Hierarchical modeling of heterogeneous plates

The use of asymptotic limits to model heterogeneous plates can be troublesome, because it requires a priori knowledge on the ratio between characteristic lengths of heterogeneities and thickness. Moreover, it also relies on some assumption on the inclusions, like periodicity. We propose and analyze here hierarchical modeling techniques and show that such approach not only avoids such pitfalls, but it is actually simpler to obtain, and it provably converges to the correct asymptotic limits. Its derivation does not requires any restrictive assumptions on the heterogeneities. Copyright © 2014 John Wiley & Sons, Ltd.