Mathematical models for characterizing non-Hertzian contacts

•A concept of simulating the contact with a set of independent Kelvin-Voigt elements was tested.•Analytical contact models were developed for conformal, soft and viscoelastic contacts.•The proposed contact force approaches resolved the discontinuity issue with Kelvin-Voigt model.•The developed contact constitute laws had nonlinear deformation and damping force terms. In soft and conformal contacts, the assumptions made in the Hertz theory are violated to some extent, leading to inaccurate outcomes. An alternative contact approach is the Kelvin-Voigt model that suffers from a discontinuity existing in its constitutive law. The finite element method is also expensive computationally to be used for contact simulation. The present study introduces a concept to simulate either soft or conformal contacts and develops mathematically closed-form contact models, which are nonlinear, promising, and easy-to-implement while resolving the discontinuity issue with the Kelvin-Voigt model. Two demonstrative applications, i.e. a ball-on-plate contact and a spherical joint, are considered. The developed approaches are integrated into forward dynamics algorithms to be assessed and compared against available contact approaches in the literature. Moreover, a finite element analysis is constructed for comparison purposes. It can be concluded that the proposed contact models are robust and easy-to-implement for non-Hertzian soft and conformal contacts.