A new finite element strategy to simulate microstructural evolutions

Abstract

The Level-set (LS) method has been shown to be a powerful approach to model dynamic interfaces in the context of large deformations. The LS method has been applied to the simulation of microstructural evolutions as Grain Growth (GG) and Recrystallization (ReX) at the mesoscale Maire et al. (2017). Interfaces between grains are implicitly described in an Eulerian framework, as the zero-isovalue of the LS fields and their evolution is governed by convective-diffusive partial differential equations (PDEs). The LS approach circumvents the notoriously difficult problem of generating interface-conforming meshes for geometries subjected to large displacements and to changes in the topology of the domains.Generally, in order to maintain high accuracy when using the LS method, moving interfaces are generally captured by a locally refined FE mesh with the help of mesh adaptation techniques. In a microstructural problem, the large number of interfaces and the fine mesh required in their vicinity make the mesh adaptation process very costly in terms of CPU-time, particularly in 3D Scholtes (2016).In this work, a different adaptation strategy is used. It maintains the benefits of the classical Eulerian LS framework, while enforcing at all times the conformity of the FE mesh to implicit interfaces by means of local remeshing operations, special treatments for vacuum regions have been adopted and will be presented within the generalization of a previous adaptation algorithm presented in Shakoor et al. (2015). Source of errors will be presented and compared for different test cases. Finally, we will illustrate how the new method decreases the requirement in mesh density while maintaining the accuracy at the interfaces, hence reducing the computational cost of the simulations.