Guaranteed upper and lower bounds on the uniform load of contact problems in elasticity

TL;DR

This paper develops mathematical models to establish guaranteed upper and lower bounds on the uniform load in contact problems within large strain elasticity, aiding in the analysis of hyperelastic bodies in contact scenarios.

Contribution

It introduces two continuous optimization models with inequality constraints to bound the total strain energy and external load in contact problems, advancing theoretical methods in elasticity.

Findings

Provides rigorous bounds on uniform external load in contact problems.

Models applicable to hyperelastic bodies in unilateral contact.

Enhances understanding of load distribution in large strain elasticity.

Abstract

Two mathematical models are developed within the theoretical framework of large strain elasticity for the determination of upper and lower bounds on the total strain energy of a finitely deformed hyperelastic body in unilateral contact with a rigid surface or with an elastic substrate. The model problems take the form of two continuous optimization problems with inequality constraints, the solutions of which are used to provide an enclosure on the uniform external load acting on the body's surface away from the contact zone.