Modelling of polymorphic uncertainty in the mesoscopic scale of reinforced concrete structures

Abstract

The realistic modelling of structures is essential for their numerical simulations and is mainly characterized by the mechanical model and the consideration of the available data at hand by an adequate uncertainty model. The key idea in this contribution is the consideration of polymorphic uncertainty at the numerical structural analysis and 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 carbon fibres mats). Typically, the reinforcement is denoted by another length scale, compared to the overall structure size. The formulation and development of a computational homogenization approach, considering the different homogeneous and heterogeneous characteristics of a macroscopic structure, is essential for a precise 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 connected with certain disadvantages and limits. In this contribution, a generalized uncertainty model is utilized in order to take variability, impression and incompleteness in to account. That allows a separated evaluation of the influence for each uncertainty source on the results. Therefore, polymorphic uncertainty models are applied and developed by combining and extending aleatoric and epistemic uncertainty, resulting e.g. in the formulation of the uncertainty model fuzzy p-box or 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 mesoscale. Subsequently, the uncertainty of the behaviour of a macro structure is derived from uncertain results on the meso structure. Since the computational effort of such investigations is tremendous, highly developed meta-models (recurrent neural networks) are applied in order to replace the uncertain RVE responses.