Spherical to Planar Formulation

This formulation is used to model contact between a spherical source and a planar surface of a rigid body. The planar surface is assumed to be infinitely long, defined by a point on the surface and a surface normal. The gap between the spherical object and the planar surface is computed by finding the shortest distance between source center and the plane. If the gap is smaller than zero, a penalty force is applied to prevent penetration. The gap is defined as

Here, d is the shortest distance between the source center and the destination plane, and rs is the radius of the source sphere.

Figure 3-29: Rigid body contact between a spherical source and a planar destination.

The shortest distance between the spherical source and the planar destination (d) is the projection of the distance between source center and a point located on the plane in the direction of the surface normal. It is calculated as

Here, Xsrc and Xdst are the undeformed locations of the source center and a point on the destination plane, and usrc and udst are the corresponding displacements. nd is the outward normal of the destination plane.

The direction vector from the source center to the contact point on destination plane (ec) is defined as

The contact force for the penalty and the penalty dynamic methods are same as in the Spherical to Spherical Formulation.