A method for analyzing three-dimensional dynamic contact problems in visco-elastic media with kinetic and static friction

A solution method is presented for analyzing three-dimensional dynamic contact problems in visco-elastic media with kinetic and static friction considered. The approach is an extension to three dimensions of our previous work where a two-dimensional case was considered. The time integration scheme adopted in the algorithm is explicit and has second-order accuracy. No iteration is performed when dynamic contact is determined and dynamic contact conditions are exactly satisfied. Determining friction in a three-dimensional problem is very different from that in a two-dimensional case. Formulations integrating static and kinetic friction are given. In addition a sub-procedure for calculating the direction of kinetic friction is employed. Finally several numerical examples including one benchmark test and four general problems are given to illustrate the precision and effectiveness of the algorithm.