Why does an elastomer layer confined between two rigid blocks grow numerous cavities?

Abstract

For a thin layer of elastomer sandwiched between two rigid blocks, when the blocks are pulled, numerous cavities grow in the elastomer like cracks. Why does the elastomer grow numerous small cracks instead of a single large crack? Here we answer this question by analyzing an idealized model, in which the elastomer is an incompressible neoHookean material and contains a penny-shaped crack. To simulate one representative crack among many, the model is axisymmetric with zero radial displacement at the edge. When the rigid blocks are pulled by a pair of forces, a hydrostatic tension develops in the elastomer. At a critical hydrostatic tension, a small crack deforms substantially, as predicted by an elastic instability, resulting in an unbounded energy release rate. Consequently, the small crack initiates its growth, regardless of the toughness of the elastomer. As the crack grows, the energy release rate decreases, so that the crack arrests. Meanwhile, the rigid blocks constrain deformation of the elastomer far away from the crack, where hydrostatic tension remains high, allowing other cracks to grow. For an elastomer of thickness H, shear modulus μ, and toughness Gc, the crack radius and spacing decrease as the normalized toughness Gc/(μH) increases. Therefore, a tough elastomer of small modulus and thickness will grow numerous small cracks when confined by two rigid blocks and pulled beyond a critical force.