On the contact detection for contact-impact analysis in multibody systems

One of the most important and complex parts of the simulation of multibody systems with contact-impact involves the detection of the precise instant of impact. In general, the periods of contact are very small and, therefore, the selection of the time step for the integration of the time derivatives of the state variables plays a crucial role in the dynamics of multibody systems. The conservative approach is to use very small time steps throughout the analysis. However, this solution is not efficient from the computational view point. When variable time-step integration algorithms are used and the preimpact dynamics does not involve high-frequencies, the integration algorithms may use larger time steps and the contact between two surfaces may start with initial penetrations that are artificially high. This fact leads either to a stall of the integration algorithm or to contact forces that are physically impossible which, in turn, lead to post-impact dynamics that is unrelated to the physical problem. The main purpose of this work is to present a general and comprehensive approach to automatically adjust the time step, in variable time-step integration algorithms, in the vicinity of contact of multibody systems. The proposed methodology ensures that for any impact in a multibody system the time step of the integration is such that any initial penetration is below any prescribed threshold. In the case of the start of contact, and after a time step is complete, the numerical error control of the selected integration algorithm is forced to handle the physical criteria to accept/reject time steps in equal terms with the numerical error control that it normally uses. The main features of this approach are the simplicity of its computational implementation, its good computational efficiency, and its ability to deal with the transitions between non-contact and contact situations in multibody dynamics. A demonstration case provides the results that support the discussion and show the validity of the proposed methodology.