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

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