Rocking dynamics of a planar rectangular block on a rigid surface

The motion of a rigid rectangular block rocking on a rigid surface involves several motion modes, including rotation around the base corner of the block, point or surface impacts between the block and the surface, and possible uplift following an impact event. With the exception of the surface impact, all other motion states can be easily simulated using the conventional classical mechanics theory. However, the surface impact is closely related to the rapid evolution of the stress field caused by the relative motion of the contact interface, making the associated dynamics relatively complex. Here, we report a novel model of the surface impact that is established by carefully considering the effects from the interface separation and the stick–slip transition of the Coulomb’s friction. This model provides a set of first-order differential equations with respect to the stress impulse, for which numerical methods can be used to obtain the output of the surface impact. In particular, the model can avoid the use of small variables, such as the time of impact and the length of local deformation, thus it is highly beneficial for numerical calculations. We validate this model using the experimental data reported in the existing literature, and then numerically investigate how the material properties of the contact interface affect the rocking motion.