Vertex and front-tracking methods for the modeling of microstructure evolution at the solid state: a brief review

TL;DR

This review compares front-capturing and front-tracking methods, especially vertex models, for simulating microstructure evolution at the mesoscopic scale, emphasizing recent advances and challenges in 2D and 3D modeling.

Contribution

It provides a concise overview of vertex and front-tracking methods, highlighting recent developments, advantages, and challenges in modeling microstructure evolution.

Findings

Vertex models describe polygonal structure evolution via boundary point motion.

FT approaches improve spatial resolution in 2D and 3D problems.

Recent advances enhance computational efficiency and analysis capabilities.

Abstract

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 field variable changes. On the contrary, FT models explicitly define interfaces using interconnected segments or surfaces. In historical FT methodologies, Vertex models were first developed and consider the description of the evolution of polygonal structures in terms of the motion of points where multiple boundaries meet. Globally, FT-type approaches, often associated with Lagrangian movement, enhance spatial resolution in 3D surfacic and 2D lineic problems using techniques derived from finite element meshing and remeshing algorithms. These efficient approaches, by nature, are well adapted to physical mechanisms correlated to interface properties and geometries. They also face challenges in managing complex topological events, especially in 3D. However, recent advances highlight their potential in computational efficiency and analysis of mobility and energy properties, with possible applications in intragranular phenomena.