Edge Contact Forces and Quasi-Balanced Power

TL;DR

This paper introduces the concept of quasi-balanced contact force distribution in continuous media with edge forces, proving conjectures on force representation and extending classical theorems to include higher-order stress tensors.

Contribution

It generalizes the Hamel-Noll theorem and provides a new representation theorem involving second and third order stress tensors for media with contact edge forces.

Findings

Proves conjectures by Noll and Virga on contact edge force representation

Extends the Cauchy postulate to include edge forces and higher-order stresses

Establishes a relationship between interstitial working and contact edge forces

Abstract

We consider continuous media in which contact edge forces are present. Introducing the notion of quasi-balanced contact force distribution, we are able to prove the conjectures by Noll and Virga [1] concerning the representation of contact edge forces. We generalize the Hamel-Noll theorem on the Cauchy postulate. Then we adapt the celebrated tetrahedron construction of Cauchy in order to obtain a representation theorem for stress states. In fact, we show that two stress tensors of order two and three are necessary for such a representation. Moreover we f nd the relationship between the notion of interstitial working introduced by Dunn and Serrin [2] and the notion of contact edge force.