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Dislocations in second strain gradient elasticity
International Journal of Solids and Structures, 2006 AbstractA second strain gradient elasticity theory is proposed based on first and second gradients of the strain tensor. Such a theory is an extension of first strain gradient elasticity with double stresses. In particular, the strain energy depends on the strain tensor and on the first and second gradient terms of it.
Markus Lazar, Elias C Aifantis
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Weak Solutions within the Gradient-Incomplete Strain-Gradient Elasticity [PDF]
Lobachevskii Journal of Mathematics, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eremeyev V. A., dell'Isola F.
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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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Second Law of Thermodynamics and Strain Gradient Theories of Elasticity [PDF]
EntropyThe paper addresses the second law of thermodynamics through the Clausius–Duhem inequality in its general form, with entropy flux and entropy production given by suitable constitutive functions.
Claudio Giorgi, Angelo Morro
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Irreducible decomposition of strain gradient tensor in isotropic strain gradient elasticity [PDF]
ZAMM Zeitschrift Fur Angewandte Mathematik Und Mechanik, 2016 In isotropic strain gradient elasticity, we decompose the strain gradient tensor into its irreducible pieces under the n‐dimensional orthogonal group . Using the Young tableau method for traceless tensors, four irreducible pieces (), which are canonical, are obtained.
Markus Lazar
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The strain gradient elasticity via nonlocal considerations
International Journal of Solids and Structures, 2023 Strain gradient elasticity and nonlocal elasticity are two enhanced elastic theories intensively used over the last fifty years to explain static and dynamic phenomena that classical elasticity fails to do. The nonlocal elastic theory has a clear differentiation from the classical case by considering stresses in a point of the continuum as an integral ...
Dimitrios G Aggelis, Theodore V Gortsas
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Gradient Elasticity with Interfaces as Surfaces of Discontinuity for the Strain Gradient
Journal of the Mechanical Behavior of Materials, 2007 Aifantis, K.E., Askes, H.
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Displacement potential functions for elastodynamic problems in transversely isotropic media based on nonlocal strain gradient theory [PDF]
مهندسی عمران شریف, 2022 Today nanotechnology has become important in many fields, including industry, medicine, engineering, aerospace, national security and electronics. As the dimensions of the structures decrease, the effects of size play a crucial role in properties of the ...
P. Nateghi Babagi +2 more
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Strain gradient elasticity within the symmetric BEM formulation [PDF]
Fracture and Structural Integrity, 2014 The symmetric Galerkin Boundary Element Method is used to address a class of strain gradient elastic materials featured by a free energy function of the (classical) strain and of its (first) gradient.
S. Terravecchia +2 more
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Gradient elasticity solutions of 2D nano-beams
Applications in Engineering Science, 2023 In this study, the exact analytical solutions of a two-dimensional linear homogeneous isotropic nano-beam in gradient elasticity are studied. Four different types of two-dimensional cantilever beams and related boundary conditions are considered.
Teoman Özer
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