Stopping of a solid object in an elasto viscoplastic material

Abstract

The impact and stopping of a spherical object freely falling onto the surface of an elasto-viscoplastic material (an aqueous solution of Carbopol® Ultrez 10) is studied both experimentally and theoretically. Accurate measurements of the instantaneous position of the centre of mass of the falling object allow one to calculate both the speed and acceleration of the object. To rationalise the experimental results we resort to a simple 1−D toy model initially proposed by Putz and Burghelea [1]. At early stages of the motion, the deformation of the gel is dominated by viscous effects, the model by Putz and Burghelea reduces to the well-known Herschel–Bulkley relationship and an equation of motion for the sphere can be derived. By comparing the measured trajectories, speeds and accelerations with the “viscous” analytical solution one may estimate the yield stress, the consistency and the power law index. After long enough times, the spherical object oscillates around its final stopping position and the deformation of the material is no longer viscous but elastic. Within this second asymptotic limit the model by Putz and Burghelea reduces to the Hooke’s law and once more an analytical solution for the equation of motion may be readily obtained. By measuring the period of the oscillatory motion observed during this regime one may estimate the elastic modulus of the gel.