A generalized continuum approach to predict local buckling patterns of thin structures - Damil, Noureddine; Potier-Ferry, Michel (European Journal of Computational Mechanics, 2008)
Macroscopic descriptions of instability pattern formation can be predicted by generic amplitude equations of Ginzburg-Landau type. A variant of this approach is presented, that permits to account for the coupling between local and global instabilities. The mean field and the amplitude of the fluctuations are governed by similar equations. The resulting model is a generalized continuum, where the macroscopic stresses are Fourier coefficients of the microscopic stresses. This new double scale description of cellular instabilities is applied to beam on an elastic foundation and to 3D nonlinear elasticity. We shall also discuss the behaviour of these new continuum models after a finite element discretisation.