Therefore, the regions where the magnetic field is independent of the star formation rate are more common. In addition, B ord /B turb decreases, leading to a diffusion lengthscale that is smaller than the streaming lengthscale. Therefore, cosmic ray electron streaming dominates in most of the Virgo spiral galaxies.
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deciphering the radio star formation correlation on kpc scales i adaptive Kernel Smoothing experiments
arXiv: Astrophysics of Galaxies, 2019Co-Authors: B Vollmer, M Soida, R Beck, M PowalkaAbstract:(abridged) Within nearby galaxies, variations in the radio-FIR correlation have been observed, mainly because the cosmic ray electrons migrate before they lose their energy via synchrotron emission or escape. The major cosmic ray electron transport mechanisms within the plane of galactic disks are diffusion and streaming. A predicted radio continuum map can be obtained by convolving the map of comic ray electron sources, represented by that of the star formation, with adaptive Gaussian and exponential Kernels. The ratio between the Smoothing lengthscales at 6cm and 20cm can be used to distinguish between diffusion and streaming as the dominant transport mechanism. Star formation maps of eight rather face-on local and Virgo cluster spiral galaxies were constructed from Spitzer and Herschel infrared and GALEX UV observations.These maps were convolved with adaptive Gaussian and exponential Smoothing Kernels to obtain model radio continuum emission maps. It is found that in asymmetric ridges of polarized radio continuum emission the total power emission is enhanced with respect to the star formation rate. The typical lengthscale for the transport of cosmic ray electrons is l=0.9kpc at 6cm and l=1.8kpc at 20cm. Perturbed spiral galaxies tend to have smaller lengthscales. This is a natural consequence of the enhancement of the magnetic field caused by the interaction. The discrimination between the two cosmic ray electron transport mechanisms, diffusion and streaming, is based on (i) the convolution Kernel (Gaussian or exponential),(ii) the dependence of the Smoothing Kernel on the local magnetic field and hence on the local star formation rate, (iii) the ratio between the two Smoothing lengthscales via the frequency-dependence of the Smoothing Kernel, and (iv) the dependence of the Smoothing Kernel on the ratio between the ordered and the turbulent magnetic field.
B Vollmer - One of the best experts on this subject based on the ideXlab platform.
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deciphering the radio star formation correlation on kpc scales i adaptive Kernel Smoothing experiments
Astronomy and Astrophysics, 2020Co-Authors: B Vollmer, M Soida, R Beck, M PowalkaAbstract:One of the tightest correlations in astronomy is the relation between the integrated radio continuum and the far-infrared (FIR) emission. Within nearby galaxies, variations in the radio-FIR correlation have been observed, mainly because the cosmic ray electrons migrate before they lose their energy via synchrotron emission or escape. The major cosmic-ray electron transport mechanisms within the plane of galactic disks are diffusion, and streaming. A predicted radio continuum map can be obtained by convolving the map of cosmic-ray electron sources, represented by that of the star formation, with adaptive Gaussian and exponential Kernels. The ratio between the Smoothing lengthscales at 6 cm and 20 cm can be used to determine, between diffusion and streaming, which is the dominant transport mechanism. The dependence of the Smoothing lengthscale on the star formation rate bears information on the dependence of the magnetic field strength, or the ratio between the ordered and turbulent magnetic field strengths on star formation. Star formation maps of eight rather face-on local and Virgo cluster spiral galaxies were constructed from Spitzer and Herschel infrared and GALEX UV observations. These maps were convolved with adaptive Gaussian and exponential Smoothing Kernels to obtain model radio continuum emission maps. It was found that in asymmetric ridges of polarized radio continuum emission, the total power emission is enhanced with respect to the star formation rate. At a characteristic star formation rate ofΣ * = 8 × 10 −3 M yr −1 kpc −2 , the typical lengthscale for the transport of cosmic-ray electrons is l = 0.9 ± 0.3 kpc at 6 cm, and l = 1.8 ± 0.5 kpc at 20 cm. Perturbed spiral galaxies tend to have smaller lengthscales. This is a natural consequence of the enhancement of the magnetic field caused by the interaction. The discrimination between the two cosmic-ray electron transport mechanisms, diffusion, and streaming is based on (i) the convolution Kernel (Gaussian or exponential); (ii) the dependence of the Smoothing Kernel on the local magnetic field, and thus on the local star formation rate; (iii) the ratio between the two Smoothing lengthscales via the frequency dependence of the Smoothing Kernel, and (iv) the dependence of the Smoothing Kernel on the ratio between the ordered and the turbulent magnetic field. Based on our empirical results, methods (i) and (ii) cannot be used to determine the cosmic ray transport mechanism. Important asymmetric large-scale residuals and a local dependence of the Smoothing length on B ord /B turb are most probably responsible for the failure of methods (i) and (ii), respectively. On the other hand, the classifications based on l 6 cm /l 20 cm (method iii) and B ord /B turb (method iv), are well consistent and complementary. We argue that in the six Virgo spiral galaxies, the turbulent magnetic field is globally enhanced in the disk. Therefore, the regions where the magnetic field is independent of the star formation rate are more common. In addition, B ord /B turb decreases, leading to a diffusion lengthscale that is smaller than the streaming lengthscale. Therefore, cosmic ray electron streaming dominates in most of the Virgo spiral galaxies.
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deciphering the radio star formation correlation on kpc scales i adaptive Kernel Smoothing experiments
arXiv: Astrophysics of Galaxies, 2019Co-Authors: B Vollmer, M Soida, R Beck, M PowalkaAbstract:(abridged) Within nearby galaxies, variations in the radio-FIR correlation have been observed, mainly because the cosmic ray electrons migrate before they lose their energy via synchrotron emission or escape. The major cosmic ray electron transport mechanisms within the plane of galactic disks are diffusion and streaming. A predicted radio continuum map can be obtained by convolving the map of comic ray electron sources, represented by that of the star formation, with adaptive Gaussian and exponential Kernels. The ratio between the Smoothing lengthscales at 6cm and 20cm can be used to distinguish between diffusion and streaming as the dominant transport mechanism. Star formation maps of eight rather face-on local and Virgo cluster spiral galaxies were constructed from Spitzer and Herschel infrared and GALEX UV observations.These maps were convolved with adaptive Gaussian and exponential Smoothing Kernels to obtain model radio continuum emission maps. It is found that in asymmetric ridges of polarized radio continuum emission the total power emission is enhanced with respect to the star formation rate. The typical lengthscale for the transport of cosmic ray electrons is l=0.9kpc at 6cm and l=1.8kpc at 20cm. Perturbed spiral galaxies tend to have smaller lengthscales. This is a natural consequence of the enhancement of the magnetic field caused by the interaction. The discrimination between the two cosmic ray electron transport mechanisms, diffusion and streaming, is based on (i) the convolution Kernel (Gaussian or exponential),(ii) the dependence of the Smoothing Kernel on the local magnetic field and hence on the local star formation rate, (iii) the ratio between the two Smoothing lengthscales via the frequency-dependence of the Smoothing Kernel, and (iv) the dependence of the Smoothing Kernel on the ratio between the ordered and the turbulent magnetic field.
