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184.108.40.206 Slip Kinematics
During contact slip, and move relative to one another as their configurations evolve. Performing a contact analysis requires mapping points between these surfaces. For the spatial position of each material point on the primary surface, we define the intersection point on the secondary surface as the point intersected by a ray directed along the unit outward normal to the primary surface , where the gap function is defined to be positive when the surfaces and are separated, and negative when they penetrate, The ray intersects at a spatial position through which different material points identified by parametric coordinates may convect. Computationally, this ray intersection and contact detection is performed with an Octree method .
The projection approach of eq.(220.127.116.11-1), described in our previous study  and commonly termed ray-tracing , can be characterized as an inverse projection relative to the classical contact mechanics approach used for NTS contact [66, 111]. Although the definition of this projection and its associated gap function is not new, it has typically been employed mostly for mortar contact (e.g. as in Tur et al. ). The benefits associated with a projection method such as eq.(18.104.22.168-1) for non-mortar contact have been developed in detail . Here it suffices to note that avoiding a reliance on secondary surface normal vectors eliminates many contact-searching difficulties that plague NTS algorithms , and also serves to greatly reduce the complexity of the linearizations and the resulting stiffness matrices.