On the partial wrinkling of imperfectly guided webs

Flexible webs such as those used in roll-to-roll process machines are prone to various detrimental forms of elastic instabilities. This study revisits recent numerical work pertaining to the divergence buckling of non-uniformly tensioned axially moving thin webs. We show that the eigen-deformations experienced by these configurations are characterised by localised short-wavelength spatial patterns (typically referred to as ‘partial wrinkling’). The broader asymptotic structure of the associated bifurcation problem is also highlighted, while our theoretical predictions are further substantiated by additional assessments through direct numerical simulations.