Physically-Based Approach to the Mechanics of Strong Non-Local Linear Elasticity Theory

Risultato della ricerca: Article

78 Citazioni (Scopus)

Abstract

In this paper the physically-based approach to non-local elasticity theory is introduced. It is formulated by reverting the continuum to an ensemble of interacting volume elements. Interactions between adjacent elements are classical contact forces while long-range interactions between non-adjacent elements are modelled as distance-decaying central body forces. The latter are proportional to the relative displacements rather than to the strain field as in the Eringen model and subsequent developments. At the limit the displacement field is found to be governed by an integro-differential equation, solved by a simple discretization procedure suggested by the underlying mechanical model itself, with corresponding static boundary conditions enforced in a quite simple form. It is then shown that the constitutive law of the proposed model coalesces with the Eringen constitutive law for an unbounded domain under suitable assumptions, whereas it remains substantially different for a bounded domain. Thermodynamic consistency of the model also has been investigated in detail and some numerical applications are presented for different parameters and different functional forms for the decay of the long range forces. For simplicity, the problem is formulated for a 1D continuum while the general formulation for a 3D elastic solid has been reported in the appendix.
Lingua originaleEnglish
pagine (da-a)103-130
Numero di pagine27
RivistaJournal of Elasticity
Volume97
Stato di pubblicazionePublished - 2009

Fingerprint

Elasticity
Mechanics
Integrodifferential equations
Boundary conditions
Thermodynamics

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Mechanical Engineering
  • Mechanics of Materials

Cita questo

@article{36305636d6fd48b2a2154085f617ecbc,
title = "Physically-Based Approach to the Mechanics of Strong Non-Local Linear Elasticity Theory",
abstract = "In this paper the physically-based approach to non-local elasticity theory is introduced. It is formulated by reverting the continuum to an ensemble of interacting volume elements. Interactions between adjacent elements are classical contact forces while long-range interactions between non-adjacent elements are modelled as distance-decaying central body forces. The latter are proportional to the relative displacements rather than to the strain field as in the Eringen model and subsequent developments. At the limit the displacement field is found to be governed by an integro-differential equation, solved by a simple discretization procedure suggested by the underlying mechanical model itself, with corresponding static boundary conditions enforced in a quite simple form. It is then shown that the constitutive law of the proposed model coalesces with the Eringen constitutive law for an unbounded domain under suitable assumptions, whereas it remains substantially different for a bounded domain. Thermodynamic consistency of the model also has been investigated in detail and some numerical applications are presented for different parameters and different functional forms for the decay of the long range forces. For simplicity, the problem is formulated for a 1D continuum while the general formulation for a 3D elastic solid has been reported in the appendix.",
keywords = "Non-local elasticity; Long-range interactions; Central volume forces; Equivalent mechanical models; Thermodynamic consistency",
author = "{Di Paola}, Mario and Massimiliano Zingales and Giuseppe Failla",
year = "2009",
language = "English",
volume = "97",
pages = "103--130",
journal = "Journal of Elasticity",
issn = "0374-3535",
publisher = "Springer Netherlands",

}

TY - JOUR

T1 - Physically-Based Approach to the Mechanics of Strong Non-Local Linear Elasticity Theory

AU - Di Paola, Mario

AU - Zingales, Massimiliano

AU - Failla, Giuseppe

PY - 2009

Y1 - 2009

N2 - In this paper the physically-based approach to non-local elasticity theory is introduced. It is formulated by reverting the continuum to an ensemble of interacting volume elements. Interactions between adjacent elements are classical contact forces while long-range interactions between non-adjacent elements are modelled as distance-decaying central body forces. The latter are proportional to the relative displacements rather than to the strain field as in the Eringen model and subsequent developments. At the limit the displacement field is found to be governed by an integro-differential equation, solved by a simple discretization procedure suggested by the underlying mechanical model itself, with corresponding static boundary conditions enforced in a quite simple form. It is then shown that the constitutive law of the proposed model coalesces with the Eringen constitutive law for an unbounded domain under suitable assumptions, whereas it remains substantially different for a bounded domain. Thermodynamic consistency of the model also has been investigated in detail and some numerical applications are presented for different parameters and different functional forms for the decay of the long range forces. For simplicity, the problem is formulated for a 1D continuum while the general formulation for a 3D elastic solid has been reported in the appendix.

AB - In this paper the physically-based approach to non-local elasticity theory is introduced. It is formulated by reverting the continuum to an ensemble of interacting volume elements. Interactions between adjacent elements are classical contact forces while long-range interactions between non-adjacent elements are modelled as distance-decaying central body forces. The latter are proportional to the relative displacements rather than to the strain field as in the Eringen model and subsequent developments. At the limit the displacement field is found to be governed by an integro-differential equation, solved by a simple discretization procedure suggested by the underlying mechanical model itself, with corresponding static boundary conditions enforced in a quite simple form. It is then shown that the constitutive law of the proposed model coalesces with the Eringen constitutive law for an unbounded domain under suitable assumptions, whereas it remains substantially different for a bounded domain. Thermodynamic consistency of the model also has been investigated in detail and some numerical applications are presented for different parameters and different functional forms for the decay of the long range forces. For simplicity, the problem is formulated for a 1D continuum while the general formulation for a 3D elastic solid has been reported in the appendix.

KW - Non-local elasticity; Long-range interactions; Central volume forces; Equivalent mechanical models; Thermodynamic consistency

UR - http://hdl.handle.net/10447/42038

M3 - Article

VL - 97

SP - 103

EP - 130

JO - Journal of Elasticity

JF - Journal of Elasticity

SN - 0374-3535

ER -