Extension of dashpot model with elastoplastic deformation and rough surface in impact behavior

This investigation proposes a more general dashpot model with elastoplastic deformation and rough surface based on the fractal theory in allusion to the rough surface with fractal characteristic. Firstly, the rough surface of the contact body is depicted using the Weierstrass-Mandelbrot (W-M) function. The entire contact process of a single asperity is divided into the elastic, elastoplastic, and plastic phases, which are assumed to be governed by the Ma-Liu model. The contact stiffness coefficients between two rough surfaces at different contact phases can be derived according to the Ma-Liu model and the size distribution function of the Majumdar and Bhushan (M-B) model. Secondly, based on the energy and momentum conservation during impact, the corresponding hysteresis damping factors at different contact phases can be derived. A continuous dashpot model can be formulated by the different stiffness coefficients in conjunction with the hysteresis damping factors in the different contact phases. The effect of the fractal parameters on the contact stiffness coefficients and novel dashpot model is implemented, which illustrates that the proposed dashpot model can reproduce the available dashpot models by regulating the fractal parameters. Finally, the simulation shows that the proposed dashpot model inherits the continuity of the Ma-Liu model and is more accurate than the available dashpot models, and the energy dissipation during impact is validated to be independent of the roughness of the contact surface. Moreover, its effectiveness and correctness are verified by the experimental data from a vertical granular chain. Simultaneously, the simulation shows that the new dashpot model can accurately depict the solitary wave propagation, and proves that the effect of the roughness cannot be ignored in the impact behavior.