Matched asymptotic solution for crease nucleation in soft solids
Thursday 13th July 2017
A soft solid subjected to a finite compression can suddenly develop sharp self-contacting folds at its free surface, also known as creases. This singular instability is of utmost importance in material science, since it can be positively used to fabricate objects with adaptive surface morphology at different length-scales. Creasing is physically different from other instabilities in elastic materials, like buckling or wrinkling. Indeed, it is a scale-free, fully nonlinear phenomenon displaying similar features as phase-transformations, but lacking an energy barrier. Despite recent experimental and numerical advances, the theoretical understanding of crease nucleation remains elusive, yet crucial for driving further progress in engineering applications. This work solves the quest for a theoretical explanation of crease nucleation. Creasing is proved to occur after a global bifurcation allowing the co-existence of an affine outer deformation and an inner discontinuous solution with localised self-contact at the free surface. The most fundamental insight is the theoretical prediction of the crease nucleation threshold, in excellent agreement with experiments and numerical simulations. A matched asymptotic approximation is also provided within the intermediate region between the two co-existing inner and outer solutions. The near-field incremental problem becomes singular because of the surface self-contact, acting like the point-wise disturbance in the Oseen's correction for the 2D Stokes problem of the flow past a circle. Using Green's functions in the half-space, analytic expressions of the matching solution and the relative range of validity are derived, perfectly fitting the results of numerical simulations without any adjusting parameter.