Contact is the most abundant phenomena in the field of multi-body dynamics, experienced when two or more bodies come in close vicinity to each other. During contact, one body virtually penetrates within other and therefore is subjected to a large impulsive force due to the deformation; this is the essence of the compliance based models. Subsequently, different compliance models were proposed, each having a different formulation for the impulsive force variation, which is always a function of time and deformation. A novel multi-linear compliance model, calculated on the basis of the Poisson’s law, is introduced in this work. The responses of all the available compliance models have been critically reviewed in previous studies and using the same study and the observed significant models, a comparative study is presented in this work for establishing the proposed model. A few significant models were selected according to the minimum amount of error induced by each while estimating the coefficient of restitution, impulse, and dissipating energy.

The contact force-penetration relationship in the compression phase and restitution phase are assumed to be linear with a sharp jump at their transition. The slope of the compression phase of the force-displacement diagram of the non-dimensional system is exactly as desired (1+coefficient of restitution) and moreover, the slope of the restitution phase is equal to the coefficient of restitution helping in retrieving the exact coefficient of restitution pertaining in the pre-impact condition. Also, the post-impact coefficient of restitution, impulse, and dissipating energy are exactly accurate, having 0% error, in accordance with that of the stereo-mechanical model, for the full range of the co-efficient of restitution.

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