Premium
Second order homogenization method based on higher order finite elements
Author(s) -
D?ster A.,
Rank E.,
Diebels S.,
Ebinger T.,
Steeb H.
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510172
Subject(s) - homogenization (climate) , microstructure , discretization , finite element method , boundary value problem , curvature , constitutive equation , mechanics , materials science , mathematics , mathematical analysis , physics , geometry , composite material , thermodynamics , biodiversity , ecology , biology
Modeling materials with lattice‐like microstructures like open‐cell foams requires an extended continuum mechanical setting on the macroscopic scale, e. g. a micropolar or micromorphic theory. In order to avoid the formulation of constitutive equations a higher order numerical homogenization scheme (FE 2 ) is proposed. Therefore, each integration point possesses its own microstructure which, in the present case, consists of beam‐like elements representing the cell walls. In this paper, the microstructures are discretized by continuum‐based higher order locking free finite elements with high aspect ratios, leading to a numerically efficient treatment of a local displacement‐driven boundary value problem according to the macroscopic strain and curvature. The resulting stress distributions in the microstructures are homogenized to macroscopic stresses and couple stresses. The approach is demonstrated by a numerical example. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)