@article {agostiniani2018foldable, title = {Foldable structures made of hydrogel bilayers}, year = {2018}, author = {Virginia Agostiniani and Antonio DeSimone and Alessandro Lucantonio and Danka Lu{\v c}i{\'c}} } @article {agostiniani2018heterogeneous, title = {Heterogeneous elastic plates with in-plane modulation of the target curvature and applications to thin gel sheets}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, year = {2018}, publisher = {EDP Sciences}, doi = {https://doi.org/10.1051/cocv/2018046}, author = {Virginia Agostiniani and Alessandro Lucantonio and Danka Lu{\v c}i{\'c}} } @article {2013, title = {Attainment results for nematic elastomers}, year = {2013}, institution = {SISSA}, abstract = {We consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy functional satisfying a nontrivial boundary condition. Other attainment results, both for the nonlinear and the linearized model, are obtained by using the theory of convex integration introduced by Mueller and Sverak in the context of crystalline solids.}, url = {http://hdl.handle.net/1963/7174}, author = {Virginia Agostiniani and Gianni Dal Maso and Antonio DeSimone} } @article {2012, title = {Linear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire}, volume = {29}, number = {SISSA;30/2011/M}, year = {2012}, pages = {715-735}, publisher = {Gauthier-Villars;Elsevier}, abstract = {

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

}, keywords = {Nonlinear elasticity}, doi = {10.1016/j.anihpc.2012.04.001}, url = {http://hdl.handle.net/1963/4267}, author = {Virginia Agostiniani and Gianni Dal Maso and Antonio DeSimone} } @article {2012, title = {Ogden-type energies for nematic elastomers}, journal = {International Journal of Non-Linear mechanics }, volume = {47}, year = {2012}, pages = {402-412}, publisher = {Elsevier}, abstract = {

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).

}, keywords = {Nonlinear elasticity}, doi = {10.1016/j.ijnonlinmec.2011.10.001}, author = {Virginia Agostiniani and Antonio DeSimone} } @article {1078-0947_2012_4_1125, title = {Second order approximations of quasistatic evolution problems in finite dimension}, journal = {Discrete \& Continuous Dynamical Systems - A}, volume = {32}, number = {1078-0947_2012_4_112}, year = {2012}, pages = {1125}, abstract = {

In this paper, we study the limit, as ε goes to zero, of a particular solution of the equation $\epsilon^2A\ddot u^ε(t)+εB\dot u^ε(t)+\nabla_xf(t,u^ε(t))=0$, where $f(t,x)$ is a potential satisfying suitable coerciveness conditions. The limit $u(t)$ of $u^ε(t)$ is piece-wise continuous and verifies $\nabla_xf(t,u(t))=0$. Moreover, certain jump conditions characterize the behaviour of $u(t)$ at the discontinuity times. The same limit behaviour is obtained by considering a different approximation scheme based on time discretization and on the solutions of suitable autonomous systems.

}, keywords = {discrete approximations, perturbation methods, saddle-node bifurcation, Singular perturbations, vanishing viscosity}, issn = {1078-0947}, doi = {10.3934/dcds.2012.32.1125}, url = {http://aimsciences.org//article/id/560b82d9-f289-498a-a619-a4b132aaf9f8}, author = {Virginia Agostiniani} } @article {2011, title = {Gamma-convergence of energies for nematic elastomers in the small strain limit}, journal = {Continuum. Mech. Therm.}, volume = { 23}, number = {SISSA;07/2011/M}, year = {2011}, publisher = {Springer}, chapter = {257}, abstract = {

We study two variational models recently proposed in the literature to describe the mechanical behaviour of nematic elastomers either in the fully nonlinear regime or in the framework of a geometrically linear theory. We show that, in the small strain limit, the energy functional of the first one I\\\"-converges to the relaxation of the second one, a functional for which an explicit representation formula is available.

}, keywords = {Liquid crystals}, doi = {10.1007/s00161-011-0180-2}, url = {http://hdl.handle.net/1963/4141}, author = {Virginia Agostiniani and Antonio DeSimone} }