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In this work, a field representation of the conservation law of linear momentum is derived from the atomistic, using the theory of distributions as the mathematical tool, and expressed in terms of temperature field by defining temperature as a derived quantity as that in molecular kinetic theory and atomistic simulations. The formulation leads to a unified atomistic and continuum description of temperature and a new linear momentum equation that, supplemented by an interatomic potential, completely governs thermal and mechanical processes across scales from the atomic to the continuum. The conservation equation can be used to solve atomistic trajectories for systems at finite temperatures, as well as the evolution of field quantities in space and time, with atomic or multiscale resolution. Four sets of numerical examples are presented to demonstrate the efficacy of the formulation in capturing the effect of temperature and thermal fluctuations, including phonon density of states, thermally activated dislocation motion, dislocation formation during epitaxial processes, and attenuation of longitudinal acoustic waves as a result of their interaction with thermal phonons.
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This content will become publicly available on November 4, 2025
Bridging length and time scales in predictive simulations of thermo-mechanical processes
Abstract This work introduces a theoretical formulation and develops numerical methods for finite element implementation of the formulation so as to extend the concurrent atomistic-continuum (CAC) method for modeling and simulation of finite-temperature materials processes. With significantly reduced degrees of freedom, the CAC simulations are shown to reproduce the results of atomically resolved molecular dynamics simulations for phonon density of states, velocity distributions, equilibrium temperature field of the underlying atomistic model, and also the density, type, and structure of dislocations formed during the kinetic processes of heteroepitaxy. This work also demonstrates the need of a mesoscale tool for simulations of heteroepitaxy, as well as the unique advantage of the CAC method in simulation of the defect formation processes during heteroepitaxy.
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- PAR ID:
- 10573835
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Modelling and Simulation in Materials Science and Engineering
- Volume:
- 32
- Issue:
- 8
- ISSN:
- 0965-0393
- Page Range / eLocation ID:
- 085015
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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