Combining Finite Elements and Random Fields to Quantify Uncertainty in a Multi‐phase Structural Analysis. Issue 1 (17th December 2018)

• Record Type: Journal Article
• Authors: Henning, Carla; Herbrandt, Swetlana; Ickstadt, Katja; Ricken, Tim
• Other Names: Müller G. guestEditor.; Ulbrich M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 18:Issue 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-12-17
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201800333
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: For a wide range of mechanical application fields, computational analyses are already indispensable due to their advanced impact on engineering developments. They provide a lot of information about the functioning and structural response of an arbitrary structure and the interaction with its surrounding. Nevertheless, despite preliminary investigations or the knowledge about manufacturing process of structures, assumptions of geometrical or material properties are often sources of uncertainties. These can be distinguished into aleatoric (e.g. natural scattering of properties) and epistemic (e.g. accuracy of the numerical approximation) uncertainties. Although measuring devices or process workflows are continuously improved, there always remains a residual risk. In order to provide and improve decision‐making tools for end users, the priority program SPP 1886 has been installed by the DFG with the focus on polymorphic uncertainty quantification. The present subproject, which is part of the SPP 1886 (sp12), is focused on fluid saturated soil and earth structures and their multiple uncertainty sources. The very complex micro‐structural consolidation mechanism of soil requires a suitable numerical description. For the strongly coupled fluid‐solid response behavior, the Theory of Porous Media (TPM) will be used, a macroscopic homogenization approach based on the mixture theory restricted by the concept of volume fraction. In the framework of the Finite Element Method (FEM), arbitrary Boundary Value Problems (BVP) can be investigated. Uncertainty modelling takes place on the stochastic level by introducing random fields with a defined correlation structure for the generation of model initial material parameters. By generating many random field realizations for a FEM material parameter, we receive various FEM outputs for selected scenarios of the stated BVP. These results can be used to identify typical output scenarios, which allows to identify critical material parameter combinations which may cause instabilities.