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We investigate the deformation of a longitudinally stretched rectangularsheet which is clamped at two opposite boundaries and free otherwise withexperiments, numerical analysis and asymptotic analysis of the biharmonicelastic equation governing their planar equilibrium configurations. Thedisplacement field of the sheet is measured by tracking embedded fluorescenttracers with a digital image correlation (DIC) technique. The experiments andnumerical finite element analysis (FEA) are found to be in overall goodagreement except at the very corners where large deformations occur. We findthat the deformed sheet can be broadly divided into a uniaxially stretchedcentral region and two clamp dominated side regions. A subregion characterizedby a diverging stress can be identified at each of the four clamped-freecorners within the clamp dominated region. We postulate that the divergence atthe corners is regularized by nonlinear elastic deformations occurring in thissubregion at the very corners and provide a nontrivial scaling for its size.Within the intermediate corner dominated subregion, measured displacements growwith distance $r$ from the corners as $r^{\alpha}$, with power $\alpha < 1$consistent with the development of stress singularities at the intersection ofthe free and clamped edges.

Corner singularities and shape of stretched elastic sheets