Computational Mechanics

, Volume 64, Issue 6, pp 1621–1637 | Cite as

Quantification of uncertain macroscopic material properties resulting from variations of microstructure morphology based on statistically similar volume elements: application to dual-phase steel microstructures

  • Niklas Miska
  • Daniel BalzaniEmail author
Original Paper


A method to quantify uncertain macroscopic material properties resulting from variations of a material’s microstructure morphology is proposed. Basis is the computational homogenization of virtual experiments as part of a Monte-Carlo simulation to obtain the associated uncertain macroscopic material properties. A new general approach is presented to construct a set of artificial microstructures, which exhibits a statistically similar variation of the morphology as the real material’s microstructure. The individual artificial microstructures are directly constructed in a way that a lower discretization effort is required compared to real microstructures. The costs to perform the computational homogenization for all considered SSVEs are reduced by an adapted form of the Finite Cell concept and by applying the multilevel Monte-Carlo method. As an illustrative example, the proposed method is applied to a real Dual-Phase steel microstructure.


Microstructure morphology variation Homogenization Finite cells Multilevel Monte Carlo DP-steel 



The authors greatly appreciate financial funding by the German Science Foundation (Deutsche Forschungsgemeinschaft, DFG) as part of the priority program “Polymorphic uncertainty modeling for the numerical design of structures” (SPP 1886), project BA2823/12-1. Furthermore the authors thank the ZIH of TU Dresden for providing computing capabilities on its Taurus cluster. Additionally the authors thank Dr. Bojana Rosić for valuable discussions and hints regarding the multilevel Monte-Carlo method.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringChair of Mechanics - Continuummechanics, Ruhr-Universität BochumBochumGermany

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