Stamping and wrinkling of elastic plates

TL;DR

This paper investigates the wrinkling patterns of elastic plates in spherical molds, deriving a model that predicts wrinkle behavior and force response, validated through experiments and extending existing tension field theories.

Contribution

It introduces a new model for elastic plate wrinkling that accounts for amplitude-dependent wavelength and force maxima, extending tension field theory with experimental validation.

Findings

Wrinkle wavelength decreases with amplitude, reaching a maximum at thickness scale.

Force required for compression peaks independently of plate thickness.

Theoretical predictions align well with experimental results.

Abstract

We study the peculiar wrinkling pattern of an elastic plate stamped into a spherical mold. We show that the wavelength of the wrinkles decreases with their amplitude, but reaches a maximum when the amplitude is of the order of the thickness of the plate. The force required for compressing the wrinkled plate presents a maximum independent of the thickness. A model is derived and verified experimentally for a simple one-dimensional case. This model is extended to the initial situation through an effective Young modulus representing the mechanical behavior of wrinkled state. The theoretical predictions are shown to be in good agreement with the experiments. This approach provides a complement to the "tension field theory" developed for wrinkles with unconstrained amplitude.