Modelling damage in composites using shell-based computational homogenisation and immersogeometric analysis

  • Börjesson, Elias (Chalmers University of Technology)
  • Verhoosel, Clemens (TU Eindhoven)
  • Remmers, Joris (TU Eindhoven)
  • Larsson, Fredrik (Chalmers University of Technology)
  • Fagerström, Martin (Chalmers University of Technology)

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Advanced fibre composites are often designed with complex sub-scale features. While having a complex sub-structure often increases the performance and functionality of the composite, the analysis and design process of structures made from these materials becomes more challenging. For example, failure initiation and progression are often directly linked to these subscale features (which could also be defects), something that a traditional macro-level modelling approach cannot easily capture. This in turn means that important design information is lost. To achieve the desired level of accuracy in the simulation models for these advanced composite materials, relevant influence from the sub-structure must therefore be included. One way of achieving this is to make use of multi-scale modelling approaches, e.g. computational homogenisation and coupled finite element models on (at least) two geometrical scales (often denoted FE2). As such, macro-scale deformations are prolonged (down-scaled) as boundary conditions to the sub-scale Statistical Volume Element (SVE) analysis, whereafter possible non-linear damage and geometrical effects of the sub-structure are homogenised (up-scaled) the macro-model via computational homogenisation. In this contribution, we present a plate-based Variationally Consistent Homogenisation (VCH) [1] framework to analyse initiation (and initial progression) of damage in heterogeneous materials, where the macro-scale is discretised with Reissner-Mindlin type plate elements [1]. Thereby, the framework is a step towards facilitating easier and more efficient use of multi-scale methods in industry, as opposed to standard homogenisation techniques developed for continuum representations on both scales. More specifically, we have utilised the VCH framework to analyse the sequence of mechanisms leading up to localised failure, and how these vary with sub-scale architecture (e.g. ply thickness and ply architecture) for various types of fibre-reinforced polymers. A particular challenge in this respect is the generation of discretised SVE models, as the geometrical features at this lower scale can be rather complex. For this purpose, we have adopted an immersogeometric analysis [2] approach, which is a flexible way to incorporate geometrical sub-scale features without the need of conformal meshing. Long-term, we envision that the proposed method can aid the development of more performant composite shell structures.