Simulating Contact and Friction within the Discrete Body Dynamics Formalism

Abstract Contact and friction significantly influence the dynamics of mechanical systems. This study presents an approach for modeling contact and friction forces within the discrete body dynamics (DBD) framework, which solves the equations of motion as ordinary differential equations by replacing kinematic constraints with compliant elements. This formulation preserves the main advantages of DBD, body-wise force evaluation, and efficient element-wise computations, thereby avoiding costly matrix decompositions. The proposed model represents both normal contact and tangential friction forces using spring–damper elements defined between dynamically generated virtual contact points, so that relative tangential displacement reflects slip-related motion. The friction coefficient is defined over the entire range of motion as a function of tangential displacement and is governed by physically measurable parameters: static and kinetic friction coefficients, presliding displacement, and critical displacement. Unlike conventional regularized Coulomb models that depend on relative velocity, the present formulation relies on relative displacement and remains continuous and differentiable, ensuring stable behavior at zero velocity and during sticking phases. The method is assessed in three representative case studies: a box on an inclined plane (stiction and frictional lag), a slider–rod interaction (jamming), and a spring-driven box on a plane (stick–slip). Results are compared with simulations performed in a commercial multibody dynamics solver that uses a velocity-dependent friction law. In these comparisons, the DBD-based model maintains perfect stiction when expected, reproduces presliding and a delayed build-up of sliding velocity consistent with a frictional-lag-type response, captures the onset of jamming in the slider–rod system, and generates sustained stick–slip cycles with clear stick intervals. An additional application-oriented cart–obstacle case study is included to demonstrate the sphere-to-sphere contact/friction formulation. Overall, the proposed approach provides a simple and computationally efficient tool for simulating friction-dominated multibody systems, and, while naturally aligned with DBD, its displacement-based friction formulation can be adapted for use within conventional multibody dynamics methods.