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FFT-based simulation using a reduced set of frequencies adapted to the underlying microstructure

Gierden Christian, Waimann Johanna, Svendsen Bob, Reese Stefanie

Computer Methods in Materials Science

2021

Vol. 21, No. 1

51--58

Instead of the classical finite element (FE) based microstructure simulation, a Fast Fourier transform (FFT) based microstructure simulation, introduced by Moulinec and Suquet (1994, 1998), also enables the computation of highly resolved microstructural fields. In this context, the microscopic boundary value problem is captured by the Lippmann-Schwinger equation and solved by using Fast Fourier transforms (FFT) and fixed-point iterations. To decrease the computational effort of the fixed-point solver, Kochmann et al. (2019) introduced a model order reduction (MOR) technique based on solving the Lippmann-Schwinger equation in Fourier space with a reduced set of frequencies. Thereby, the accuracy of this MOR technique depends on the number of used frequencies and the choice of frequencies that are considered within the simulation. Instead of the earlier proposed fixed (Kochmann et al., 2019) or geometrically adapted (Gierden et al., 2021b) sampling patterns, we propose a sampling pattern which is updated after each load step based on the current strain. To show the precision of such a strain-based sampling pattern, an elasto-plastic two-phase composite microstructure is investigated.

The simulation of dendritic growth in Ni-Cu alloy using the phase field model

Adrian H., Spiradek-Hahn K.

Archives of Materials Science and Engineering

2009

Vol. 40, nr 2

89-93

Purpose: The aim of this work was to develop a computer program for simulation of dendritic growth in a selected alloy using the phase field model. This model becomes very popular for modelling a variety of technological processes at the mesoscale level. Design/methodology/approach: In the phase field model a new variable, the phase field variable is introduced, which defines the physical state of the system (liquid or solid) at each point and the governing differential equations system. The main advantage of this method is to avoid interphase tracking in contrast to the conventional method with sharp interface. Findings: In this work an algorithm for calculation of the microstructural evolution formed during dendritic solidification is presented by application of a numerical finite difference method for solving partial differential equations. Research limitations/implications: The presented model for dendritic solidification will be extended for modelling of phase transformations in the solid state during technological processes in metallurgy. The calculation still has to be verified using experimental methods of microstructure analysis. Practical implications: The phase field method becomes very popular for modelling of variety of technological processes at the mesoscale. In the actual work the methodology for simulation of microstructural development during solidification is presented.