WIAS Preprint No. 2928, (2022)

Local surrogate responses in the Schwarz alternating method for elastic problems on random voided domains


  • Drieschner, Martin
  • Gruhlke, Robert
  • Petryna, Yuri
  • Eigel, Martin
  • Hömberg, Dietmar

2020 Mathematics Subject Classification

  • 35R60 65N12 65N22 65J10 97N50


  • Domain decomposition, Schwarz alternating method, random domain, artificial neural network (ANN), linear elasticity, stress concentrations, experimental validation




Imperfections and inaccuracies in real technical products often influence the mechanical behavior and the overall structural reliability. The prediction of real stress states and possibly resulting failure mechanisms is essential and a real challenge, e.g. in the design process. In this contribution, imperfections in elastic materials such as air voids in adhesive bonds between fiber-reinforced composites are investigated. They are modeled as arbitrarily shaped and positioned. The focus is on local displacement values as well as on associated stress concentrations caused by the imperfections. For this purpose, the resulting complex random one-scale finite element model is numerically solved by a new developed surrogate model using an overlapping domain decomposition scheme based on Schwarz alternating method. Here, the actual response of local subproblems associated with isolated material imperfections is determined by a single appropriate surrogate model, that allows for an accelerated propagation of randomness. The efficiency of the method is demonstrated for imperfections with elliptical and ellipsoidal shape in 2D and 3D and extended to arbitrarily shaped voids. For the latter one, a local surrogate model based on artificial neural networks (ANN) is constructed. Finally, a comparison to experimental results validates the numerical predictions for a real engineering problem.

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