vis·cous  (vsks)

adj.
1. Having relatively high resistance to flow.
2. Viscid; sticky.

[Middle English, from Old French, from Late Latin viscsus; see viscose.]
... many liquids (including water) will briefly react like elastic solids when subjected to sudden stress. Conversely, many "solids" (even granite) will flow like liquids, albeit very slowly, even under arbitrarily small stress.[7] Such materials are therefore best described as possessing both elasticity (reaction to deformation) and viscosity (reaction to rate of deformation); that is, being viscoelastic.
(from Wikipedia, http://en.wikipedia.org/wiki/Viscosity     section on viscosity in solids)

When we begin to think of time-dependent material properties, the first ideas that come to mind are perhaps the creep behavior or the stress relaxation behavior (or damping, or hysteresis).  The keyword *creep in Abaqus originated for use with metals and is used to describe time-dependent plasticity.  The keyword *viscoelastic has its origins more aligned with elastomer and polymer behaviors and is used to describe time-dependent elasticity, aka viscoelasticity.  By definition viscoelastic means that the material will recover its original shape when unloaded, though it will take some time to do so.  Viscoelasticity is often depicted with diagrams like the one shown above, using a series of springs and dashpots.  This particular diagram is often referred to as a generalized Maxwell model.  When the dashpots behave with linear viscoelasticity, then this can be described in Abaqus using *elastic or *hyperelastic in conjunction with *viscoelastic, linear (aka Prony series viscoelasticity). 

The narrated video below uses an Excel spreadsheet to show the shape of the Prony series equation. In addition the video gives some general rules of thumb on how many terms should be included in the series and how to derive the Prony coefficients from test data using Abaqus/CAE.   (The video will play more clearly if downloaded first).

In the video, a comment was made that if too few Prony terms are used the response will look 'bumpy', or 'wavy'.  In the image below we have used the spreadsheet (attached and downloadable) and given only 4 Prony terms (pairs of g's and tau's) over 7 decades of time - roughly one pair per 2 decades of time - and you notice the bumpy or wavy response of the Prony model (blue diamond symbols).  

One last note, in the video, as we were entering the shear test data, the input dialog box (shown below) has a place to enter a value for the "Long-term normalized shear compliance or modulus".  This is optional input and can help in the fitting, especially when you have a good idea of what the value at very long time (infinity) is.  It is a best practice however to have material test data that spans the range of time (and strain) that you expect in your analysis.

If you would like to dive a little deeper, visit this post:

Hyper-visco rubber material models in Abaqus

Attached documents, for download:

Prony_Example.xlsx      (Excel spreadsheet used in the video)

Back to: Material Modeling and Calibration - An Overview and Curriculum