Straightening wrinkles
Michel Destrade, Ray W. Ogden, Ivonne Sgura, Luigi Vergori
TL;DR
This paper analyzes the elastic deformation and instability of a soft cylindrical sector when straightened into a rectangular shape, providing a numerical algorithm and applying it to Mooney-Rivlin materials.
Contribution
It introduces a robust numerical method for analyzing the deformation and instability of incompressible soft solids during straightening, with specific application to Mooney-Rivlin materials.
Findings
Identification of conditions for localized instability development.
Development of a numerical algorithm for stiff boundary value problems.
Application to Mooney-Rivlin materials and asymptotic analysis for thin sectors.
Abstract
We consider the elastic deformation of a circular cylindrical sector composed of an incompressible isotropic soft solid when it is straightened into a rectangular block. In this process, the circumferential line elements on the original inner face of the sector are stretched while those on the original outer face are contracted. We investigate the geometrical and physical conditions under which the latter line elements can be contracted to the point where a localized incremental instability develops. We provide a robust algorithm to solve the corresponding two-point boundary value problem, which is stiff numerically. We illustrate the results with full incremental displacement fields in the case of Mooney-Rivlin materials and also perform an asymptotic analysis for thin sectors
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