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Symmetry classes for even-order tensors [PDF]
, 2013 The purpose of this article is to give a complete and general answer to the recurrent problem in continuum mechanics of the determination of the number and the type of symmetry classes of an even-order tensor space.
Auffray, N., Olive, M.
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General lattice model of gradient elasticity [PDF]
Modern Physics Letters B, 2014 In this paper, new lattice model for the gradient elasticity is suggested. This lattice model gives a microstructural basis for second-order strain-gradient elasticity of continuum that is described by the linear elastic constitutive relation with the negative sign in front of the gradient.
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Gradient elasticity applied to a crack
Journal of the Mechanical Behavior of Materials, 2013 The aim of this paper is to investigate the stress and the displacement field of a crack within a robust version of gradient elasticity, focusing at the standard Mode I, II, III problems.
Konstantopoulos Iason, Aifantis Elias
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Anisotropic and dispersive wave propagation within strain-gradient framework [PDF]
, 2016 In this paper anisotropic and dispersive wave propagation within linear strain-gradient elasticity is investigated. This analysis reveals significant features of this extended theory of continuum elasticity. First, and contrarily to classical elasticity,
Auffray, Nicolas, Rosi, Giuseppe
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A Concise Review of Gradient Models in Mechanics and Physics
Frontiers in Physics, 2020 The various mathematical models developed over the years to interpret the behavior of materials and corresponding processes they undergo were based on observations and experiments made at that time.
Elias C. Aifantis
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On nonlinear dilatational strain gradient elasticity [PDF]
Continuum Mechanics and Thermodynamics, 2021 AbstractWe call nonlinear dilatational strain gradient elasticity the theory in which the specific class of dilatational second gradient continua is considered: those whose deformation energy depends, in an objective way, on the gradient of placement and on the gradient of the determinant of the gradient of placement.
Eremeyev V. A. +2 more
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Application of gradient elasticity to benchmark problems of beam vibrations
Journal of the Mechanical Behavior of Materials, 2016 The gradient approach, specifically gradient elasticity theory, is adopted to revisit certain typical configurations on mechanical vibrations. New results on size effects and scale-dependent behavior not captured by classical elasticity are derived ...
Kateb K.M. +6 more
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Normality condition in elasticity [PDF]
, 2013 Strong local minimizers with surfaces of gradient discontinuity appear in variational problems when the energy density function is not rank-one convex. In this paper we show that stability of such surfaces is related to stability outside the surface via ...
Grabovsky, Yury, Truskinovsky, Lev
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The Boussinesq problem in dipolar gradient elasticity [PDF]
Archive of Applied Mechanics, 2014 The three-dimensional axisymmetric Boussinesq problem of an isotropic half-space subjected to a concentrated normal quasi-static load is studied within the framework of linear dipolar gradient elasticity. Our main concern is to determine possible deviations from the predictions of classical linear elastostatics when a more refined theory is employed to
Georgiadis, H. G. +2 more
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Latin American Journal of Solids and StructuresIn the present paper, a critique study on some models available in the literature for bending analysis of nano-beams using the gradient elasticity theory is accomplished.
Mahmood Mehrdad Shokrieh, Iman Zibaei
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