9755

Fractional Rheological Constitutive Equations

This Demonstration shows the simplest two-element fractional rheological constitutive models. Choose between the constitutive model, the type of rheological experiment, and the plot type. Use the sliders to vary the fractional power-law exponents of the two springpots independently ( and ), and their corresponding quasi-properties ( and ). The convention for the exponents used here is .
Variable definitions:
, : springpot exponents
, : quasi-properties
: relaxation modulus
: creep compliance
, : storage and loss modulus
: time-dependent stress
: time-dependent strain

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

More details about fractional constitutive equations and power-law rheology can be found in the references.
References
[1] A. Jaishankar and G. H. McKinley, "Power-Law Rheology in the Bulk and at the Interface: Quasi-Properties and Fractional Constitutive Equations," Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 469(2149), 2013. doi.10.1098/rspa.2012.0284.
[2] C. Friedrich, "Relaxation and Retardation Functions of the Maxwell Model with Fractional Derivatives," Rheologica Acta, 30(2), 1991 pp. 151–158. www.springerlink.com/index/j3523m37x311557l.pdf.
[3] H. Schiessel, R. Metzler, A. Blumen, and T. Nonnenmacher, "Generalized Viscoelastic Models: Their Fractional Equations with Solutions," Journal of Physics A: Mathematical and General, 28(23), 1995 pp. 6567–6584. iopscience.iop.org/0305-4470/28/23/012.
[4] I. Podlubny, Fractional Differential Equations (Mathematics in Science and Engineering, Vol. 198), San Diego: Academic Press, 1999.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+