Abstract
Macroscale continuum mechanics simulations rely on material properties stemming from the microscale, which are normally described using phenomenological equations of state (EOS). A method is proposed for the automatic generation of first-principles unconstrained EOSs using a Gaussian process on a set of ab initio molecular dynamics simulations, thereby closing the continuum equations. We illustrate it on a hyperelasticity simulation of bulk silicon using density-functional theory (DFT), following the dynamics of shock waves after a cylindrical region is instantaneously heated.
Highlights
Continuum mechanics simulations are of great importance for the simulation of macroscopic condensed matter, from flows in the oil and gas industry [1,2] or the modeling of high strain-rate structural deformation [3], to shock waves and detonation in condensed-phase media [4,5,6]
Validation of the multiscale method proposed here is provided by the comparison shown in Fig. 4 for properties of silicon shocked with a flat two-dimensional perturbation, giving rise to a flat shock wave propagating in one dimension, following Hugoniot relations
A two-scale method has been demonstrated for the generation of equations of state (EOS) for macroscopic continuum simulations of condensed matter based on first-principles molecular dynamics
Summary
Continuum mechanics simulations are of great importance for the simulation of macroscopic condensed matter, from flows in the oil and gas industry [1,2] or the modeling of high strain-rate structural deformation [3], to shock waves and detonation in condensed-phase media [4,5,6]. The phenomena these simulations describe have their origin in the interactions and dynamics of electrons and nuclei at a much smaller scale. Temperature adds an extra dimension to the effective parameter space, totalling seven in the case of a general, anisotropic solid
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