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A physical basis for fractional derivatives in constitutive equations
Author(s) -
Pfitzenreiter T.
Publication year - 2004
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.200310112
Subject(s) - viscoelasticity , fractional calculus , non equilibrium thermodynamics , constitutive equation , basis (linear algebra) , statistical physics , coincidence , term (time) , physics , mathematics , thermodynamics , classical mechanics , mathematical analysis , quantum mechanics , geometry , medicine , alternative medicine , pathology , finite element method
In good coincidence with experimental data the damping properties of viscoelastic media can be described by fractional derivatives. We present a model, which under certain assumptions on the interactions between macromolecules leads to a macroscopic stress strain relation with fractional derivatives in the damping term. For this purpose we use the Kubo formula of nonequilibrium thermodynamics.