The plane problem of the impact of a rigid body on a half-space modelled by a Cosserat medium

The formulation and method of solving of a plane time-varying contact problem with moving boundaries is developed for an absolutely rigid impactor and a half-space filled with a Cosserat medium. A new function, the surface influence function for a Cosserat medium, is constructed and investigated. An original algorithm for constructing it, based on the small-parameter method in conjunction with a simultaneous Fourier–Laplace integral transformation, is developed and implemented. The quantitative and qualitative differences between the influence function constructed and the well-known solution of the plane Lamb problem for an elastic half-space are indicated.