International Journal for Multiscale Computational Engineering

ISSN for PRINT: 1543-1649

For Online Access

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2005, Volume3

Issue 4

145 pages

DOI: 10.1615/IntJMultCompEng.v3.i4

Issue price - $178.00

Jacob Fish
Multiscale Science and Engineering Center, Rensselaer Polytechnic Institute, Troy, NY 12189, USA

Wen Chen
Rensselaer Polytechnic Institute, Troy, NY 12180

Yuye Tang
Rensselaer Polytechnic Institute, Troy, NY 12180

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.

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

Article price - $35.00

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