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Journal ArticleDOI

Nonlocal polar elastic continua

01 Jan 1972-International Journal of Engineering Science (Pergamon)-Vol. 10, Iss: 1, pp 1-16
TL;DR: In this article, a continuum theory of non-local polar bodies is developed for nonlinear micromorphic elastic solids, and the balance laws and jump conditions are given.
About: This article is published in International Journal of Engineering Science.The article was published on 1972-01-01. It has received 1788 citations till now.
Citations
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Book
01 Jan 2002
TL;DR: Memory-dependent nonlocal nonlocal Electromagnetic Elastic Solids as mentioned in this paper have been shown to be memory-dependent on nonlocal elasticity and nonlocal linear elasticity, as well as nonlocal Linear Elasticity and Nonlocal Fluid Dynamics.
Abstract: 1. Motion and Deformation.- 2. Stress.- 3. Constitutive Axioms.- 4. Nonlocal Electromagnetic Theory.- 5. Constitutive Equations of Memory-Dependent Nonlocal Electromagnetic Elastic Solids.- 6. Nonlocal Linear Elasticity.- 7. Nonlocal Fluid Dynamics.- 8. Nonlocal Linear Electromagnetic Theory.- 9. Memory-Dependent Nonlocal Thermoelastic Solids.- 10. Memory-Dependent Nonlocal Fluids.- 11. Memory-Dependent Nonlocal Electromagnetic Elastic Solids.- 12. Memory-Dependent Nonlocal Electromagnetic Thermofluids.- 13. Nonlocal Microcontinua.- 14. Memory-Dependent Nonlocal Micropolar Electromagnetic Elastic Solids.- 15. Nonlocal Continuum Theory of Liquid Crystals.

1,967 citations

Journal ArticleDOI
TL;DR: In this article, the Euler-Bernoulli, Timoshenko, Reddy, and Levinson beam theories are reformulated using the nonlocal differential constitutive relations of Eringen.

1,519 citations

Journal ArticleDOI
TL;DR: In this paper, a nonlocal elasticity theory is employed to develop a non-local Benoulli/Euler beam model and some representative problems are solved to illustrate the magnitude of predicted nonlocal effects.

1,171 citations

Journal ArticleDOI
TL;DR: In this article, the dispersion relations for one dimensional plane waves were obtained by fitting the nonlocal material moduli to exactly the acoustical branch of elastic waves within one Brillouin zone in periodic one dimensional lattices.

1,101 citations

Journal ArticleDOI
TL;DR: The equations of motion of the Euler-Bernoulli and Timoshenko beam theories were reformulated using the nonlocal differential constitutive relations of Eringen [International Journal of Engineering Science 10, 1−16 (1972) as mentioned in this paper.
Abstract: The equations of motion of the Euler–Bernoulli and Timoshenko beam theories are reformulated using the nonlocal differential constitutive relations of Eringen [International Journal of Engineering Science 10, 1–16 (1972)]. The equations of motion are then used to evaluate the static bending, vibration, and buckling responses of beams with various boundary conditions. Numerical results are presented using the nonlocal theories to bring out the effect of the nonlocal behavior on deflections, buckling loads, and natural frequencies of carbon nanotubes.

642 citations

References
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Journal ArticleDOI
TL;DR: In this paper, the formulation of the basic field equations, boundary conditions and constitutive equations of simple micro-elastic solids is discussed. And explicit expressions of constitutive expressions of several simple micro elastic solids are given and applied to some special problems.

1,309 citations

Book
01 Jan 1967

983 citations

Journal ArticleDOI
TL;DR: In this paper, the authors derived a linear model for the elastic long-range strain energy of a deformed material with spatial interaction, which can be expressed in a differential (multipolar) form or in a non-local form.

661 citations

BookDOI
01 Jan 1968

324 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present an attempt to organize and unify the mechanics, thermodynamics and constitutive equations of nonpolar materials subject to thermal effects and mechanical forces.

275 citations