Granular computational homogenisation of composite structures with imprecise parameters

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Authors

  • W. Beluch Silesian University of Technology, Department of Computational Mechanics and Engineering, Poland
  • M. Hatłas Silesian University of Technology, Poland
  • J. Ptaszny Silesian University of Technology, Department of Computational Mechanics and Engineering, Poland

Abstract

The paper presents the formulation of a granular computational homogenisation problem and the proposition of a method to solve it, which enables multiscale analysis of materials with uncertain microstructure parameters. The material parameters and the geometry, represented by the interval and fuzzy numbers, are assumed to be unprecise. An α-cut representation of fuzzy numbers allows the use of interval arithmetic for epistemic uncertainties. Directed interval arithmetic is used to reduce the effect of interval widening during arithmetic operations. Response surfaces of diverse types, including Artificial Neural Networks, are used as model reduction methods. The finite element method is employed to solve the boundary value problem on a micro scale. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.

Keywords:

computational homogenisation, granular computations, fuzzy numbers, directed interval arithmetic, response surfaces, finite element method