A parallel algorithm for the concurrent atomistic-continuum methodology

Díaz, Adrián; Gu, Boyang; Li, Yang; Plimpton, Steven J.; Chen, Youping

doi:10.1016/j.jcp.2022.111140

Cited by 8 publications

(1 citation statement)

References 72 publications

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“…To extend the CAC method for finite temperature processes, equation (5.12) has been tested though implementation in the CAC codes using a modified finite-element method with tri-linear shape functions [53–55]. To test the formulation and numerical implementations, we build four sets of computer models that are discretized with 8-node rhombohedral elements, with each element containing 8×8×8 primitive unit cells and the surfaces of the elements corresponding to the slip and/or the cleavage planes of the crystals.…”

Section: Numerical Examplesmentioning

confidence: 99%

Unifying temperature definition in atomistic and field representations of conservation laws

Chen

2024

Proc. R. Soc. A.

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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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