© 1979 by Oxford University Press
THE PROBLEM OF A MOVING RIGID PUNCH ON AN UNLUBRICATED VISCO ELASTIC HALF-PLANE
( Road Safety Section, National Institute for Physical Planning and Construction Research St. Martin's House, Waterloo Road, Dublin 4 )
The problem of an infinitely long rigid punch of uniform cross-section, moving at constant velocity across a viscoelastic half-plane, is considered in the case where frictional forces exist between the punch and the half-plane. Acceleration terms are neglected and linear viscoelastic behaviour is assumed. A complete solution is given for any smooth punch shape and any viscoelastic behaviour of the half-plane, with the simplifying restriction that it behaves similarly under shear and bulk deformation. For the case of a cylindrical punch and viscoelastic behaviour described by a discrete spectrum of decay constants, the solution is examined in detail and numerical results are presented. Because of the difficulty in extracting numerical results from these exact solutions, a general approximate solution is also given, based on the assumption that viscoelastic effects are small compared with elastic effects. This solution is entirely explicit and numerical results may trivially be deduced from it. This work generalizes previous results for the case of lubricated contact (1). The approach adopted here is similar to that in the earlier paper, though certain improvements have been made.