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Francesco Marotti De Sciarra - One of the best experts on this subject based on the ideXlab platform.
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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.
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A Nonlocal Model of Plasticity and Damage with Different Internal Lengths
Inelastic Behavior of Materials and Structures Under Monotonic and Cyclic Loading, 2015Co-Authors: Francesco Marotti De SciarraAbstract:A Nonlocal thermodynamically consistent Model of plasticity and damage is presented using an integral approach. The theory is developed in the framework of the generalized standard material and the constitutive Model is identified by the specification of a Nonlocal first law of thermodynamics and of a local second one. The constitutive Model is then addressed by defining a suitable expression of the free energy which yields a Nonlocal plastic Model in the stress space and a Nonlocal damage Model in the strain space. A variational formulation depending on local and Nonlocal state variables is thus provided.
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Exact solutions for a coupled Nonlocal Model of nanobeams
2014Co-Authors: Francesco Marotti De Sciarra, Raffaele BarrettaAbstract:Bernoulli-Euler nanobeams under concentrated forces/couples with the Nonlocal constitutive behavior proposed by Eringen do not exhibit small-scale effects. A new Model obtained by coupling the Eringen and gradient Models is formulated in the present note. A variational treatment is developed by imposing suitable thermodynamic restrictions for Nonlocal Models and the ensuing differential and boundary conditions of elastic equilibrium are provided. The Nonlocal elastostatic problem is solved in a closed-form for nanocantilever and clamped nanobeams.
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a Nonlocal Model for carbon nanotubes under axial loads
Advances in Materials Science and Engineering, 2013Co-Authors: Raffaele Barretta, Francesco Marotti De SciarraAbstract:Various beam theories are formulated in literature using the Nonlocal differential constitutive relation proposed by Eringen. A new variational framework is derived in the present paper by following a consistent thermodynamic approach based on a Nonlocal constitutive law of gradient-type. Contrary to the results obtained by Eringen, the new Model exhibits the Nonlocality effect also for constant axial load distributions. The treatment can be adopted to get new benchmarks for numerical analyses.
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a Nonlocal Model with strain based damage
International Journal of Solids and Structures, 2009Co-Authors: Francesco Marotti De SciarraAbstract:A thermodynamically consistent formulation of Nonlocal damage in the framework of the internal variable theories of inelastic behaviours of associative type is presented. The damage behaviour is defined in the strain space and the effective stress turns out to be additively splitted in the actual stress and in the Nonlocal counterpart of the relaxation stress related to damage phenomena. An important advantage of Models with strain-based loading functions and explicit damage evolution laws is that the stress corresponding to a given strain can be evaluated directly without any need for solving a nonlinear system of equations. A mixed Nonlocal variational formulation in the complete set of state variables is presented and is specialized to a mixed two-field variational formulation. Hence a finite element procedure for the analysis of the elastic Model with Nonlocal damage is established on the basis of the proposed two-field variational formulation. Two examples concerning a one-dimensional bar in simple tension and a two-dimensional notched plate are addressed. No mesh dependence or boundary effects are apparent.
J. Rafa - One of the best experts on this subject based on the ideXlab platform.
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Lp – Lq time decay estimate to the solution of the Cauchy problem for the system of equations describing Nonlocal Model of the thermoviscoelastic body
PAMM, 2009Co-Authors: J. Gawinecki, Jaroslaw Lazuka, J. RafaAbstract:The aim of this paper is to present a new system of equations describing Nonlocal Model of thermoviscoelastic theory. We used the Papkin and Gurtin approach based on the constitutive relations for stress tensor σ(x), internal energy e(x) and heat flux q(x), with integral terms. Using the modified Cagniard-de Hoop's method we constructed the matrix of fundamental solutions for this system of equations in three-dimensional space. Basing on this matrix we represent in the explicit formula the solution of the Cauchy problem to this system of equations. Next, applying the method of Sobolev spaces, we proved the Lp–Lq time decay estimate to the solution of the Cauchy problem. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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Lp‐Lq time decay estimate to the solution of the Cauchy problem of the system of equations for Nonlocal Model of hyperbolic thermoelasticity theory
PAMM, 2008Co-Authors: J. Gawinecki, Jaroslaw Lazuka, J. RafaAbstract:The aim of this paper is to present a new system of equations describing Nonlocal Model of hyperbolic thermoelasticity theory. We used the Papkin and Gurtin approach based on the constitutive relations for internal energy e(x), and heat flux q(x), with integral terms. Such system of equations describes the propagation of thermal perturbation with finite velocity. Using the modified Cagniard–de Hoop's method we constructed the matrix of fundamental solutions for this system of equations in three–dimensional space. Basing on the constructed matrix of fundamental solutions in the explicit formula we represent the solution of the Cauchy problem to this system of equations in the form of some kind of convolutions. Next, applying the method of Sobolev spaces, we obtain the Lp−Lq time decay estimate to the solution of the Cauchy problem. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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Mathematical and physical aspect of the solution of the Cauchy problem for a system of equations describing a Nonlocal Model of propagation of heat with finite speed
PAMM, 2007Co-Authors: J. Gawinecki, Jarosław Łazuka, J. RafaAbstract:In our paper we present a new system of equations describing a Nonlocal Model of propagation of heat with finite speed in three-dimensional space. Such a system of equations is described by a system of integral – differential equations. At first using the modiffied Cagniard de Hoop method, we construct the fundamental solution of this system of equations. On the basis of the constructed fundamental solution we obtain the explicite formulate of the solution of the Cauchy problem for this system of equations and applying the method of Sobolev and Biesov spaces, we get Lp – Lq time decay estimate for the solution of the Cauchy problem. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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L∞-L1-time decay estimate of the solution of the Cauchy problem of the system of equations describing Nonlocal Model of heat propagation with finite speed
Technical Physics, 1994Co-Authors: J. Gawinecki, J. Rafa, E. WłodarczykAbstract:A new system of equations describing Nonlocal Model of propagation of heat with finite speed in three-dimensional space has been considered. At first, using Cagniard-de Hoop's method, we constructed the fundamental solutions to this system of equations. Basing on the constructed fundamental solutions, we obtained the explicit formula for the solution of the Cauchy problem of this system of equation and next, applying the method of Sobolev spaces, we have got the L∞ − L 1 time decay estimate of the above solution of the Cauchy problem
Hossein Bakhshi Khaniki - One of the best experts on this subject based on the ideXlab platform.
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Vibration analysis of rotating nanobeam systems using Eringen's two-phase local/Nonlocal Model
Physica E: Low-dimensional Systems and Nanostructures, 2018Co-Authors: Hossein Bakhshi KhanikiAbstract:Abstract Due to the inability of differential form of Nonlocal elastic theory in Modelling cantilever beams and inaccurate results for some type of boundaries, in this study, a reliable investigation on transverse vibrational behavior of rotating cantilever size-dependent beams is presented. Governing higher order equations are written in the framework of Eringen's two-phase local/Nonlocal Model and solved using a modified generalized differential quadrature method. In order to indicate the influence of different material and scale parameters, a comprehensive parametric study is presented. It is shown that increasing the Nonlocality term leads to lower natural frequency terms for cantilever nanobeams especially for the fundamental frequency parameter which differential Nonlocal Model is unable to track appropriately. Moreover, it is shown that rotating speed and hub radius have a remarkable effect in varying the mechanical behavior of rotating cantilever nanobeams. This study is a step forward in analyzing nanorotors, nanoturbines, nanoblades, etc.
M Ortiz - One of the best experts on this subject based on the ideXlab platform.
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a Nonlocal Model of fracture by crazing in polymers
Mechanics of Materials, 2015Co-Authors: S Heyden, Sergio Conti, M OrtizAbstract:We derive and numerically verify scaling laws for the macroscopic fracture energy of polymers undergoing crazing from a micromechanical Model of damage. The Model posits a local energy density that generalizes the classical network theory of polymers so as to account for chain failure and a Nonlocal regularization based on strain-gradient elasticity. We specifically consider periodic deformations of a slab subject to prescribed opening displacements on its surfaces. Based on the growth properties of the energy densities, scaling relations for the local and Nonlocal energies and for the specific fracture energy are derived. We present finite-element calculations that bear out the heuristic scaling relations.
J. Gawinecki - One of the best experts on this subject based on the ideXlab platform.
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Lp – Lq time decay estimate to the solution of the Cauchy problem for the system of equations describing Nonlocal Model of the thermoviscoelastic body
PAMM, 2009Co-Authors: J. Gawinecki, Jaroslaw Lazuka, J. RafaAbstract:The aim of this paper is to present a new system of equations describing Nonlocal Model of thermoviscoelastic theory. We used the Papkin and Gurtin approach based on the constitutive relations for stress tensor σ(x), internal energy e(x) and heat flux q(x), with integral terms. Using the modified Cagniard-de Hoop's method we constructed the matrix of fundamental solutions for this system of equations in three-dimensional space. Basing on this matrix we represent in the explicit formula the solution of the Cauchy problem to this system of equations. Next, applying the method of Sobolev spaces, we proved the Lp–Lq time decay estimate to the solution of the Cauchy problem. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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Lp‐Lq time decay estimate to the solution of the Cauchy problem of the system of equations for Nonlocal Model of hyperbolic thermoelasticity theory
PAMM, 2008Co-Authors: J. Gawinecki, Jaroslaw Lazuka, J. RafaAbstract:The aim of this paper is to present a new system of equations describing Nonlocal Model of hyperbolic thermoelasticity theory. We used the Papkin and Gurtin approach based on the constitutive relations for internal energy e(x), and heat flux q(x), with integral terms. Such system of equations describes the propagation of thermal perturbation with finite velocity. Using the modified Cagniard–de Hoop's method we constructed the matrix of fundamental solutions for this system of equations in three–dimensional space. Basing on the constructed matrix of fundamental solutions in the explicit formula we represent the solution of the Cauchy problem to this system of equations in the form of some kind of convolutions. Next, applying the method of Sobolev spaces, we obtain the Lp−Lq time decay estimate to the solution of the Cauchy problem. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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Mathematical and physical aspect of the solution of the Cauchy problem for a system of equations describing a Nonlocal Model of propagation of heat with finite speed
PAMM, 2007Co-Authors: J. Gawinecki, Jarosław Łazuka, J. RafaAbstract:In our paper we present a new system of equations describing a Nonlocal Model of propagation of heat with finite speed in three-dimensional space. Such a system of equations is described by a system of integral – differential equations. At first using the modiffied Cagniard de Hoop method, we construct the fundamental solution of this system of equations. On the basis of the constructed fundamental solution we obtain the explicite formulate of the solution of the Cauchy problem for this system of equations and applying the method of Sobolev and Biesov spaces, we get Lp – Lq time decay estimate for the solution of the Cauchy problem. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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L∞-L1-time decay estimate of the solution of the Cauchy problem of the system of equations describing Nonlocal Model of heat propagation with finite speed
Technical Physics, 1994Co-Authors: J. Gawinecki, J. Rafa, E. WłodarczykAbstract:A new system of equations describing Nonlocal Model of propagation of heat with finite speed in three-dimensional space has been considered. At first, using Cagniard-de Hoop's method, we constructed the fundamental solutions to this system of equations. Basing on the constructed fundamental solutions, we obtained the explicit formula for the solution of the Cauchy problem of this system of equation and next, applying the method of Sobolev spaces, we have got the L∞ − L 1 time decay estimate of the above solution of the Cauchy problem
