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Nonlinear reduced order homogenization of materials including cohesive interfaces

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Abstract

The mechanical response of composite materials is strongly influenced by the nonlinear behavior of the interface between the constituents. In order to make reliable yet computationally efficient predictions for such materials, a reduced order model is developed. Conceptual ideas of the NTFA (Michel and Suquet, Int J Solids Struct 40:6937–6955, 2003, Comput Methods Appl Mech Eng 193:5477–5502, 2004) and of the pRBMOR (Fritzen, Hodapp and Leuschner Comput Methods Appl Mech Eng 260:143–154, 2013, Fritzen et al., Comput Methods Appl Mech Eng 278:186–217, 2014) are adopted. The key idea is to parameterize the displacement jumps on the cohesive interfaces by a reduced basis of global ansatz functions. Micromechanical considerations and the potential structure of the constitutive models lead to a variational formulation and reduced equilibrium conditions. The effect of the preanalysis phase on the accuracy is investigated using geometrically optimal training directions. The reduced model is tested for three-dimensional microstructures. Besides the effective stress response, the tension–compression asymmetry and the distribution of the separation of the interface are investigated. Memory savings on the order of \(10^5\) are realized. The computing time is reduced considerably.

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Notes

  1. Except for two cases: (a) the minor increase of the max. error in Fig. 10, bottom left for \(N_\mathrm{dir}=64\) and \(N_\zeta \) around 48; (b) the better accuracy for \(N_\mathrm{dir}=64\) over \(128\) for \(N_\zeta =20\).

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Acknowledgments

The authors acknowledge the financial support of the German research foundation (DFG), grant numbers FR-2702/3, FR-2702/4, FR-2702/7 and within the Emmy Noether program of DFG via grant DFG-FR2702/6. The valuable input in the context of the CoSiMOR scientific network (funded by DFG grants FR-2702/4 and FR-2702/7) and, in particular, the discussions with Bernard Haasdonk regarding kernel methods are acknowledged. Additionally, funding of this work within the KIT YIG Computer Aided Material Modeling via the Karlsruhe Institute of Technology (KIT) in the context of the Excellence Initiative of the German Research Foundation (DFG) is highly acknowledged.

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  1. Emmy Noether Group EMMA – Efficient Methods for Mechanical Analysis, Chair of Continuum Mechanics, Institute of Applied Mechanics (CE), University of Stuttgart, Pfaffenwaldring 7, 70569, Stuttgart, Germany

    Felix Fritzen & Matthias Leuschner

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  1. Felix Fritzen
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Correspondence to Felix Fritzen.

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Fritzen, F., Leuschner, M. Nonlinear reduced order homogenization of materials including cohesive interfaces. Comput Mech 56, 131–151 (2015). https://doi.org/10.1007/s00466-015-1163-0

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