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In various engineering applications, components subjected to high mechanical or multi‐physical loads such as thermal, thermo‐mechanical, or electro‐thermal loads are predominantly made of metals or composites. These materials are characterized by polycrystalline or multi‐phase microstructures which determine the overall material response. However, since the microscopic material behavior is directly...
In general, the overall macroscopic material behavior of any structural component is directly dependent on its underlying microstructure. For metal components, the associated microstructure is given in terms of a polycrystal. To enable the simulation of the related microstructural and overall elasto‐viscoplastic material behavior, a two‐scale simulation approach can be used. In this context, we use...
The mechanical behavior of a periodic heterogeneous microstructure may be predicted by using a fast Fourier transform (FFT) based simulation approach. To reduce the computational effort of this method, we introduced a model order reduction (MOR) technique utilizing a reduced set of Fourier modes for the computations in Fourier space. To increase the accuracy of this MOR technique we developed a geometrically...
Due to the general pursuit of technological advancement, structural components need to meet increasingly higher standards. In order to optimize the performance behavior of the used materials, detailed knowledge of the overall as well as microscopic material behavior under certain mechanical and thermal loading conditions is required. Hence, we present a two‐scale finite element (FE) and fast Fourier...
To capture the material behavior of composite microstructures, Moulinec and Suquet [5] proposed a homogenization scheme making use of fast Fourier transforms (FFT) and fixed‐point iterations. To reduce the computational effort of this spectral method, Kochmann et al. [3] introduced a model order reduction technique, which is based on using a fixed reduced set of frequencies for the computations in...
The FFT‐based method introduced by Moulinec and Suquet [9] serves as an alternative for the classical finite element based simulation of periodic microstructures. This simulation approach makes use of fast Fourier transforms (FFT) as well as fixed‐point iterations to solve the microscopic boundary value problem which is captured by the Lippmann‐Schwinger equation. Kochmann et al. [5] introduced a...
To capture all the individual microstructural effects of complex and heterogeneous materials in structural finite element simulations, a two‐scale simulation approach is necessary. Since the computational effort of such two‐scale simulations is extremely high, different methods exist to overcome this problem. In terms of a FFT‐based microscale simulation, one possibility is to use a reduced set of...
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...
Heterogeneous materials are important for a vast amount of applications e.g. in automotive industry or in aerospace. For instance when producing components, it can be desired to use materials with a heterogeneous microstructure in order to achieve specific material properties. Thus, it is beneficial to take the materials' microscopic structure into account and couple its behavior to the macroscopic...
We present a model order reduction (MOR) method for finite strain FFT solvers to reduce the computational costs of the FFT simulation scheme of a two‐scale FE‐FFT simulation. The underlying method is based on a reduced set of frequencies which leads to a reduced fixed‐point scheme. The reduced set of frequencies is determined offline, based on the Fourier grid and predominantly consists of low frequencies...
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