A class of Finite difference Methods for solving inhomogeneous damped wave equations

Hadadifard, Fazel; Malhi, Satbir; Xiao, Zhengyi

doi:10.48550/arxiv.2008.08043

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2022

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“…The new model outlined in equation ( 21) can be restructured into a 1st order matrix equation. This is done by introducing the vector P = ρ ρ as highlighted by Hadadifard et al in their study of the generic damped wave equation [67]. Namely,…”

Section: General Formmentioning

confidence: 99%

Time-scale investigation with the modified phase field crystal method

Burns

Provatas

Grant

2022

Modelling Simul. Mater. Sci. Eng.

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This paper extends the two time-scale modified phase-field crystal model to examine crystal plasticity. Two non-linear density dependent functions are constructed to effectively represent hydrostatic strain and dislocation density. The functions are then used to develop a new modified phase field crystal model, which accounts for strain and strain-rate couplings to the density dynamics. The non-linear additions provide tunable parameters for controlling dislocation climb versus glide, as well as phonon softening mechanisms. A short-wavelength dampening is also introduced as arising from phonon scattering and thermoelastic dissipation. Finally, a novel semi-implicit numeric scheme for efficient simulations of this model is presented, which also serves as a generalization of the commonly used Fourier pseudo-spectral method. The technique gives rise to unconditionally stable dynamics with simple numeric implementation requirements.

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Section: General Formmentioning

confidence: 99%