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A two-stage homogenization for modelling of elastic-plastic functionally graded composites

Witold Ogierman (Faculty of Mechanical Engineering, Silesian University of Technology, Gliwice, Poland)

Engineering Computations

ISSN: 0264-4401

Article publication date: 6 April 2020

Issue publication date: 15 June 2021




The purpose of this study is to develop a homogenization approach that ensures both high accuracy and time-efficient solution for elastic-plastic functionally graded composites.


The paper presents a novel two-stage hybrid homogenization approach that combines advantages of the mean field homogenization and homogenization based on the finite element method (FEM). The groundbreaking nature of the developed approach is associated with division of the hybrid homogenization procedure into two stages, which allows to very efficiently determine the solution for arbitrary volume fraction of the reinforcement. This paper concerns also on modelling of composites with randomly distributed prolate and oblate particles. For this purpose, the hybrid homogenization was implemented in the framework of the discrete orientation averaging procedure involving pseudo-grain discretization method.


Agreement between the results obtained using the proposed approach and the standard FEM-based homogenization is very good (up to the volume fraction of 0.3).


The proposed two-stage homogenization approach allows to obtain the solution for materials with arbitrary volume fraction of the reinforcement very efficiently; therefore, it is highly beneficial for the two-scale modeling of nonlinear functionally graded materials and structures.



The research for this paper was financially supported by the National Science Centre, Poland (Grant No. UMO-2016/21/N/ST8/01119) and by the Rector’s Grant for Research and Development, Silesian University of Technology (Grant No. 10/040/RGJ19/0081).


Ogierman, W. (2021), "A two-stage homogenization for modelling of elastic-plastic functionally graded composites", Engineering Computations, Vol. 38 No. 3, pp. 1099-1116.



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