A Sliding Element in Rheological Models

Mechanical analogs composed of springs and dashpots have been used extensively to describe qualitative and sometimes quantitative rheological properties of solids and liquids. However, there are deformation or flow patterns whose description requires additional elements. Among them is the sliding frictional or St. Venant element (see Details). This Demonstration represents these phenomena in simple arrays of force-displacement curves involving springs and/or dashpots.


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


The definition of the sliding (frictional or St. Venant) element is: if , then , else , where is the sliding force. Thus, in a series combination with a spring with spring constant (model A), the array's constitutive definition is: if , then , else . If the sliding element is parallel to the spring (model B), the array's definition is: . With a dashpot having viscosity in series (model C), the definition is: if , then , else , where is the displacement rate. With the dashpot in parallel (model D), the definition is: . The definition of a model composed of two springs and sliders in series and ) placed in parallel to each other (model E) is: if , then , else ) + (if , then , else ).
Choose model A, B, C, D or E by clicking its setter. You can set the magnitudes of , , , , , and , all in arbitrary units, to plot the corresponding array's force-displacement curve. A horizontal dotted black line on the plot marks the magnitude of and a dashed gray line that of .
[1] J. L. White, Principles of Polymer Engineering Rheology, New York: John Wiley & Sons, 1990.
[2] N. S. Ottosen and M. Ristinmaa, The Mechanics of Constitutive Modeling, Amsterdam: Elsevier, 2005.
    • 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.

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 © 2017 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+