Journal ArticleDOI
On Some Aspects in the Special Theory of Gradient Elasticity
B.S. Altan,Elias C. Aifantis +1 more
TLDR
In this article, a special form of gradient-dependent elasticity is considered and the motivation for considering higher-order gradients of strains in elasticity was discussed, where equilibrium equations and boundary conditions are discussed and solutions to certain problems including propagation of harmonic waves, the longitudinal vibrations of a beam, and the displacement field in an infinite medium weakened by a line crack are given.Abstract:
In this paper a special form of gradient-dependent elasticity is considered. The motivation for considering higher-order gradients of strains in elasticity is discussed. Equilibrium equations and boundary conditions are discussed. The relationship between the special form of gradient elasticity adopted in this study and mixture or nonlocal theories is considered. Solutions to certain problems including the propagation of harmonic waves, the longitudinal vibrations of a beam, and the displacement field in an infinite medium weakened by a line crack are given.read more
Citations
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Journal ArticleDOI
A microstructure-dependent Kirchhoff plate model based on a reformulated strain gradient elasticity theory
TL;DR: In this paper, a microstructure-dependent non-classical model for Kirchhoff plates is developed by using a reformulated strain gradient elasticity theory that incorporates both the strain gradient and couple elasticity.
Journal ArticleDOI
Griffith's theory versus gradient elasticity in the evaluation of porous materials tensile strength
TL;DR: In this paper, the authors compare the results of Griffith's theory and gradient elasticity in the interpretation of size effect and provide a more detailed study of the stress concentration factor for the normalized failure stress of a hole contained in an elastic plate.
Book ChapterDOI
Dislocations in Generalized Continuum Mechanics
TL;DR: An overview on dislocations in the framework of different types of generalized continua is given in this article, where the authors discuss the constitutive relations for the linear and isotropic case and demonstrate the characteristic length scales are given in terms of the material parameters.
Journal ArticleDOI
On chiral effects in strain gradient elasticity
Dorin Ieşan,Ramón Quintanilla +1 more
TL;DR: In this paper, the deformation of an isotropic chiral bar subjected to body forces, to tractions on the lateral surface and to resultant forces and moments on the ends is studied.
References
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Journal ArticleDOI
Effects of couple-stresses in linear elasticity
Journal ArticleDOI
On nonlocal elasticity
TL;DR: In this article, a theory of non-local elasticity is presented via the vehicles of global balance laws and the second law of thermodynamics via the use of a localized Clausius-Duhem inequality and a variational statement of Gibbsian global thermodynamics.
Journal ArticleDOI
Second gradient of strain and surface-tension in linear elasticity
TL;DR: In this article, a linear theory of deformation of an elastic solid was formulated, in which the potential energy-density is a function of the strain and its first and second gradients.
Journal ArticleDOI
On first strain-gradient theories in linear elasticity
Raymond D. Mindlin,N.N. Eshel +1 more
TL;DR: In this paper, a study of the linear theory of elasticity in which the potential energy-density depends on the gradient of the strain in addition to the strain was performed, and the relations connecting the stresses in the three forms and the boundary conditions in three forms were derived.