ANZIAM  J.  48 (2007), 449-459
Initial deformation about convex surfaces formed from identical, rough elastic-plastic bodies which approach along their normal at first contact

Graham Weir
  Applied Mathematics
  Industrial Research Limited
  Wellington
  New Zealand
    g.weir@irl.cri.nz


Abstract
The low-velocity impact of two convex surfaces comprised of identical material, which approach each other along the direction of the normal at first contact, and obey a J_2 = k^2 plastic yield condition, is shown for very early times to satisfy the following conditions: the interior surface which separates the two bodies is equivalent to either the locus of points formed by the intersecting curves resulting from moving the two bodies towards each other along their normal; or to the locus of points formed from the level surfaces (suitably parametrized) drawn about each body at the time of first contact. This separating surface lies midway between the geometrical overlap of the two approaching surfaces for times sufficiently short for inertial effects not to significantly affect the approaching velocities.
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