Improved friction model applied to plane sliding connections by a large deformation FEM formulation

Friction is an important source of dissipation in dynamical systems. Properly considering it in the numerical model is fundamental to obtain stable and representative responses in structures and mechanisms. This is especially significant for the well-known Coulomb model due to discontinuity in force when stick-slip transition occurs. In this work an improved friction force model is proposed to smooth the force transition at null velocity, with an additional parameter obtained from the own system state. The improved model is employed in sliding connections of plane frames finite elements. A total Lagrangian Finite Element Method (FEM) formulation based on a positional description of the motion is employed. Using a variational principle, frictional dissipation is added to the total mechanical energy to develop the equations of motion. The resulting nonlinear equations are solved by the Newton-Raphson method accounting for the friction force update in the iterative process. Examples are presented to show the formulation effectiveness and possibilities in simulating dynamical systems that present the stick-slip effect.

Automated summary

Friction is a crucial factor in dissipative dynamical systems, and its accurate consideration in numerical models is essential for obtaining stable and representative responses in structures and mechanisms. This paper proposes an improved friction force model that smooths the force transition at zero velocity by incorporating an additional parameter based on the system state. The model is applied to sliding connections in plane frames finite elements. A total Lagrangian Finite Element Method (FEM) formulation is employed, where frictional dissipation is incorporated into the equations of motion through a variational principle. The resulting nonlinear equations are solved using the Newton-Raphson method, accounting for the update of friction forces during the iterative process. Examples are provided to demonstrate the effectiveness of the formulation in simulating dynamical systems with stick-slip effects.