Sensitivity analysis of statistical measures for the reconstruction of microstructures based on the minimization of generalized least-square functionals

In: Technische Mechanik, Jg. 30 (2009) ; Nr. 4, S. 297-315
ISSN: 0232-3869
Zeitschriftenaufsatz / Fach: Bauwissenschaften
Abstract:
For the simulation of micro-heterogeneous materials the FE2-method provides incorporation of the mechanical
behavior at the microscale in a direct manner by taking into account a microscopic boundary value problem based
on a representative volume element (RVE). A main problem of this approach is the high computational cost, when
we have to deal with RVEs that are characterized by a complex geometry of the individual constituents. This leads
to a large number of degrees of freedom and history variables at the microscale which needs a large amount of
memory, not to mention the high computation time. Therefore, methods that reduce the complexity of such RVEs
play an important role for efficient direct micro-macro transition procedures. In this contribution we focus on random
matrix-inclusion microstructures and analyze several statistical measures with respect to their influence on
the characterization of the inclusion phase morphology. For this purpose we apply the method proposed in Balzani
and Schr¨oder (2008); Balzani et al. (2009a), where an objective function is minimized which takes into account
differences between statistical measures computed for the original binary image of a given real microstructure and
a simplified statistically similar representative volume element (SSRVE). The analysis with respect to the capability
of the resulting SSRVEs to reflect the mechanical response in some simple independent virtual experiments allows
for an estimation of the importance of the investigated statistical measures.