Journal Article10.1016/S0997-7538(02)01218-4
One-dimensional dynamically consistent gradient elasticity models derived from a discrete microstructure: Part 1: Generic formulation
Andrei V. Metrikine,Harm Askes +1 more
217
TL;DR: In this paper, a new continualization method is proposed in which each higher-order stiffness term is accompanied by a higherorder inertia term, and the resulting models are dynamically consistent.
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Abstract: This paper is the first in a series of two that focus on gradient elasticity models derived from a discrete microstructure. In this first paper, a new continualization method is proposed in which each higher-order stiffness term is accompanied by a higher-order inertia term. As such, the resulting models are dynamically consistent. A new parameter is introduced that accounts for the nonlocal interaction between variables of the discrete model and of the continuous model. When this parameter is set to proper values, physically realistic behavior is obtained in statics as well as in dynamics. In this sense, the proposed methodology is superior to earlier approaches to derive gradient elasticity models, in which anomalies in the dynamic behavior have been found. A generic formulation of field equations and boundary conditions is given based on Hamilton's principle. In the second paper, analytical and numerical results of static and dynamic response of the second-order model and the fourth-order model will be treated.
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Citations
Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results
Harm Askes,Elias C. Aifantis +1 more
TL;DR: In this article, various formats of gradient elasticity and their performance in static and dynamic applications are discussed and an overview of length scale identification and quantification procedures is given, together with the variationally consistent boundary conditions.
849
A novel atomistic approach to determine strain-gradient elasticity constants: Tabulation and comparison for various metals, semiconductors, silica, polymers and the (Ir) relevance for nanotechnologies
R. Maranganti,Pradeep Sharma +1 more
TL;DR: In this paper, the authors derived the strain-gradient constants for some representative semiconductor, metallic, amorphous and polymeric materials using the developed relations and numerical atomistic calculations.
304
Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory
TL;DR: In this paper, the bending, buckling and vibration problems of axially functionally graded (FG) beams are solved by a generalized differential quadrature method, and the influence of power-law variation and size-dependent parameters on the axially FG beam behavior is investigated.
300
Gradient elasticity and flexural wave dispersion in carbon nanotubes
TL;DR: In this paper, higher-order elasticity theories have been used to predict the dispersion characteristics of flexural waves in carbon nanotubes (CNTs), in particular, nonlocal elasticity and gradient elasticity (with unstable strain gradients) have been employed within the framework of classical Euler-Bernoulli or improved Timoshenko beam theory.
207
Wave dispersion in gradient elastic solids and structures: A unified treatment
TL;DR: In this paper, an analytical wave propagation study in gradient elastic solids and structures is presented, where wave dispersion is observed as a result of introducing microstructural effects into the classical elastic material behavior through a simple gradient elasticity theory involving both micro-elastic and micro-inertia characteristics.
185
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