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On the Construction of Statistically Similar Representative Volume Elements Based on the Lineal‐Path Function
Author(s) -
Brands Dominik,
Balzani Daniel,
Schröder Jörg
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010192
Subject(s) - path (computing) , function (biology) , homogeneous , volume (thermodynamics) , boundary (topology) , mathematics , statistical physics , algorithm , mathematical optimization , computer science , mathematical analysis , combinatorics , physics , thermodynamics , evolutionary biology , biology , programming language
Abstract In this contribution we propose a method for the construction of statistically similar representative volume elements (SSRVEs) which are characterized by a much less complexity than usual random RVEs and which represent quite accurately the mechanical response of the real material. For the design of such SSRVEs an objective function is minimized taking into account least‐square functionals based on suitable statistical measures, that characterize the inclusion morphology. Here, we find that the incorporation of the lineal‐path function leads to promising results in FE 2 ‐simulations of macroscopically homogeneous boundary value problems as well as inhomogenous ones. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)