A bridging technique to analyze the influence of boundary conditions on instability patterns

In this paper, we present a new numerical technique that permits to analyse the effect of boundary conditions on the appearance of instability patterns. Envelope equations of Landau–Ginzburg type are classically used to predict pattern formation, but it is not easy to associate boundary conditions for these macroscopic models. Indeed, envelope equations ignore boundary layers that can be important, for instance in cases where the instability starts first near the boundary. In this work, the full model is considered close to the boundary, an envelope equation in the core and they are bridged by the Arlequin method [1]. Simulation results are presented for the problem of buckling of long beams lying on a non-linear elastic foundation.