Comparative study for the efficient construction of statistically similar RVEs: Lineal-path and minkowski functionals
L. Scheunemann, D. Brands, D. Balzani, J. Schröder.
11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014, 3393-3402, (2014)
Advanced high strength steels, such as Dual-Phase steel (DP steel), provide advantageous material properties for engineering applications compared to conventional high strength steel mainly originating from a ferritic-martensitic microstructure. A way to include these heterogeneities on the microscale into the modeling of the material is the FE2- method. Herein, in every integration point of a macroscopic finite element problem a microscopic boundary value problem based on the definition of a representative volume element (RVE) is attached. From this representation, high computational costs arise due to the complexity of the discretization which can be circumvented by the use of a statistically similar RVE (SSRVE) showing a lower complexity. For the construction of such SSRVEs, a least-square functional is minimized which takes into account differences of statistical measures evaluated for the real microstructure and the SSRVE. The choice of the statistical measures which are considered in the least-square functional however influences the quality of the SSRVE and on the other hand the computing time required for the construction. Therefore, in this contribution we analyze statistical measures of different type and complexity. We focus on the volume fraction, the spectral density, the lineal-path function and measures based on Minkowski functionals. The performance is checked in virtual tests where the response of the individual SSRVEs is compared with the real target microstructure of a DP steel.
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