2014/12/29 by Vaibhav Agrawal, Kaushik Dayal, Agrawal, Vaibhav +1
Computer Science · Engineering · Materials Science · #Advanced Mathematical Modeling in Engineering #Aluminum Alloy Microstructure Properties #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Solidification and crystal growth phenomena
paper · pdf · doi:10.48550/arxiv.1412.8491
openalex publication_date 2014/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The motion of microstructural interfaces is important in modeling materials that undergo twinning and structural phase transformations. Continuum models fall into two classes: sharp-interface models, where interfaces are singular surfaces; and regularized-interface models, such as phase-field models, where interfaces are smeared out. The former are challenging for numerical solutions because the interfaces need to be explicitly tracked, but have the advantage that the kinetics of existing interfaces and the nucleation of new interfaces can be transparently and precisely prescribed. In contrast, phase-field models do not require explicit tracking of interfaces, thereby enabling relatively simple numerical calculations, but the specification of kinetics and nucleation is both restrictive and extremely opaque. This prevents straightforward calibration of phase-field models to experiment and/or molecular simulations, and breaks the multiscale hierarchy of passing information from atomic to continuum. We present the formulation of a phase-field model -- i.e., a model with regularized interfaces that do not require explicit numerical tracking -- that allows for easy and transparent prescription of complex interface kinetics and nucleation. The key ingredients are a re-parametrization of the energy density to clearly separate nucleation from kinetics; and an evolution law that comes from a conservation statement for interfaces. This enables clear prescription of nucleation through the source term of the conservation law and of kinetics through an interfacial velocity field. A formal limit of the kinetic driving force recovers the classical continuum sharp-interface driving force, providing confidence in both the re-parametrized energy and the evolution statement. We present a number of numerical calculations in one and two dimensions to characterize and demonstrate the formulation.