Modeling of structures with polymorphic uncertainties at different length scales

• Published in: Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik 2019-03, Vol.42 (1), p.n/a
• Main Authors: Kremer, Katharina, Edler, Philipp, Miska, Niklas, Leichsenring, Ferenc, Balzani, Daniel, Freitag, Steffen, Graf, Wolfgang, Kaliske, Michael, Meschke, Günther
• Format: Article
• Language: English
• Subjects: Aggregates; Coefficient of friction; Concrete; Concrete structures; dual‐phase steel; Durability; Mathematical models; Metal forming; Metal sheets; Modelling; Modulus of elasticity; Mortars (material); Multiscale analysis; Parameter uncertainty; polymorphic uncertainty; Reinforced concrete; Reinforcing steels; Stress concentration
• ISSN: 0936-7195; 1522-2608
• DOI: 10.1002/gamm.201900006

Multiscale analyses require to consider the scale bridging influences of uncertain parameters. In this paper, approaches for polymorphic uncertainty quantification at different length scales are presented. Especially, the effect of uncertain material parameters computed at lower structural scales is investigated with respect to the resulting macroscopic structural behavior. Also the dependencies of uncertain parameters at the macroscale on the structural response evaluated with submodels are discussed. Three examples are shown, where interval and stochastic uncertainty quantification approaches are combined. Two examples deal with material modeling of concrete and the durability of reinforced concrete structures under consideration of polymorphic uncertainties. A mesoscale model of concrete is developed based on a representative volume element containing aggregates, pores, and the cement phase, where the values of the Young's moduli for mortar and the aggregates as well as the volume fraction of the cement phase to aggregates are considered as intervals. Within the durability assessment of reinforced concrete structures, the influence of stochastic distributed loading and concrete material parameters onto the cracking behavior is analyzed by means of a submodeling strategy. In another application, the metal forming process of dual‐phase steel sheets is investigated using statistical information of the microscopic material behavior in combination with epistemic uncertainties of the failure criterion and the friction coefficient between the sheet metal and the forming tools.