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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 schemearXiv:1711.06352v1 fatcat:txnak6cgwzb47h47za7aeqyiky