Impact mechanics of elastic bodies with point contact

TL;DR

This paper presents a novel modeling framework transforming impact problems into delay differential equations, enabling analysis of singularities and regularity in elastic body impacts, with applications to beam models.

Contribution

It introduces an exact transformation that converts continuum impact problems into delay differential equations, clarifying the source of singularities and regularity criteria.

Findings

The transformation reveals the source of impact singularities.

Comparison of Euler-Bernoulli and Timoshenko beam models.

A simple criterion for impact regularity is proposed.

Abstract

This paper introduces a modeling framework that is suitable to resolve singularities of impact phenomena encountered in applications. The method involves an exact transformation that turns the continuum, often partial differential equation description of the contact problem into a delay differential equation. The new form of the physical model highlights the source of singularities and suggests a simple criterion for regularity. To contrast singular and regular behavior the impacting Euler-Bernoulli and Timoshenko beam models are compared.