The Dynamics of a Detaching Rigid Body

Consider a rigid block perfectly bonded to an elastic half-space. Suppose the block is impulsively struck so that it starts to oscillate with respect to its initial position. In the absence of dissipation, the motion will be harmonic. However, it may happen that the displacement becomes so large that the bond between the block and the half-space will begin to rupture. In this case, the subsequent motion of the rigid body is described by a second-order nonlinear ordinary differential equation, derived from the principle of conservation of mechanical energy. There is a critical bond length, with respect to a pre-assigned length scale. Below it the block will undergo harmonic motion with no rupture at low impact or eventual catastrophic rupture and instantaneous detachment at high impact. Above it the block will also undergo harmonic motion with no rupture at low impact. At very high impact, the block will undergo a period of controlled rupture ending with catastrophic rupture and instantaneous detachment. There is also an intermediate range of impacts which result in a period of controlled partial rupture after which rupture ceases and periodic motion ensues.