caa a22 4500 445811676 CHVBK 20180317145213.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s00419-010-0462-3 doi (NATIONALLICENCE)springer-10.1007/s00419-010-0462-3 Approximation of random microstructures by periodic statistically similar representative volume elements based on lineal-path functions [Elektronische Daten] [Jörg Schröder, Daniel Balzani, Dominik Brands] For the direct incorporation of micromechanical information into macroscopic boundary value problems, the FE2-method provides a suitable numerical framework. Here, an additional microscopic boundary value problem, based on evaluations of representative volume elements (RVEs), is attached to each Gauss point of the discretized macrostructure. However, for real random heterogeneous microstructures the choice of a "large” RVE with a huge number of inclusions is much too time-consuming for the simulation of complex macroscopic boundary value problems, especially when history-dependent constitutive laws are adapted for the description of individual phases of the mircostructure. Therefore, we propose a method for the construction of statistically similar RVEs (SSRVEs), which have much less complexity but reflect the essential morphological attributes of the microscale. If this procedure is prosperous, we arrive at the conclusion that the SSRVEs can be discretized with significantly less degrees of freedom than the original microstructure. The basic idea for the design of such SSRVEs is to minimize a least-square functional taking into account suitable statistical measures, which characterize the inclusion morphology. It turns out that the combination of the volume fraction and the spectral density seems not to be sufficient. Therefore, a hybrid reconstruction method, which takes into account the lineal-path function additionally, is proposed that yields promising realizations of the SSRVEs. In order to demonstrate the performance of the proposed procedure, we analyze several representative numerical examples. Springer-Verlag, 2010 Numerical homogenization nationallicence Random microstructure nationallicence Statistically similar RVE nationallicence Lineal-path function nationallicence Spectral-density nationallicence Finite plasticity nationallicence Schröder Jörg Fakultät für Ingenieurwissenschaften, Institut für Mechanik, Abteilung Bauwissenschaften, Universität Duisburg-Essen, Universitätsstr. 15, 45117, Essen, Germany aut Balzani Daniel Fakultät für Ingenieurwissenschaften, Institut für Mechanik, Abteilung Bauwissenschaften, Universität Duisburg-Essen, Universitätsstr. 15, 45117, Essen, Germany aut Brands Dominik Fakultät für Ingenieurwissenschaften, Institut für Mechanik, Abteilung Bauwissenschaften, Universität Duisburg-Essen, Universitätsstr. 15, 45117, Essen, Germany aut Archive of Applied Mechanics Springer-Verlag 81/7(2011-07-01), 975-997 0939-1533 81:7<975 2011 81 419 https://doi.org/10.1007/s00419-010-0462-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00419-010-0462-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Schröder Jörg Fakultät für Ingenieurwissenschaften, Institut für Mechanik, Abteilung Bauwissenschaften, Universität Duisburg-Essen, Universitätsstr. 15, 45117, Essen, Germany aut NATIONALLICENCE 700 1- Balzani Daniel Fakultät für Ingenieurwissenschaften, Institut für Mechanik, Abteilung Bauwissenschaften, Universität Duisburg-Essen, Universitätsstr. 15, 45117, Essen, Germany aut NATIONALLICENCE 700 1- Brands Dominik Fakultät für Ingenieurwissenschaften, Institut für Mechanik, Abteilung Bauwissenschaften, Universität Duisburg-Essen, Universitätsstr. 15, 45117, Essen, Germany aut NATIONALLICENCE 773 0- Archive of Applied Mechanics Springer-Verlag 81/7(2011-07-01), 975-997 0939-1533 81:7<975 2011 81 419 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer