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Parameter Identification and FE Implementation of a Viscoelastic Constitutive Equation Using Fractional Derivatives
Author(s) -
Schmidt A.,
Gaul L.
Publication year - 2002
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/1617-7061(200203)1:1<153::aid-pamm153>3.0.co;2-j
Subject(s) - viscoelasticity , constitutive equation , identification (biology) , fractional calculus , range (aeronautics) , mathematics , materials science , structural engineering , engineering , finite element method , composite material , botany , biology
Damping in viscoelastic materials can be described in several ways. In FE codes for transient calculations with direct integration usually Rayleigh‐damping is provided. However, it is known that this model is not qualified to represent the damping properties of viscoelastic material over a broad range of time or frequency. Another approach uses fractional time derivatives of stresses and strains in the constitutive equations. This model requires few parameters, provides good curve fitting properties and is physically proved. In this paper a parameter identification for the fractional 3‐parameter model will be carried out and its implementation into an FE code will be demonstrated.