asymptotic methods

Spatial pattern formation in stiff thin films on soft substrates is investigated from a multi-scale point of view based on a technique of slowly varying Fourier coefficients. A general macroscopic modeling framework is developed and then a simplified macroscopic model is derived. The model incorporates Asymptotic Numerical Method (ANM) as a robust path-following technique to trace the post-buckling evolution path and to predict secondary bifurcations.

F. Xu, Y. Koutsawa, M. Potier-Ferry, S. Belouettar

http://dx.doi.org/10.1016/j.ijsolstr.2015.06.007

Abstract:

Dominique Chapelle and Klaus-Jürgen Bathe

Singular elastic stress fields are generally developed at sharp re-entrant corners and at the end of bonded interfaces between dissimilar elastic materials. This behaviour can present difficulties in both analytical and numerical solution of such problems. For example, excessive mesh refinement might be needed in a finite element solution.