The infinite hierarchy of elastic shell models: some recent results and a conjecture

TL;DR

This paper reviews recent advances in deriving thin elastic shell models from 3D nonlinear elasticity and proposes a conjecture about an infinite hierarchy of such models across different force scales.

Contribution

It introduces a conjecture on the existence of infinitely many limiting 2D shell models corresponding to various force scaling regimes.

Findings

Summarizes recent derivations of shell models from 3D elasticity.

Proposes a conjecture on an infinite hierarchy of shell models.

Abstract

We summarize some recent results of the authors and their collaborators, regarding the derivation of thin elastic shell models (for shells with mid-surface of arbitrary geometry) from the variational theory of 3d nonlinear elasticity. We also formulate a conjecture on the form and validity of infinitely many limiting 2d models, each corresponding to its proper scaling range of the body forces in terms of the shell thickness.