Finite Element Formulation of Viscoelastic Constitutive Equations Using Fractional Time Derivatives

By A. Schmidt, Lothar Gaul. 2002

200 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/8fbc7e6bf82c4f83e2dfb4f23039316c08bb1678

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In Civil and Structural Engineering

In Mechanics of Materials

In Modeling and Simulation

Citations in the corpus

Finite element formulations for transient dynamic analysis in structural systems with viscoelastic treatments containing fractional derivative models (2007, methodology): “Schmidt and Gaul [11] implemented these algorithms into an elastic finite element code and a three-dimensional model was studied, in which the parameters of the material model were identified from the curve fitting in timedomain as well as in frequency-domain.”
A discrete mechanical model of fractional hereditary materials (2013, methodology): “In more details in [15, 16] the fractional operators have been discretized by using the definition of GrünwaldLetnikov (see Appendix).”
On the Fractional Order Model of Viscoelasticity (2005, background): “This means, when numerically calculating the constitutive response, the complete previous history of at least one quantity (e.g., the strain) must be saved and included in each time step (see, e.g., Enelund et al., 1999; Schmidt and Gaul, 2002).”
Visco-elastic behavior through fractional calculus: An easier method for best fitting experimental results (2011, background): “(13) for the constitutive law of a visco-elastic material directly descends in assuming that the kernel in the convolution integral is of power law type (Schiessel and Blumen, 1993; Bagley and Torvik, 1979, 1983a,b, 1986; Evangelatos and Spanos, 2011; Schmidt and Gaul, 2002; Di Paola et al., 2011).”
Adaptive discretization of fractional order viscoelasticity using sparse time history (2004, unknown): “, [7–9]).”
Identification of the parameters of the Kelvin-Voigt and the Maxwell fractional models, used to modeling of viscoelastic dampers (2010, unknown): “It has been proved in [4,15] that the fractional derivative models can better capture the frequency dependent properties of VE dampers.”
Simulation of a viscoelastic flexible multibody system using absolute nodal coordinate and fractional derivative methods (2009, methodology): “In order to make the three-parameter fractional model reduce to a classical model for pure elastic material, based on previous research [11, 13, 27], for isotropic viscoleastic materials with shear deformation, the three-parameter fractional model can be rewritten in a similar matrix form:”