Rubber material is an excellent cushioning material in daily life and engineering applications. In this paper, the influence of rubber combination types and the corrugated surface roughness on cushioning performance are analyzed. By controlling the friction coefficients at different positions, the influence on the cushioning performance is also explored. Solving the numerical instability and energy nonconservation that are prone to occur in collisions is crucial for the accuracy of numerical simulation. The complexities of collision solution are overcome by separating nonlinear factors. The dynamics equation is derived according to the principle of virtual displacement, the geometric nonlinear problem of materials is described by the total Lagrangian formulation. Under the bipotential framework, the boundary nonlinear problem is solved based on the complete contact law. To reduce the solution cost and to improve the numerical accuracy, the prediction-correction step is used to solve the collision force. The bipotential coefficient is automatically updated with time steps, without the need for manual adjustment by users, achieving better convergence. Then, the collision force is substituted into the dynamic equation in the form of external load, which will not increase the degrees of freedom, and has better numerical robustness. In addition, the Newton–Raphson iterative method is embedded in the Tamma–Namburu scheme to solve the material nonlinearity problem and improve the numerical stability. Several numerical examples are presented to demonstrate the effectiveness of the proposed algorithm in the simulation of collision problems. Moreover, the proposed algorithm is proved to be stable and strictly satisfy the law of energy conservation/dissipation. Even for the corrugated surface structure with nonuniform friction, it can also better complete simulating the collision process.