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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

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

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v3.i2.50
pages 177-197

Thermomechanical Continuum Interpretation of Atomistic Deformation

Min Zhou
Georgia Institute of Technology

ABSTRACT

This paper describes a framework for obtaining thermomechanical continuum interpretations of the results of molecular dynamics calculations. This theory is a further advancement from a pure mechanical equivalent continuum theory developed recently. The analysis is based on the decomposition of atomic particle velocity into a structural deformation part and a thermal oscillation part. On one hand, balance of momentum at the structural level yields fields of stress, body force, traction, mass density, and deformation as they appear to a macroscopic observer. The full dynamic equivalence between the discrete system and continuum system includes (i) preservation of linear and angular momenta; (ii) conservation of internal, external, and inertial work rates; and (iii) conservation of mass. On the other hand, balance of momentum for the thermal motions as it appears to an observer moving at the structural velocity yields the fields of heat flux and temperature. These quantities can be cast in a manner as to conform to the continuum phenomenological equation for heat conduction and generation, yielding scale-sensitive characterizations of specific heat, thermal conductivity, and thermal relaxation time. The coupling between the structural deformation and the thermal conduction processes results from the fact that the equations for structural deformation and for heat conduction are two different forms of the same balance of momentum equation at the fully time-resolved atomic level. This coupling occurs through an inertial force term in each of the two equations, induced by the other process. For the structural deformation equation, the inertial force term induced by thermal oscillations of atoms gives rise to the phenomenological dependence of deformation on temperature. For the heat equation, the inertial force term induced by structural deformation takes the phenomenological form of a heat source.


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