Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals.

By K. Elder, Martin Grant. Physical review. E, Statistical, nonlinear, and soft matter physics, 2003

666 citations recorded by the source corpus.

A continuum field theory approach is presented for modeling elastic and plastic deformation, free surfaces, and multiple crystal orientations in nonequilibrium processing phenomena. Many basic properties of the model are calculated analytically, and numerical simulations are presented for a number of important applications including, epitaxial growth, material hardness, grain growth, reconstructive phase transitions, and crack propagation.

Subfields: Aerospace Engineering, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/e8f63a68c8915028ad747edf798bf6f79926318e

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Citations in the corpus

A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows (2017, neutral): “Examples of these problems include interface dynamics [4, 38, 42, 48, 49, 72], crystallization [24, 23, 25], thin films [34, 53], polymers [52, 30, 31, 32] and liquid crystals [45, 20, 43, 44, 29, 28, 55, 71].”
The phase field technique for modeling multiphase materials (2008, methodology): “While a direct simulation is possible and was used in [249], the allowed time steps are rather small.”
Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation (2009, methodology): “[3,4] solved the PFC equation using an explicit Euler scheme, where a high-order time step restriction ðs < Ch(6)Þ is required”
An unconditionally energy-stable method for the phase field crystal equation (2012, methodology): “The phase field crystal equation describes the microstructure of solid–liquid systems at interatomic length scales, and at a diffusive time scale [17,18].”
Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview (2012, methodology): “Already the first paper on the PFC method [12, 50] has addressed grain boundaries and shown that the model automatically recovers the Read-Shockley relationship between grain-boundary energy and misorientation (see figure 34).”
Classical dynamical density functional theory: from fundamentals to applications (2020, methodology): “On the other hand, DDFT has influenced the development of other theories such as phase field crystal (PFC) models [44,135,136,629,630].”
Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows (2018, background): “The SAV approach is proposed for a large class of gradient flows that describe energy dissipative physical systems [1, 4, 8, 14, 6, 3].”