Useful Conservation Sums in Molecular Dynamics and Atomistics

Configuration forces of an arbitrary molecular dynamics domain are derived in which the energetic characteristics are approximated as those of a non-local gradient elastic field. The configuration forces include not only the effects of the strain gradients but also those of micro-polar energetics. T...

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Bibliographic Details
Published in:Mathematics and mechanics of solids 2010-11, Vol.15 (8), p.885-895
Main Authors: Kim, Saeja O., Earmme, Yoon Y., Kim, Kyung-Suk
Format: Article
Language:English
Subjects:
Approximation
Classical transport
Conservation
Continuums
Dynamical systems
Dynamics
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Homogenizing
Molecular dynamics
Physics
Solid mechanics
Static elasticity (thermoelasticity...)
Statistical physics, thermodynamics, and nonlinear dynamical systems
Structural and continuum mechanics
Sums
Theorems
Transport processes
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Summary:Configuration forces of an arbitrary molecular dynamics domain are derived in which the energetic characteristics are approximated as those of a non-local gradient elastic field. The configuration forces include not only the effects of the strain gradients but also those of micro-polar energetics. The useful sums represent approximate expressions of translational, expansional and rotational configuration forces. Particular homogenization of the field makes the continuum limits of the sums approximately obey configurational transformation symmetries to satisfy Noether’s theorem, and to converge to generalized J integral for static non-local elastic fields of homogeneous media; however, the non-local M and L integrals do not have corresponding conservation laws. Interpolation and projection schemes of a molecular dynamics or atomistics system onto a system of continuum motions and energetics are also derived for elastic as well as non-elastic cases.
ISSN:1081-2865
1741-3028
DOI:10.1177/1081286509357338