Averaging techniques for microstructures with localization bands due to damage progression

PAMM, vol. 22

Abstract

Abstract In multiscale analysis, homogenization methods are needed to up‐scale the micromechanical response obtained from investigating the underlying microstructure to the next higher scale. The standard homogenization schemes are based on volume averaging over the entire microstructure following Hill's approach, which requires that the virtual energies generated on the two involved scales equalize. However, these standard homogenization schemes are not applicable to softening phenomena due to localization, and representativeness of the considered microscale volume is lost. One way to overcome these drawbacks is to perform the volume averaging only within the localizing failure zone. Thereby, representative results can be achieved even in the softening region. In this paper, we apply the failure zone homogenization approach to both, mode I and mode II loading scenarios, as well as mixed‐mode loading of long fiber reinforced plastics. For an accurate description of material failure within the epoxy matrix, a scalar damage model at large strains with gradient enhancement is used, such that the obtained results are mesh‐independent. As a result, we show that for all considered cases representative volume element (RVE) sizes can be determined by using the failure zone homogenization scheme. Nevertheless, the energy distributions of all involved mechanisms have to be considered carefully in order to allow generalizations.

Authors 3

1. Jaan‐Willem Simon corresponding Aachen Institute of Applied Mechanics

   RWTH Aachen University · University of Wuppertal

   Affiliation as printed

   Civil Engineering Mechanics University of Wuppertal Pauluskirchstr. 7 42285 Wuppertal Germany

   Institute of Applied Mechanics RWTH Aachen University Mies-van-der-Rohe-Str. 1 52074 Aachen Germany

   Civil Engineering Mechanics, University of Wuppertal, Pauluskirchstr. 7, 42285 Wuppertal, Germany

   Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany

   Jaan-Willem Simon

2. Lukas Poggenpohl Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Mies-van-der-Rohe-Str. 1 52074 Aachen Germany

   Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany

3. Hagen Holthusen Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Mies-van-der-Rohe-Str. 1 52074 Aachen Germany

   Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany