Return Mapping Procedure for Frictional Force Calculation: Some Insights

The return mapping procedure is studied to gain insights for its numerical implementation to calculate the frictional force during contact analysis. A simple quasistatic truss-wall frictional contact analysis problem is used in the study. The problem has closed-form solutions which provide exact target solutions for a numerical algorithm. The penalty method and a true augmented Lagrangian method that automatically determines an accurate value of the penalty parameter are employed in the numerical study. It is determined that the return mapping procedure is not applicable unless the contacting node is constrained to stay at the initial contact point, and the total normal reaction force, the tangential reaction force and the friction limit have been determined. If these requirements are not met, inaccurate or even incorrect solutions are obtained. This characteristic of the procedure is studied by solving slip and stick cases with several different load increments. It is concluded that the return mapping procedure for friction force calculation should be implemented carefully to obtain accurate solutions for contact analysis problems.