Journal ArticleDOI
On nonlocal elasticity
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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.About:
This article is published in International Journal of Engineering Science.The article was published on 1972-03-01. It has received 2201 citations till now. The article focuses on the topics: Second law of thermodynamics & Elasticity (economics).read more
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Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces
TL;DR: In this paper, a peridynamic formulation for the basic equations of continuum mechanics is proposed, and the propagation of linear stress waves in the new theory is discussed, and wave dispersion relations are derived.
Journal ArticleDOI
Nonlocal damage theory
TL;DR: In this paper, the authors proposed a nonlocal damage theory, which is based on the nonlocal treatment of damage from the local treatment of elastic behavior, and the only required modification is to replace the usual local damage energy release rate with its spatial average over the representative volume of the material whose size is a characteristic of a material.
Journal ArticleDOI
Nonlocal theories for bending, buckling and vibration of beams
J. N. Reddy,J. N. Reddy +1 more
TL;DR: In this article, the Euler-Bernoulli, Timoshenko, Reddy, and Levinson beam theories are reformulated using the nonlocal differential constitutive relations of Eringen.
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Application of nonlocal continuum models to nanotechnology
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.
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Nonlocal integral formulations of plasticity and damage: Survey of progress
Zdenek P. Bazant,Milan Jirásek +1 more
TL;DR: The nonlocal continuum concept has emerged as an effective means for regularizing the boundary value problems with strain softening, capturing the size effects and avoiding spurious localization that gives rise to pathological mesh sensitivity in numerical computations as mentioned in this paper.
References
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Journal ArticleDOI
Elasticity theory of materials with long range cohesive forces
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.
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A unified theory of thermomechanical materials
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.
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A Continuum theory of chemically reacting media—I
A. Cemal Eringen,John D. Ingram +1 more
TL;DR: In this paper, a unified approach for the derivation of conservation of mass, balance of momenta, conservation of energy and balance of entropy across a moving surface of discontinuity in a chemically reacting continuum is presented.