A Shell Frictionally Coupled to an Elastic Foundation and a Comparison Against the Two-Body Coulomb's Law of Static Friction

TL;DR

This paper develops a new displacement-based friction law for a shell on an elastic foundation and compares it with Coulomb's law, providing the first such derivation and analysis for a 3D contact problem with friction.

Contribution

It introduces a novel displacement-based static-friction law for shells on elastic foundations and compares it with Coulomb's law through numerical analysis.

Findings

High Young's modulus or Poisson's ratio improves model agreement.

High friction coefficient or radius of curvature enhances model accuracy.

First derivation of displacement-based friction law for 3D shell contact problems.

Abstract

In this article, we derive a model for a shell that is frictionally coupled to an elastic foundation. We use Kikuchi and Oden's model for Coulomb's law of static friction to derive a displacement-based static-friction law for a shell on an elastic foundation model, and we prove the existence and the uniqueness of solutions with the aid of the work of Kinderlehrer and Stampacchia. For numerical analysis, we modify Kikuchi and Oden's model for Coulomb's law of static friction to model a full two-body contact problem in curvilinear coordinates. Our numerical results indicate that if the shell has a relatively high Young's modulus or has a relatively high Poisson's ratio, and the contact region has a high coefficient of friction or has a high radius of curvature, then the displacement field of the foundation predicted by both models are in better agreement. As far as we are aware, this is the first derivation of a displacement-based friction law and a two-body 3D elasticity contact problem with friction in the literature.