Nematic elastomers are polymeric materials which combine the
elastic properties of rubbers with the optical properties of
nematic liquid crystals. Their mechanical behavior is extremely
rich, as a consequence of the symmetry-breaking phase transition
which transforms the isotropic, high temperature phase into a
uniaxial nematic phase. Typical equilibrium configurations exhibit
fine-scale oscillations of the state variables. The free-energy
density that has been proposed to model their behavior is not
quasiconvex.
In this talk, recent results on the mathematical modelling of the
soft elastic response of nematic elastomers will be reviewed,
including the explicit evaluation of the quasiconvex envelope of
the free-energy density (joint work with G. Dolzmann), and
numerical simulations based on such envelope (joint work with S.
Conti and G. Dolzmann)
Presented by A. De Simone
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