Hello All,
I am presently creating a transfer matrix to represent a wave propagation in a multi-layered plate. I m intended to use this transfer matrix for elastic materials.
On what grounds can rubber be considered as a linear material to study the acoustic properties.
Thank you.
Rubber-like materials have been modelled as nonlinear hyperelastic materials since the first experimental results on natural gum reported by Rivlin & Saunders (1951).
See, for example (the current literature on this topic is indeed very extensive):
[1] Treloar LRG, Hopkins HG, Rivlin RS, Ball JM. 1976. The mechanics of rubber elasticity [and discussions], Proceedings of the Royal Society of London A 351, 301-330.
http://rspa.royalsocietypublishing.org/content/351/1666/301
or the recent paper
[2] Destrade M, Saccomandi G, Sgura I. 2017. Methodical fitting for mathematical models of rubberlike materials, Proceedings of the Royal Society A 473, 20160811.
http://rspa.royalsocietypublishing.org/content/473/2198/20160811
or the review article
[3] Steinmann P, Hossain M, Possart G. 2012. Hyperelastic models for rubber-like materials: consistent tangent operators and suitability for Treloar's data, Archive of Applied Mechanics 82, 1183-1217.
As all the stress-strain (or force-displacement) curves show in these papers, rubber can be treated as a linear-elastic (hyperelastic) material only under small (infinitesimal) elastic deformations.
Hi Mohan
I agree with the above authors that rubber is everything but linear.
In fact, it is all of the above plus viscoelastic (https://en.wikipedia.org/wiki/Williams%E2%80%93Landel%E2%80%93Ferry_equation) and there is the Mullins effect (https://en.wikipedia.org/wiki/Mullins_effect )
The best model for rubber that I have seen (i.e. not tested) is the Bergström-Boyce model which appears to capture the above.
https://www.sharcnet.ca/Software/Ansys/16.2.3/en-us/help/ans_thry/thy_bb.html
http://saifulamin.info/rpdf/a3-1.pdf
To summarize, on very few grounds and then only piece wise linear (wrt temperature and frequency) and at very low vibration amplitude.
Sincerely
Claes
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