%0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire %D 2012 %T Linear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions %A Virginia Agostiniani %A Gianni Dal Maso %A Antonio DeSimone %K Nonlinear elasticity %X

The energy functional of linear elasticity is obtained as G-limit of suitable rescalings of the energies of finite elasticity...

%B Ann. Inst. H. Poincare Anal. Non Lineaire %I Gauthier-Villars;Elsevier %V 29 %P 715-735 %G en %U http://hdl.handle.net/1963/4267 %1 3996 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-26T15:11:45Z\\r\\nNo. of bitstreams: 1\\r\\nAgostiniani_DalMaso_30_M.pdf: 407057 bytes, checksum: 2009d1218f7735191a1c768a73b400a3 (MD5) %R 10.1016/j.anihpc.2012.04.001 %0 Journal Article %J International Journal of Non-Linear mechanics %D 2012 %T Ogden-type energies for nematic elastomers %A Virginia Agostiniani %A Antonio DeSimone %K Nonlinear elasticity %X

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).

%B International Journal of Non-Linear mechanics %I Elsevier %V 47 %P 402-412 %G en %N 2 %1 6971 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-07-15T14:33:38Z No. of bitstreams: 0 %R 10.1016/j.ijnonlinmec.2011.10.001