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arXiv 2012.148762020-12math.APcond-mat.soft

Gamma-convergence results for nematic elastomer bilayers: relaxation and actuation

Pierluigi Cesana, Andres A Leon Baldelli

备注：: 38 pages, 2 figures

英文摘要：

We compute effective energies of thin bilayer structures composed by soft nematic elastic-liquid crystals in various geometrical regimes and functional configurations. Our focus is on order-strain interaction in elastic foundations composed of an isotropic layer attached to a nematic substrate. We compute Gamma-limits as the layers thickness vanishes in two main scaling regimes exhibiting spontaneous stress relaxation and shape-morphing, allowing in both cases out-of-plane displacements. This extends the plane strain modelling of [*], showing the asymptotic emergence of fully coupled macroscopic active-nematic foundations. Subsequently, we focus on actuation and compute asymptotic configurations of an active plate on nematic foundation interacting with an applied electric field. From the analytical standpoint, the presence of an electric field and its associated electrostatic work turns the total energy into a non-convex and non-coercive functional. We show that equilibrium solutions are min-max points of the system, that min-maximising sequences pass to the limit and, that the limit system can exert mechanical work under applied electric fields. [*]: P. Cesana and A. A. León Baldelli. "Variational modelling of nematic elastomer foundations". In: Mathematical Models and Methods in Applied Sciences 14 (2018)

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