At present, the contact problem between the particle and the plane plate is generally equivalent to the rigid sphere impacting the elastic half space or the elastic sphere impacting the rigid surface. However, in the actual contact process, there will be no rigid body, and both contact and contacted object will deform and absorb energy. The research results obtained from the equivalent of the contact material to the rigid body are less accurate. In order to obtain the accurate mechanical relation and contact response, we took the research of impact between particles and the metal plate as a breakthrough in which the particle is equivalent to an elastic sphere and the metal plate is equivalent to an elastic half space and established the theory of vertical impact contact between elastic sphere and elastic half space by the Hertz contact theory. Through the dynamic simulation of an elastic sphere which has similar properties with rock impacting target in elastic half space in LS-DYNA, the correctness of the established theory and the feasibility of the contact process simulated by LS-DYNA are verified. Based on the established theory and 3D simulation, we studied the influence law of material parameters on the contact response and analyzed the differences of the collision vibration signals caused by the different contact objects. From the above research results, we obtain that the theoretical model is more accurate to predict the maximum contact force and contact displacement in this paper than traditional Hertz theory. And the sphere radius and both contact objects’ elastic modulus have larger influence on the contact response than sphere density, while the Poisson’s ratio has the smallest influence on the contact response results. Different material properties will cause the different contact response. The conclusions of this paper provide a theoretical calculation method for contact and a 3D simulation method for elastic half space and provide theoretical guidance for the differences analysis of the vibration signal.
Impact of an elastic sphere with an elastic half space revisited: Numerical analysis based on the method of dimensionality reduction
