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On Dislocations in a Special Class of Generalized Elasticity [PDF]
, 2005 In this paper we consider and compare special classes of static theories of gradient elasticity, nonlocal elasticity, gradient micropolar elasticity and nonlocal micropolar elasticity with only one gradient coefficient. Equilibrium equations are discussed.
Aifantis +51 more
arxiv +3 more sources
Fractional Gradient Elasticity from Spatial Dispersion Law [PDF]
ISRN Condensed Matter Physics. Vol.2014. (2014) 794097, 2013 Non-local elasticity models in continuum mechanics can be treated with two different approaches: the gradient elasticity models (weak non-locality) and the integral non-local models (strong non-locality). This article focuses on the fractional generalization of gradient elasticity that allows us to describe a weak non-locality of power-law type.
Tarasov, Vasily E.
arxiv +6 more sources
THEORY OF MICROPOLAR ELASTICITY
, 1967 In the four previous chapters we have given the complete theory of 3M continua, with and without E-M interactions. Balance laws, jump conditions, and nonlinear constitutive equations were obtained, so that the theory is complete and closed. Beginning with Chapter 5 we explore applications of these theories.
A. Cemal Eringen
openaire +3 more sources
The Cauchy Relations in Linear Elasticity Theory [PDF]
arXiv, 2002 In linear elasticity, we decompose the elasticity tensor into two irreducible pieces with 15 and 6 independent components, respectively. The {\it vanishing} of the piece with 6 independent components corresponds to the Cauchy relations. Thus, for the first time, we recognize the group-theoretical underpinning of the Cauchy relations.
Friedrich W. Hehl, Yakov Itin
arxiv +3 more sources
, 2016 We show existence of solutions for the equations of static atomistic nonlinear elasticity theory on a bounded domain with prescribed boundary values. We also show their convergence to the solutions of continuum nonlinear elasticity theory, with energy ...
J. Braun, B. Schmidt
semanticscholar +3 more sources
Rigorous solution of the problem of the state of a linearly elastic isotropic body under the action of polynomial bulk forces [PDF]
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2021 When solving boundary value problems about the construction of the stress-strain state of an linearly elastic, isotropic body, an important step is finding the internal state generated by the forces, distributed over the area occupied by the body. In the
Viktor B. Penkov +2 more
doaj +1 more source
Bioengineering, 2022 Orthodontic implants have been developed for the implementation of skeletal anchorage and are effectively used in the design of individual orthodontic devices.
Dmitriy Suetenkov +5 more
doaj +1 more source
PROBLEM OF PLATE BENDING IN THE MOMENT ASYMMETRIC THEORY OF ELASTICITY
International Journal for Computational Civil and Structural Engineering, 2023 For a number of materials used in modern practice, calculations according to the classical theory of elasticity give incorrect results. To ensure the reliable operation of structures, there is a need for new theories.
Nelly Rogacheva, Yulia Zheglova
doaj +1 more source
Journal of Applied Mechanics, 1975 This book is designed for use by students and teachers in the field of applied mechanics and mathematics, and for practitioners in civil and mechanical engineering. Since tensor calculus is an indispensable prerequisite when dealing with the theory of elasticity in a modern way, the first part of the book consists in an introduction into this subject ...
H. Leipholz, John W. Hutchinson
openaire +2 more sources
Comparative study of theoretical and real deflection of a simple and reinforced concret joist
Ingeniería e Investigación, 2021 This research aims to determine the actual deflection of a concrete joist and to correlate the result with the theoretical deflection. This is based on the theories of elasticity as the double integration method, considering the homogeneous, isotropic ...
Sócrates Pedro Muñoz +3 more
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