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An adaptive \(\hbox {FE}^2\) approach for fiber–matrix composites

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Abstract

The contribution is concerned with an adaptive scheme for the finite-element square (\(\hbox {FE}^2\)) method. The \(\hbox {FE}^2\) method allows a continuous homogenization considering the current deformation state of the heterogeneous material structure. The micro-structure is represented by a representative volume element, which differs in the fiber distribution. The fiber material behavior is assumed as elasto-plastic. The non-linear response of the fiber necessitates a numerical homogenization for every load step at each integration point, which leads to an increased computational effort. An indicator for a nested \(\hbox {FE}^2\) homogenization is introduced. It takes advantage of the fact that a accompanying homogenization is only necessary in the regions of non-linear material behavior. The present work deals with an adaptive scheme for fiber–matrix composites to reduce the computational cost. Numerical examples show the capability of the proposed scheme.

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Acknowledgements

We thank the German Research Foundation (DFG) for financial support under Grant Number KL 1345/9-1

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  1. Lehrstuhl für Baustatik und Baudynamik, RWTH Aachen, University, Mies-van-der-Rohe-Str. 1, 52074, Aachen, Germany

    Maximilian Praster, Markus Klassen & Sven Klinkel

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  1. Maximilian Praster
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  2. Markus Klassen
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  3. Sven Klinkel
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Correspondence to Maximilian Praster.

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Praster, M., Klassen, M. & Klinkel, S. An adaptive \(\hbox {FE}^2\) approach for fiber–matrix composites. Comput Mech 63, 1333–1350 (2019). https://doi.org/10.1007/s00466-018-1652-z

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