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A hybrid Sampling-Stochastic-Finite-Element-Method for polymorphic, microstructural uncertainties in heterogeneous materials

A hybrid Sampling-Stochastic-Finite-Element-Method for polymorphic, microstructural uncertainties in heterogeneous materials

(Third Party Funds Group – Sub project)

Overall project: SPP 1886: Polymorphic uncertainty modelling for the numerical design of structures
Project leader: ,
Project members:
Start date: 1. January 2016
End date: 31. March 2020
Acronym:
Funding source: DFG / Schwerpunktprogramm (SPP)
URL:

Abstract

The overarching goal of the proposed project at the methodological side is to establish a computationally tractable numerical method that is suited to capture polymorphic uncertainties in large-scale problems (as arising from the numerical analysis of heterogeneous materials microstructures). On the one hand the method will allow for fuzzy probability distributions of the random parameters (describing a microstructures geometry) and on the other hand the method will be based on only a few reduced basis modes. These ingredients will enable to capture epistemic uncertainties in addition to aleatoric uncertainties in a computationally accessible manner. The overarching goal of the proposed project at the application side is to establish a non-deterministic macroscopic material model. On the one hand the model accounts for the heterogeneity of the underlying material's microstructure by computational homogenization, and on the other hand it captures polymorphic uncertainties in the geometry description of the microstructure. The non-deterministic macroscopic material model then represents the necessary input for the mechanical design of macroscopic (engineering) structures under due consideration of polymorphic uncertainties in the heterogeneous materials microstructure.

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