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Granular computational homogenisation of composite structures with imprecise parameters
Arch. Mech. 75 (3), 271-300, 2023, DOI: 10.24423/aom.4186
Keywords: computational homogenisation; granular computations; fuzzy numbers; directed interval arithmetic; response surfaces; finite element method
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.