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Many‐scale finite strain computational homogenization via Concentric Interpolation
Author(s) -
Kunc Oliver,
Fritzen Felix
Publication year - 2020
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6454
Subject(s) - homogenization (climate) , hyperelastic material , computation , algorithm , finite element method , computer science , stiffness , finite strain theory , mathematics , computational science , structural engineering , engineering , biodiversity , ecology , biology
Summary A method for efficient computational homogenization of hyperelastic materials under finite strains is proposed. Multiple spatial scales are homogenized in a recursive procedure: starting on the smallest scale, few high fidelity FE computations are performed. The resulting fields of deformation gradient fluctuations are processed by a snapshot POD resulting in a reduced basis (RB) model. By means of the computationally efficient RB model, a large set of samples of the homogenized material response is created. This data set serves as the support for the Concentric Interpolation (CI) scheme, interpolating the effective stress and stiffness. Then, the same procedure is invoked on the next larger scale with this CI surrogating the homogenized material law. A three‐scale homogenization process is completed within few hours on a standard workstation. The resulting model is evaluated within minutes on a laptop computer in order to generate fourth‐scale results. Open source code is provided.