A hybrid Sampling-Stochastic-Finite-Element-Method for polymorphic, microstructural uncertainties in heterogeneous materials
Abstract of the planned project content, taking into account the results from the first project phase
In Phase I of the project we developed methods for the accurate and efficient propagation of polymorphic uncertainty through the material microstructure and applied all proposed approaches to a benchmark problem. The objectives of Phase II are further development of modeling techniques and in particular their application to the engineering design of structures. The later task is computationally prohibitive without an adequate metamodel describing the material response in the presence of polymorphic uncertainty.
Work distribution between project phases
The outcome of Phase II will be an accomplished methodology allowing the uncertainty propagation from the lower level of a material microstructure through the macroscopic structure simulation to the engineering design and decision making. More precisely in Phase II the following challenges are considered. We continue the development of advanced fuzzy-stochastic benchmark RVE for the microstructure of heterogeneous materials, resulting thus in a more realistic and precise description of polymorphic uncertainty in the material microstructure. Modeling techniques for spectral non-deterministic finite element analysis will be enriched to non-deterministic eXtended Isogeometric Analysis. The computational cost of full-order large scale simulations of systems in the presence of uncertainty is unacceptably high, in particular considering many-query or real-time applications. Thus, reduced order modeling is an essential tool which allows a speed up of microscale simulations. Reduced order models and metamodels provide a necessary bridge to the final stage of the project, in which a suitable metamodel will be used on the macroscale and to run large size simulations of macroscopic (engineering) structures. Finally, the influence of uncertainty in the macrostructure on the static and the dynamic behavior of engineering structures under random loading will be analyzed.
Essential project goals and objectives
- Advanced design of benchmark RVE with polymorphic uncertainty
- Development of the non-deterministic spectral IGA and XIGA FEM
- Reduced order models and of the fuzzy-stochastic material response
- Design of a non-deterministic metamodels
- Macroscopic large scale simulations and design of engineering structures
Hr. Pivovarov
M. Sc. Dmytro Pivovarov
Friedrich-Alexander-Universität
Erlangen-Nürnberg
Lehrstuhl für Technische Mechanik (LTM)