Volumetric modification of the Hertz contact problem and its application to the multibody dynamics simulation

A method of computational reduction of an elastic contact model for rigid bodies in frame of the Hertz contact model is considered. An algorithm to transform outer surfaces’ geometric properties to the local contact coordinates system is described. It tracks permanently in time the surfaces of the bodies which are able to contact. An approach to compute the normal elastic force is represented. That one deals with the reduction to one transcendental scalar equation that includes the complete elliptic integrals of the first and second kinds. Simulation of the Hertz model was accelerated essentially due to use of the differential technique to compute the complete elliptic integrals and due to the replacement of the implicit transcendental equation by the differential one. Based on the Hertz contact problem classic solution, an invariant form for the force function which depends on the geometric properties of an intersection for undeformed rigid bodies’ volumes, so-called volumetric model, is proposed then. The resulting force function reduced expression is supposed to be in use in cases when the classical contact theory hypotheses are broken. The expression derived has been applied to several cases of the elastic bodies contacting, and in particular back to the source Hertz model itself.