Computational Mechanics

, Volume 57, Issue 1, pp 123–147 | Cite as

Modified SFEM for computational homogenization of heterogeneous materials with microstructural geometric uncertainties

Original Paper

Abstract

In the current work we examine the application of the stochastic finite element method (SFEM) to the modeling of representative volume elements for heterogeneous materials. Uncertainties in the geometry of the microstructure result in the random nature of the solution fields thus requiring use of the stochastic version of the finite element method. For considering large differences in the material properties of matrix and inclusions a standard SFEM approach proves not stable and results in high numerical errors compared to a brute-force Monte-Carlo evaluation. Therefore in order to stabilize the SFEM we propose an alternative Gauss integration rule as resulting from a truncation of the probability density function for the random variable. In addition we propose new basis functions substituting the common polynomial chaos expansion, resulting in higher accuracy for the standard deviation in the homogenized stress at the macro scale.

Keywords

Stochastic FEM Computational homogenization Random geometry 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Chair of Applied MechanicsUniversity of Erlangen-NurembergErlangenGermany
  2. 2.Chair of Applied MechanicsUniversity of Erlangen-NurembergErlangenGermany

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