Edge effects in elastic bulging. (November 2018) - Benoist, Félix; Box, Finn; Goriely, Alain
Abstract: Elastic bulging occurs when an elastic material deforms through a small opening in a rigid boundary. This problem is complementary to the indentation problem where displacement is applied to a small part of an elastic material. Understanding bulging is crucial in a number of applications related to swelling such as the deformation of the brain following a decompressive craniectomy. In particular, it is known that large stresses develop close to the opening leading to potential material damage. To alleviate this problem, it is conceivable to modify the shape of the edge to reduce stress increases. Here, we study edge effects during planar bulging and show how an opening should be shaped to remove stress singularities. Highlights: The problem of elastic bulge of an elastic half-plane through a finite opening is considered both theoretically and experimentally. A full solution for stresses and strains within the theory of linear elasticity is given. The shape of a bulge in this case is a semi-ellipsoid of revolution. This solution is shown to be in excellent agreement with experimental data produced by monitoring the bulging of a soft solid through a circular opening. The effect of curving the edge on stresses and strains is considered and it is shown that a curve edge remove the singularity at the contact boundary but slightly increases the height of the bulge.