  Methods for finding the optimal choices of the applied remote loads -- the
applied normal force, moment, shear force and remote bulk stresses -- needed to
solve frictional contact problems in partial-slip using half-plane theory are
derived by using data from contacts analysed by the finite element method.
While the normal and shear forces and moment are readily found from equilibrium
considerations, in order to determine the bulk stresses we must exploit details
of the traction ratio and the direct strain within the contact, both of which
are readily extracted from simulations. These contact loads enable the
formulation of an equivalent half-plane problem for the contact, which can be
used to determine much more precise estimates of the slip-zone sizes than are
obtainable from direct use of frictional finite element analysis, as aggregated
data from the finite element output is employed, and the half-plane analysis
will add precision in terms of satisfaction of the laws of frictional slip and
stick.
