New approach for elastic collisions with singular stress functions

TL;DR

This paper introduces a new mathematical model for elastic collisions involving singular stress functions, validated through numerical results and proven to have unique solutions for initial boundary value problems.

Contribution

It proposes a novel model using beam equations with singular stress functions and establishes existence and uniqueness results for the associated initial boundary value problems.

Findings

Numerical results support the validity of the new model.

Existence and uniqueness of solutions are proven.

The model effectively captures collision phenomena with singular stresses.

Abstract

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.