Geometry and fragmentation of soft brittle impacted bodies

Abstract

Some mechanisms of shape selection and fragmentation patterns of impacted or strongly solicited elastic bodies of simple geometry are reviewed. By strongly solicited we mean objects whose shape undergoes order one deformations, a situation typically encountered with soft bodies, possibly leading to fracture. We are particularly interested in the development of elastic instabilities and their relevance to interpret fragmentation experiments. We review how the shape of elastic slender objects like rods and membranes is affected by buckling instabilities when impacted, and how brittle sheets break through a well-defined pattern of cracks. Central to the understanding of this pattern is the concept of optimal fragmentation. The crack pattern of thin elastic bodies, including the diverging concertina tearing, the perforation of a thin sheet by a cone and the star shape pattern of impacted windows are optimal objects, ruled by a balance between stored elastic energy and surface creation energy.