scholarly journals Numerical convergence of nonlinear nonlocal continuum models to local elastodynamics

2018 ◽  
Vol 114 (13) ◽  
pp. 1389-1410 ◽  
Author(s):  
Prashant K. Jha ◽  
Robert Lipton
Keyword(s):  
Continuum Models ◽  
Nonlocal Continuum ◽  
Numerical Convergence

A NONLOCAL CONTINUUM MECHANICS MODEL TO ESTIMATE THE MATERIAL PROPERTY OF SINGLE-WALLED CARBON NANOTUBES

2012 ◽  
Vol 11 (01) ◽  
pp. 1250007 ◽  
Author(s):  
S. NARENDAR ◽  
S. GOPALAKRISHNAN
Keyword(s):  
Carbon Nanotubes ◽  
Continuum Mechanics ◽  
Nonlocal Parameter ◽  
Nonlocal Theory ◽  
Accurate Estimate ◽  
Continuum Models ◽  
Nonlocal Continuum ◽  
Length Scales ◽  
Mechanics Model ◽  
Carbon Carbon Bond

A subject of current technological interest is that of nanotechnology. It would appear that nonlocal continuum mechanics could potentially play a useful role in analysis related to nanotechnology applications. The present work explores this potential in the context of a specific application. The length scales associated with nanotechnology are often sufficiently small to call the applicability of classical continuum models into question. Atomic and molecular models, while certainly conceptually valid for small length scales, are difficult to formulate accurately and are almost always computationally intensive. Nonlocal continuum models represent attempts to extend the continuum approach to smaller length scales while retaining most of its many advantages. Therefore, continuum models need to be extended to consider the scale effect in nanomaterial studies. This can be accomplished through proposing nonlocal continuum mechanics models, where the internal size scale could be simply considered in constitutive equations as a material parameter. Usually, the magnitude of the nonlocal parameter e0, determines the nonlocal effect in the analysis. The modeling and analyses of nanostructures based on flexural displacement, require an accurate estimate of nonlocal scaling parameter. Such an attempt is made in the present work. From the present analysis, the value of the scale coefficient (e0a, a is carbon-carbon bond length) is recommended to be about 0.11 nm for the application of the nonlocal theory in the analysis of carbon nanotubes.

Peridynamic State-Based Models and the Embedded-Atom Model

2014 ◽  
Vol 15 (1) ◽  
pp. 179-205 ◽  
Author(s):  
Pablo Seleson ◽  
Michael L. Parks ◽  
Max Gunzburger
Keyword(s):  
Molecular Dynamics ◽  
The State ◽  
Computational Experiments ◽  
Continuum Models ◽  
Nonlocal Continuum ◽  
Material Models ◽  
Atom Model ◽  
Embedded Atom ◽  
Dynamics Models

AbstractWe investigate connections between nonlocal continuum models and molecular dynamics. A continuous upscaling of molecular dynamics models of the form of the embedded-atom model is presented, providing means for simulating molecular dynamics systems at greatly reduced cost. Results are presented for structured and structureless material models, supported by computational experiments. The nonlocal continuum models are shown to be instances of the state-based peridynamics theory. Connections relating multibody peridynamic models and upscaled nonlocal continuum models are derived.

Application of nonlocal continuum models to nanotechnology

2003 ◽  
Vol 41 (3-5) ◽  
pp. 305-312 ◽  
Author(s):  
John Peddieson ◽  
George R. Buchanan ◽  
Richard P. McNitt
Keyword(s):  
Continuum Models ◽  
Nonlocal Continuum
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