Efficient Multiscale Methods for Viscoelasticity and Fatigue of Short Fiber-Reinforced Polymers

Abstract:

To predict the nonlinear mechanical behavior of components made of short fiber-reinforced plastics (SFRP) under long term and cyclic loading, coupled process and component simulations are required. The injection molding process leads to locally varying fiber orientations within the component. This varying microstructure [1] significantly influences the viscoelastic and fatigue behavior. The interaction between the microstructure [2] and the nonlinear macroscopic properties is resolved by a coupled fast Fourier transformation and finite element two-scale method (FFT-FEM), where the fiber orientation tensor is obtained by analyzing μCT images or by the corresponding process simulation. The aim of this work is to reduce the numerical costs of such a multiscale method. In a first step, the highly efficient micro-scale solver FeelMath [3,4] using an FFT-based preconditioner is presented. Afterwards, a numerical scheme based on a precomputed database trained with FeelMath simulations on the microscale and a model order reduction algorithm, is discussed. The combination of these ideas reduces the numerical effort, such that the method is applicable for industrial problems. Comparative studies of the fully coupled and reduced model document the high accuracy of this approach. The overall performance of this methodology is demonstrated by three-dimensional, industrial applications.

• Periodical: Key Engineering Materials (Volume 809)
• Pages: 473-479
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.809.473
• Online since: June 2019
• Authors: Fabian Welschinger*, Jonathan Köbler, Heiko Andrä, Ralf Müller, Matti Schneider, Sarah Staub
• Keywords: Fatigue, FFT-Based Preconditioner, Fiber Orientation Tensor, Material Database, Model Order Reduction, Multiscale Simulation, Viscoelasticity

References

[1] J. Köbler, M. Schneider, F. Ospald, H. Andrä, R. Müller: Fiber orientation interpolation for the multiscale analysis of short fiber reinforced composite parts. Computational Mechanics 61 (2018): 729–750.

DOI: 10.1007/s00466-017-1478-0

[2] M. Schneider: The sequential addition and migration method to generate representative volume elements for the homogenization of short fiber reinforced plastics. Computational Mechanics 59 (2017): 247–263.

DOI: 10.1007/s00466-016-1350-7

[3] Information on http://www.itwm.fraunhofer.de/feelmath.

[4] Information on http://www.geodict.com.

[5] J. Köbler: Efficient Multiscale Methods for Viscoelasticity and Fatigue of Short Fiber-reinforced Polymers. Doctoral thesis in preparation, Technische Universität Kaiserslautern, Chair of Applied Mechanics, (2019).

[6] Information on http://www.arburg.com.

[7] Information on http://www.bosch-presse.de.

[8] J. Spahn, H. Andrä, M. Kabel, R. Müller: A multiscale approach for modeling progressive damage of composite materials using fast Fourier transforms. Computer Methods in Applied Mechanics and Engineering 268 (2014):871–883.

DOI: 10.1016/j.cma.2013.10.017

[9] R. Schapery: Approximate methods of transform inversion in viscoelastic stress analysis. Proceedings of the 4th US National Congress on Applied Mechanics ASME (1962): 1075–1085.