A concept for data-driven computational mechanics in the presence of polymorphic uncertain properties

• Published in: Engineering structures 2022-09, Vol.267, p.114672, Article 114672
• Main Authors: Zschocke, Selina, Leichsenring, Ferenc, Graf, Wolfgang, Kaliske, Michael
• Format: Article
• Language: English
• Subjects: Composite materials; Computational mechanics; Computer applications; Data-driven computational mechanics; Datasets; Homogenization; Mathematical models; Mechanical properties; Mesoscale phenomena; Nearest neighbor search; Numerical homogenization; Numerical methods; Parameter uncertainty; Polymorphic uncertainty; Reinforced concrete; Strain; Structural analysis
• ISSN: 0141-0296; 1873-7323
• DOI: 10.1016/j.engstruct.2022.114672

The proposed concept of data-driven computational mechanics, introduced in [1], enables to bypass the material modeling step within structural analyses entirely by carrying out calculations directly based on experimentally obtained stress–strain data. The material behavior of composite materials (e.g. concrete, reinforced concrete) is strongly dependent on heterogeneities. Based on numerical homogenization methods, which are premised on the concept of scale separation, the mechanical behavior of the heterogeneous mesoscale is considered within the structural analysis of the homogeneous macroscopic continuum. Uncertainties within mesoscale material parameters cause uncertain macroscopic behavior. Aleatoric and epistemic uncertainty are distinguished, combined consideration is realized through polymorphic uncertainty models. In this contribution, a decoupled numerical homogenization scheme with the purpose of taking polymorphic mesoscale uncertainties into account utilizing the method of data-driven computing is introduced. In contrast to existing methods, material uncertainties are considered within one data set containing uncertain stress–strain states instead of multiple data sets. This enables uncertainty assessment by executing the macroscopic structural analysis only once, which leads to efficiency improvements by orders of magnitude and the opportunity to account for polymorphic uncertainties by taking advantage of the data-driven concept. The proposed methodologies are demonstrated by means of structural examples and the advantages compared to existing methods are pointed out. •Material model free structural analyses by Data-Driven solver.•Quantification of methodologically introduced and intrinsic material uncertainties.•Consideration of free- and parametric p-box valued stress–strain relations.•Development of a Data-Driven numerical homogenization algorithm.•Application to two representative structural examples.