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Nonlocal elasticity theory for graphene modeling and simulation: prospects and challenges
Journal of Modeling in Mechanics and Materials, 2017 : This paper presents a literature review of recent research studies on the applications of nonlocal elasticity theory in the modeling and simulation of graphene sheets (GSs).
Kim Meow Liew
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On the solution of the purely nonlocal theory of beam elasticity as a limiting case of the two-phase theory [PDF]
International Journal of Solids and Structures, 2020 In the recent literature stance, purely nonlocal theory of elasticity is recognized to lead to ill-posed problems. Yet, we show that, for a beam, a meaningful energy bounded solution of the purely nonlocal theory may still be defined as the limit ...
Gennadi Mikhasev, Andrea Nobili
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Nonlocal elasticity theory of polymeric liquid crystals
Physical Review A, 1990We construct a nonlocal theory of elasticity for a nematic polymer composed of rigid or semiflexible molecules. We then introduce a mean-field theory for the calculation of wave-vector-dependent elastic moduli. Because the length of the molecules can be comparable to observable elastic distortions, the wave-vector dependence of the Frank moduli, i.e ...
, Lo, , Pelcovits
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Theory of nonlocal asymmetric elastic solids
Applied Mathematics and Mechanics, 1992The continuum mechanics is based on the following theories: (i) geometric field theory describing the strains; (ii) laws of conservation of mass, linear momentum, angular momentum, energy; (iii) constitutive relations between strains or stresses; (iv) equation of state. Each of these theories may be linear or nonlinear, and global or local.
Gao, Jian, Chen, Zhida
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On correct nonlocal generalized theories of elasticity
Physical Mesomechanics, 2016The paper discusses nonlocal elasticity theories among which are models of media with defect fields, gradient elasticity theories, and hybrid nonlocal elasticity theories. Gradient theories are analyzed, and their correctness properties are examined.
V. V. Vasiliev, S. A. Lurie
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Nonlocal elasticity theory for vibration of nanoplates
Journal of Sound and Vibration, 2009Classical plate theory (CLPT) and first-order shear deformation theory (FSDT) of plates are reformulated using the nonlocal differential constitutive relations of Eringen. The equations of motion of the nonlocal theories are derived. Navier's approach has been used to solve the governing equations for simply supported boundary conditions.
S.C. Pradhan, J.K. Phadikar
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2013
Continuum theories describe a system in terms of few variables such as mass, temperature, voltage, and stress, which are highly suited for direct measurements of these variables. Their successes, expediency, and practicality, have been demonstrated and tested throughout the history of science through explaining and predicting diverse physical phenomena.
Srinivasan Gopalakrishnan +1 more
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Continuum theories describe a system in terms of few variables such as mass, temperature, voltage, and stress, which are highly suited for direct measurements of these variables. Their successes, expediency, and practicality, have been demonstrated and tested throughout the history of science through explaining and predicting diverse physical phenomena.
Srinivasan Gopalakrishnan +1 more
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Nonlocal Elasticity Theory for the Mechanical Behavior of Protein Microtubules
Physical Mesomechanics, 2021В работе представлена теория балок Редди с нелокальными дифференциальными определяющими уравнениями Эрингена, а также уравнения движения белковых микротрубочек в терминах обобщенных смещений. Приведено аналитическое решение изгиба белковых микротрубочек для выявления влияния нелокального поведения на отклонения.
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A review on stress-driven nonlocal elasticity theory
2021The behavior of materials at the nanoscale cannot be studied by classical theories. Accordingly, new theories have been developed to predict the behavior of materials at the nanoscale; some of them are nonlocal elasticity, strain gradient theory, couple stress theory, and surface effect theory.
Shariati, Mojtaba +4 more
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Saint-Venant Principle on Problems of Nonlocal Elasticity Theory
Herald of the Bauman Moscow State Technical University. Series Natural Sciences, 2023Simulating the modern structural materials requires introduction of a model that takes into account structural features at the micro-level. The Eringen’s nonlocal elasticity theory model could be referred to such models. This model introduction was considered in comparison with the elasticity classical model.
G.N. Kuvyrkin, A.A. Sokolov
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