Polymorphic Uncertain Structural Analysis: Challenges in Data‐Driven Inelasticity

Abstract

AbstractThis contribution addresses polymorphic uncertainty quantification within structural analysis of reinforced concrete structures composed of heterogeneous concrete and reinforcement (e.g. steel bars or carbon fibres). The macroscopic material behaviour of concrete is strongly dependent on the mesoscopic heterogeneities, which are considered by multiscale modelling. The heterogeneous mesoscopic material behaviour is characterized by representative volume elements (RVE) and the transition of scales is carried out by utilizing numerical homogenization methods.The concept of data‐driven computational mechanics enables material model free finite element analyses directly based on material data sets, overcoming the necessity of assumptions in material modelling. This approach mainly consists in assigning a stress‐strain state, which leads to a minimum of an objective function and fulfils equilibrium as well as compatibility constraints of every integration point. Inelastic material behaviour is taken into account through the definition of local data sets containing only data set states which are consistent with respect to the past local history . The realistic modelling of structures requires the consideration of data uncertainty. Generalized polymorphic uncertainty models are utilized in order to take variability, imprecision, inaccuracy and incompleteness of material data into account by combining aleatoric and epistemic uncertainty models.In this contribution, a computationally efficient approach for the consideration of data sets containing uncertain stress‐strain states within data‐driven analysis based on information reduction measurements is presented. Due to generalization, the approach is applicable to various aleatoric, epistemic and polymorphic uncertainty models. The identification of admissible local data sets for taking inelastic material behaviour into account within data‐driven analysis is realized by an energy based history parametrization which is extended to uncertain data. An approach for the efficient selection of these local data sets is presented and challenges in data‐driven inelasticity, particularly in the use case of polymorphic uncertain analyses of concrete structures, are pointed out.