01684nas a2200157   4500008004100000245004700041210004600088260001300134300001200147490000700159520120600166653002501372100002601397700002201423856008101445       2012                        en  d00aOgden-type energies for nematic elastomers0 aOgdentype energies for nematic elastomers  bElsevier  a402-4120 v473 a<p>Ogden-type extensions of the free-energy densities currently used to model the mechanical behavior of nematic elastomers are proposed and analyzed. Based on a multiplicative decomposition of the deformation gradient into an elastic and a spontaneous or remanent part, they provide a suitable framework to study the stiffening response at high imposed stretches. Geometrically linear versions of the models (Taylor expansions at order two) are provided and discussed. These small strain theories provide a clear illustration of the geometric structure of the underlying energy landscape (the energy grows quadratically with the distance from a non-convex set of spontaneous strains or energy wells). The comparison between small strain and finite deformation theories may also be useful in the opposite direction, inspiring finite deformation generalizations of small strain theories currently used in the mechanics of active and phase-transforming materials. The energy well structure makes the free-energy densities non-convex. Explicit quasi-convex envelopes are provided, and applied to compute the stiffening response of a specimen tested in plane strain extension experiments (pure shear).</p>10aNonlinear elasticity1 aAgostiniani, Virginia1 aDeSimone, Antonio  uhttps://www.math.sissa.it/publication/ogden-type-energies-nematic-elastomers