Jump conditions for thin bodies from an action principle

Thin, flexible bodies such as strings, sheets, and rods often sustain kinky geometric features, or experience discontinuous contact forces in their interactions with obstacles. The physics of dynamic and static versions of these phenomena differ. Kink/shock propagation, impact, peeling, unwrapping, tearing and cracking all occur at geometric locations in a body that do not correspond to material points. I will discuss how the jump conditions for momentum and energy across such moving discontinuities may be derived from an action principle for an extended body with time-dependent, non-material boundaries.