Contact Mechanics via FEM and BEM for Multibody Dynamics Modeling

Robotic systems and their mechanism assemblies are unprecedentedly leveraged in current NASA programs for on-orbit operations and space explorations in the solar system and its other planets, and the stellar spaces beyond. These robotic systems are operating in harsh and hostile environments which can potentially damage mission critical components and jeopardize mission success. It is well-known that high-quality multibody dynamics predictions of contact interaction loads are vital to achieve the optimal robotic and mechanism structural designs with reduced weight. It is also widely recognized that the well-established predictive methodology is one of the key approaches to accurately characterize contact modeling parameters for multibody dynamics predictions. This first portion of the paper focuses on deriving the contact coefficient and exponent, and the model cross validation of multibody dynamics contact loads via finite element nonlinear contact analysis. These finite element results are next compared to solutions from Hertzian contact theory and boundary element contact analysis. This comparison suggests that the boundary element method can provide an attractive approach to study a range of problems in contact mechanics. Interestingly, all these classical models show the location of peak effective stress to be inside the bodies, removed from the contact surface, yet surface failures often occur in such problems. To address this issue, a BEM-based size-dependent contact mechanics formulation is then presented utilizing couple-stress theory and results from a model problem are provided that predict a transition of the peak effective stress to the surface, depending upon the couple stress length scale material parameter.