Journal
COMPUTATIONAL MECHANICS
Volume 57, Issue 1, Pages 123-147Publisher
SPRINGER
DOI: 10.1007/s00466-015-1224-4
Keywords
Stochastic FEM; Computational homogenization; Random geometry
Funding
- ERC Advanced Grant MOCOPOLY
- Deutsche Forschungs-Gemeinschaft (DFG) through the Cluster of Excellence Engineering of Advanced Materials
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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.
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