A simple and robust Coulomb frictional algorithm based on 3 additional degrees-of-freedom and smoothing

摘要

Physical accuracy of discretization methods for frictional contact mechanics originates from precise representation of discontinuous frictional and normal interaction laws, appropriate time-integration for velocity and acceleration (which is unbounded at impacting points) and also contact discretization techniques. In terms of discontinuous behavior in the presence of inertia, two themes are of concern: the normal interaction (i.e. impact) and the jumps in tangential and normal directions arising from high frictional values. In terms of normal and tangential behavior, we propose a simple and effective algorithm, which is based on regularization of the original problem and then performing successive solutions within the same time step while reducing the smoothing parameters and hence approximating the original problem. This allows problems with impact and stick-slip behavior to be solved with an implicit code based on Newton-Raphson iterations. It is specially convenient to extend static software to the dynamic case with frictional contact. A worked example is presented, exhibiting near-insensitivity to time-step. Two complete beam verification tests are shown. An extension to node-to-face form in 3D is also presented.