Relaxation of some transversally isotropic energies and applications to smectic A elastomers
J. Adams, S. Conti, A. DeSimone, and G. Dolzmann
We determine the relaxation of some transversally-isotropic energy densities, i.e., functions![$ W:\mathbb{R}^{3\times3}\to[0,\infty]$](./img_AdamsContiDesimoneDolzmann2008_1.png){kind=small}
with the property
for all
and all
such that 
, where 
is a
fixed unit vector. One physically relevant example is a model for smectic A
elastomers. We discuss
the implications of our result for the computation of macroscopic
stress-strain curves for this material and compare with experiment.
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Published in: Math. Mod. Meth. Appl. Sci. 18, pp. 1-20, 2008.
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