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International Journal for Multiscale Computational Engineering
Impact-faktor: 1.016 5-jähriger Impact-Faktor: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Druckformat: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v3.i4.10
pages 393-413

Generalized Mathematical Homogenization of Atomistic Media at Finite Temperatures

Jacob Fish
Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, 10025, USA
Wen Chen
Rensselaer Polytechnic Institute, Troy, NY 12180
Yuye Tang
Rensselaer Polytechnic Institute, Troy, NY 12180

ABSTRAKT

In this manuscript, we derive thermomechanical continuum equations directly from molecular dynamics using the generalized mathematical homogenization (GMH) theory. GMH is a space-time multiple-scale asymptotic expansion method, which constructs the coupled atomistic unit-cell problem and the coarse-scale (continuum) problem. The fine-scale problem derived can be interpreted as a molecular dynamics problem on a unit cell, subjected to the coarse-scale fields including macroscopic deformation gradient and temperature. The coarse-scale problem derived is a constitutive law-free continuum thermomechanical equation, which calculates the overall stress and thermal flux vector directly from atomistics. Numerical experiments have been conducted to verify the formulation against the reference molecular dynamics solution. Attention is restricted to one-dimensional problems.


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