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: Paul Steinmann, Kai Willner
Project members: Dmytro Pivovarov
Start date: 1. April 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.

Publications

• Pivovarov D., Willner K., Steinmann P.:
  On spectral fuzzy–stochastic FEM for problems involving polymorphic geometrical uncertainties
  In: Computer Methods in Applied Mechanics and Engineering 350 (2019), p. 432-461
  ISSN: 0045-7825
  DOI: 10.1016/j.cma.2019.02.024
• Pivovarov D., Steinmann P.:
  Modified SFEM for computational homogenization of heterogeneous materials with microstructural geometric uncertainties
  In: Computational Mechanics 57 (2016), p. 123-147
  ISSN: 0178-7675
  DOI: 10.1007/s00466-015-1224-4
• Pivovarov D., Steinmann P.:
  On stochastic FEM based computational homogenization of magneto-active heterogeneous materials with random microstructure
  In: Computational Mechanics 58 (2016), p. 981-1002
  ISSN: 0178-7675
  DOI: 10.1007/s00466-016-1329-4
• Pivovarov D., Zabihyan R., Mergheim J., Willner K., Steinmann P.:
  On periodic boundary conditions and ergodicity in computational homogenization of heterogeneous materials with random microstructure
  In: Computer Methods in Applied Mechanics and Engineering 357 (2019)
  ISSN: 0045-7825
  DOI: 10.1016/j.cma.2019.07.032
• Pivovarov D., Steinmann P., Willner K.:
  Acceleration of the spectral stochastic FEM using POD and element based discrete empirical approximation for a micromechanical model of heterogeneous materials with random geometry
  In: Computer Methods in Applied Mechanics and Engineering (2019), Article No.: 112689
  ISSN: 0045-7825
  DOI: 10.1016/j.cma.2019.112689