ELASTIC FIELDS AT CORNERS OF HIGHLY STRETCHABLE MATERIALS ARE CONCENTRATED BUT BOUNDED

Abstract

Corners concentrate elastic fields and often initiate fracture. For small deformations, it is well established that the elastic field around a corner is power-law singular. For large deformations, we show here that the elastic field around a corner is concentrated but bounded. We conduct computation and an experiment on the lap shear of a highly stretchable material. A rectangular sample was sandwiched between two rigid substrates, and the edges of the stretchable material met the substrates at 90° corners. The substrates were pulled to shear the sample. We computed the large-deformation elastic field by assuming several models of elasticity. The theory of elasticity had no length scale, and lap shear was characterized by a single length, the thickness of the sample. Consequently, the field in the sample was independent of any length once the spatial coordinates were normalized by the thickness. We then lapped shear samples of a polyacrylamide hydrogel of various thicknesses. For all samples, the fracture initiated from the corners, at a load independent of thickness. These experimental findings agree with the computational prediction that large-deformation elastic fields at corners are concentrated but bounded.