Time-integration for lumped parameter systems obeying implicit Bingham-Kelvin constitutive models is studied. The governing system of equations describing the lumped parameter system is a non-linear differential-algebraic equation and needs to be solved numerically. The response of this system is non-smooth and the kinematic variables can not be written in terms of the dynamic variables, explicitly. To gain insight into numerical time-integration of this system, a new time-integration scheme

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... ed on the trapezoidal method is derived. This method relies on two independent parameters to adjust for damping and is stable. Numerical examples showcase the performance of the proposed time-integration method and compare it to a benchmark algorithm. Under this scheme, implicit-explicit integration of the governing equations is possible. Using this new method, the limitations of the trapezoidal time-integration methods when applied to a non-smooth differential-algebraic equation are highlighted.