Straightening: Existence, uniqueness and stability

TL;DR

This paper investigates the mathematical conditions for the existence, uniqueness, and stability of deforming a circular cylinder sector into a rectangular block, considering force requirements, geometric effects, and wrinkle formation.

Contribution

It provides a comprehensive analysis of the straightening deformation, including stability criteria, force analysis, and numerical method comparison for the first time.

Findings

Impedance matrix method offers higher precision in stability analysis.

Force requirements depend on geometric parameters and material models.

Wrinkle formation is influenced by compression and deformation conditions.

Abstract

One of the least studied universal deformations of incompressible nonlinear elasticity, namely the straightening of a sector of a circular cylinder into a rectangular block, is revisited here and, in particular, issues of existence and stability are addressed. Particular attention is paid to the system of forces required to sustain the large static deformation, including by the application of end couples. The influence of geometric parameters and constitutive models on the appearance of wrinkles on the compressed face of the block is also studied. Different numerical methods for solving the incremental stability problem are compared and it is found that the impedance matrix method, based on the resolution of a matrix Riccati differential equation, is the more precise.