New approach for elastic collisions with singular stress functions

A collision of a rubber rod to a hard floor is regarded as a simple example of obstacle problems for elastic material. In this article we have proposed a new mathematical model for the collision phenomenon by applying beam equations with singular stress functions, which is investigated in our recent works. As in the works we have established a mathematical method to deal with the singular stress function. Here, we demonstrate the validity of our modeling through observation to the numerical results. Also, we present existence and uniqueness results of the model given as initial boundary value problems.