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Numerical homogenization of foam‐like structures based on the FE2‐approach
Author(s) -
Sehlhorst HansGeorg,
Jänicke Ralf,
Düster Alexander,
Rank Ernst,
Steeb Holger,
Diebels Stefan
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810573
Subject(s) - homogenization (climate) , discretization , continuum mechanics , boundary value problem , nonlinear system , continuum hypothesis , anisotropy , microstructure , finite element method , computation , mathematics , mechanics , classical mechanics , physics , materials science , mathematical analysis , composite material , thermodynamics , biodiversity , ecology , algorithm , quantum mechanics , biology
The computation of foam–like structures is still a topic of research. There are two basic approaches: the microscopic model where the foam–like structure is entirely resolved by a discretization (e.g. with Timoshenko beams) on a micro level, and the macroscopic approach which is based on a higher order continuum theory. A combination of both of them is the FE 2 ‐approach where the mechanical parameters of the macroscopic scale are obtained by solving a Dirichlet boundary value problem for a representative microstructure at each integration point. In this contribution, we present a two–dimensional geometrically nonlinear FE 2 ‐framework of first order (classical continuum theories on both scales) where the microstructures are discretized by continuum finite elements based on the p ‐version. The p ‐version elements have turned out to be highly efficient for many problems in structural mechanics. Further, a continuum–based approach affords two additional advantages: the formulation of geometrical and material nonlinearities is easier, and there is no problem when dealing with thicker beam–like structures. In our numerical example we will investigate a simple macroscopic shear test. Both the macroscopic load displacement behavior and the evolving anisotropy of the microstructures will be discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)