Modeling of structures with polymorphic uncertainties at different length scales

Kremer, Katharina; Edler, Philipp; Miska, Niklas; Leichsenring, Ferenc; Balzani, Daniel; Freitag, Steffen; Graf, Wolfgang; Kaliske, Michael; Meschke, Günther

doi:10.1002/gamm.201900006

Cited by 1 publication

(1 citation statement)

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“…The effective coefficients of the stiffness tensor (if Hooke's law is assumed on both length scales, see [7]) are determined by numerical material testing (see [8]). By introducing the Hill-Mandel condition [9] (in case of small strains) σ σ σ : ε ε ε = σ σ σ : ε ε ε, boundary conditions, such as e.g.…”

Section: Homogenization Approach Incorporating Uncertaintiesmentioning

confidence: 99%

Application of Recurrent Neural Networks in the numerical analysis of reinforced concrete structures considering polymorphic uncertainty

Leichsenring

Fuchs

Graf

et al. 2019

Proc Appl Math and Mech

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The realistic modelling of structures is fundamental for their numerical simulation and is mainly characterized by the physical approach and the consideration of the available data by an adequate uncertainty description. The key idea in the contribution at hand is the consideration of polymorphic uncertainty in the numerical structural analysis and in the mechanical modelling for reinforced concrete structures, which are characterized by a combination of heterogeneous concrete and different types of reinforcement (e.g. steel bars or woven carbon fibres). Typically, the reinforcement is determined by another length scale compared to the overall structural size. The formulation and development of a computational homogenization approach, considering the different homogeneous and heterogeneous characteristics of a macroscopic structure, are essential for a realistic numerical computation. In recent years, focal point of research was on structural analysis considering uncertain material or geometry parameters. Probabilistic approaches are dominating the uncertainty consideration currently, although they are associated with specific disadvantages and limitations. In this contribution, a generalized uncertainty model is utilized in order to take variability, impression as well as inaccuracy, vagueness and incompleteness into account. This allows a separated evaluation of the influence for each uncertainty source on the results. Therefore, polymorphic uncertainty models are applied and developed by combining aleatoric and epistemic uncertainty descriptions, resulting e.g. in the formulation of the uncertainty model "fuzzy probability based randomness". The information of the different length scales is considered to be uncertain, e.g. the geometry or the material properties of a representative volume element (RVE) at the meso scale. Subsequently, the uncertainty of a macro structure is derived from uncertain results on the meso structure. In the contribution, a parametrized RVE for concrete structures, including cement phase as well as aggregates, is presented. Various material parameters are considered as uncertain, which results in uncertain effective quantities. Assuming, that an uncertain quantity is substitutable by a combination of a representative measure and multiple uncertainty characterizing measures, an approximation of both type of quantities by a recurrent neural network is carried out. The surrogate models are utilized as constitutive description in a numerical structural analysis on macro level, providing uncertain structural responses.

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Section: Homogenization Approach Incorporating Uncertaintiesmentioning

confidence: 99%