A method to transform a nonlocal model into a gradient one within elasticity and plasticity

Polizzotto, C

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7 Citazioni (Scopus)

Abstract

A method based on the principle of the virtual power (PVP) is presented, by which a mechanical problem of nonlocal elasticity, or plasticity, is transformed into one of gradient nature. Different Taylor series expansion techniques are applied to the driving local strain fields of the nonlocal problem, either full spatial expansion within the bulk volume, or uni-directional expansion along the normal to the thin boundary layer. This, at the limit when the boundary layer thickness tends to zero, makes the PVP of the nonlocal model transform itself into one featuring a counterpart gradient model. Also, for a class of “associated” nonlocal and gradient elasticity models (i.e. the kernel function of the former is the Green function of the latter), the mutual relationship is discussed and the existence of some related complementary formats is pointed out together with their computational relevance.
Lingua originaleEnglish
pagine (da-a)30-41
Numero di pagine12
RivistaEUROPEAN JOURNAL OF MECHANICS. A, SOLIDS
Volume46
Stato di pubblicazionePublished - 2014

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plastic properties
Plasticity
Nonlocal Elasticity
Elasticity
elastic properties
Transform
Gradient
gradients
Boundary Layer
Boundary layers
Gradient Elasticity
kernel functions
boundary layer thickness
Nonlocal Problems
expansion
Taylor Series Expansion
Taylor series
Thin Layer
Kernel Function
series expansion

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Physics and Astronomy(all)
  • Mechanical Engineering
  • Mechanics of Materials
  • Mathematical Physics

Cita questo

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abstract = "A method based on the principle of the virtual power (PVP) is presented, by which a mechanical problem of nonlocal elasticity, or plasticity, is transformed into one of gradient nature. Different Taylor series expansion techniques are applied to the driving local strain fields of the nonlocal problem, either full spatial expansion within the bulk volume, or uni-directional expansion along the normal to the thin boundary layer. This, at the limit when the boundary layer thickness tends to zero, makes the PVP of the nonlocal model transform itself into one featuring a counterpart gradient model. Also, for a class of “associated” nonlocal and gradient elasticity models (i.e. the kernel function of the former is the Green function of the latter), the mutual relationship is discussed and the existence of some related complementary formats is pointed out together with their computational relevance.",
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AU - Polizzotto, C

AU - Borino, Guido

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N2 - A method based on the principle of the virtual power (PVP) is presented, by which a mechanical problem of nonlocal elasticity, or plasticity, is transformed into one of gradient nature. Different Taylor series expansion techniques are applied to the driving local strain fields of the nonlocal problem, either full spatial expansion within the bulk volume, or uni-directional expansion along the normal to the thin boundary layer. This, at the limit when the boundary layer thickness tends to zero, makes the PVP of the nonlocal model transform itself into one featuring a counterpart gradient model. Also, for a class of “associated” nonlocal and gradient elasticity models (i.e. the kernel function of the former is the Green function of the latter), the mutual relationship is discussed and the existence of some related complementary formats is pointed out together with their computational relevance.

AB - A method based on the principle of the virtual power (PVP) is presented, by which a mechanical problem of nonlocal elasticity, or plasticity, is transformed into one of gradient nature. Different Taylor series expansion techniques are applied to the driving local strain fields of the nonlocal problem, either full spatial expansion within the bulk volume, or uni-directional expansion along the normal to the thin boundary layer. This, at the limit when the boundary layer thickness tends to zero, makes the PVP of the nonlocal model transform itself into one featuring a counterpart gradient model. Also, for a class of “associated” nonlocal and gradient elasticity models (i.e. the kernel function of the former is the Green function of the latter), the mutual relationship is discussed and the existence of some related complementary formats is pointed out together with their computational relevance.

UR - http://hdl.handle.net/10447/101314

UR - http://dx.doi.org/10.1016/j.euromechsol.2014.01.004

M3 - Article

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EP - 41

JO - European Journal of Mechanics, A/Solids

JF - European Journal of Mechanics, A/Solids

SN - 0997-7538

ER -