分野別セミナー

We explore the asymptotics of multilayer structures in the thin film regime. First, we focus on the elastic couplings of a stiff film on a soft elastic layer. Often regarded as heuristic and phenomenological, we justify the emergence of effective linear elastic foundation models, from standard, linearised, 3d elasticity with an energy minimization perspective. Then, we take into account richer material models: Liquid Crystal (LC) nematic elastomers, that is, LCs embedded into an elastic polymeric matrix. Their interest in the applications resides in the optic-elastic coupling, relating the orientation of the LC and the deformation of the surrounding matrix, producing a very rich phenomenology which becomes apparent in a thorough investigation of minimisers and minimising sequences. Their analysis sheds light on the interplay of different phenomena (optic and elastic), at different material and geometrics scales, with different convergence properties as well as convergence velocities, and allows us to establish an effective, rigorous, asymptotic theory in the vanishing thickness regime.