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A phase-field formulation is introduced to simulate quantitatively microstructural pattern formation in alloys. The thin-interface limit of this formulation yields a much less stringent restriction on the choice of interface thickness than…

Materials Science · Physics 2016-08-31 Alain Karma

Understanding the microstuctural evolution during the sintering process is of high relevance as it is a key part in many industrial manufacturing processes. Simulations are one avenue to achieve this understanding, especially field-resolved…

Materials Science · Physics 2023-05-17 Marco Seiz , Henrik Hierl , Britta Nestler

A broad range of computational models have been proposed to predict microstructure development during solidification processing but they have seldom been compared to each other on a quantitative and systematic basis. In this paper, we…

Materials Science · Physics 2022-11-08 S. M. Elahi , R. Tavakoli , I. Romero , D. Tourret

A continuum field theory approach is presented for modeling elastic and plastic deformation, free surfaces and multiple crystal orientations in non-equilibrium processing phenomena. Many basic properties of the model are calculated…

Soft Condensed Matter · Physics 2009-11-10 K. R. Elder , Martin Grant

The finite solid-liquid interface width in phase field models results in non-equilibrium effects, including solute trapping. Prior phase field modeling has shown that this extra degree of freedom, when compared to sharp-interface models,…

Materials Science · Physics 2023-04-07 Arnab Mukherjee , James A. Warren , Peter W. Voorhees

A symmetric phase field model is used to study wavelength selection in two dimensions. We study the problem in a finite system using a two-pronged approach. First we construct an action and, minimizing this, we obtain the most probable…

Statistical Mechanics · Physics 2009-11-11 R. N. Costa Filho , J. M. Kosterlitz , Enzo Granato

We propose and analyse new stabilized time marching schemes for Phase Fields model such as Allen-Cahn and Cahn-Hillard equations, when discretized in space with high order finite differences compact schemes. The stabilization applies to…

Numerical Analysis · Mathematics 2019-10-01 Matthieu Brachet , Jean-Paul Chehab

Interface energy and kinetic coefficient of crystal growth strongly depend on the face of the crystalline lattice. To investigate the kinetic anisotropy and velocity of different crystallographic faces we use the hyperbolic (modified) phase…

Materials Science · Physics 2020-04-03 Vladimir Ankudinov , Peter K. Galenko

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;…

Materials Science · Physics 2014-12-31 Vaibhav Agrawal , Kaushik Dayal

Phase field modelling offers an extremely general framework to predict microstructural evolutions in complex systems. However, its computational implementation requires a discretisation scheme with a grid spacing small enough to preserve…

Computational Physics · Physics 2018-07-18 Alphonse Finel , Yann Le Bouar , Benoît Dabas , Benoît Appolaire

Computing stationary states is an important topic for phase field crystal (PFC) models. Great efforts have been made for energy dissipation of the numerical schemes when using gradient flows. However, it is always time-consuming due to the…

Numerical Analysis · Mathematics 2019-09-04 Kai Jiang , Wei Si , Chenglong Bao

In a recent class of phase field crystal (PFC) models, the density order parameter is coupled to powers of its mean field. This effectively introduces a phenomenology of higher-order direct correlation functions acting on long wavelengths,…

Materials Science · Physics 2024-08-21 Daniel L. Coelho , Duncan Burns , Emily Wilson , Nikolas Provatas

The phase field crystal (PFC) method has emerged as a promising technique for modeling materials with atomistic resolution on mesoscopic time scales. The approach is numerically much more efficient than classical density functional theory…

Materials Science · Physics 2015-05-18 Michael Greenwood , Nikolas Provatas , Jörg Rottler

A phase field theory of polycrystalline solidification is presented that is able to describe the nucleation and growth of anisotropic particles with different crystallographic orientation in three dimensions. As opposed with the…

Materials Science · Physics 2009-11-11 T. Pusztai , G. Bortel , L. Granasy

This work deals with the one-dimensional Stefan problem with a general time-dependent boundary condition at the fixed boundary. Stochastic solutions are obtained using discrete random walks, and the results are compared with analytic…

Analysis of PDEs · Mathematics 2023-02-06 M. Ogren

In mesoscopic scale microstructure evolution modeling, two primary numerical frameworks are used: Front-Capturing (FC) and Front-Tracking (FT) ones. FC models, like phase-field or level-set methods, indirectly define interfaces by tracking…

Materials Science · Physics 2025-10-28 Marc Bernacki

Highly anisotropic interfaces play an important role in the development of material microstructure. Using the diffusive atomistic phase-field crystal (PFC) formalism, we determine the capability of the model to quantitatively describe these…

Materials Science · Physics 2018-08-29 Nana Ofori-Opoku , James A. Warren , Peter W. Voorhees

Even though our theoretical understanding of dendritic solidification is relatively well developed, our current ability to model this process quantitatively remains extremely limited. This is due to the fact that the morphological…

Materials Science · Physics 2007-05-23 Jean Bragard , Alain Karma , Youngyih H. Lee , Mathis Plapp

In this work, we consider pressurized phase-field fracture problems in nearly and fully incompressible materials. To this end, a mixed form for the solid equations is proposed. To enhance the accuracy of the spatial discretization, a…

Numerical Analysis · Mathematics 2022-09-21 Seshadri Basava , Katrin Mang , Mirjam Walloth , Thomas Wick , Winnifried Wollner

Phase transition problems on curved surfaces can lead to a panopticon of fascinating patterns. In this paper we consider finite element approximations of phase field models with a spatially inhomogeneous and anisotropic surface energy…

Numerical Analysis · Mathematics 2025-06-09 Harald Garcke , Robert Nürnberg