Stretching and bending of (really) thick elastic plates

Abstract

The mechanical energy of an elastic plate separates into stretching and bending energies. This is a result for asymptotically thin plates, but it is often a surprisingly accurate approximation for thick plates, too. Here, we address this conundrum: We compute the deformations of a thick elastic plate resulting from imposed, asymptotically small deformations of its midline to discover effective stretching and bending moduli. They soften with increasing plate thickness, but, strikingly, their ratio remains approximately constant. In this way, our calculations provide a justification for applying the thin-plate picture of stretching and bending to thick plates such as biological cell sheets.