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Implementation von Stoffgesetzen mit fraktionalen Ableitungen in die Finite Elemente Methode
Author(s) -
Schmidt A.,
Gaul L.
Publication year - 2003
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310001
Subject(s) - viscoelasticity , rheology , standard linear solid model , creep , fractional calculus , materials science , stress relaxation , mechanics , relaxation (psychology) , range (aeronautics) , mathematics , physics , mathematical analysis , composite material , psychology , social psychology
The material behavior of polymers and of rubber‐like materials can often be classified as linear viscoelastic. Typical phenomena of viscoelastic material are the appearance of creep and relaxation processes. Considering periodic loads, a part of the deformation energy is stored in the material, whereas the rest is dissipated. This phenomenon is called material damping. When describing visoelastic materials, often rheological models consisting of springs and dashpots are used. They are known to have poor curve‐fitting properties over a broad range of time or frequency. In this paper, a generalized rheological element will be deduced using fractional derivatives and the properties of some ‘fractional’ rheological models are discussed. Free decay experiments are carried out in order to perform a parameter identification of a ‘fractional’ 3‐parameter model in the frequency domain. The 3d implementation of this model into an FE code is demonstrated and one of the experiments is simulated in order to verify the implementation.