Couple-Stresses and Singular Stress Concentrations in Elastic Solids

Abstract

Continuum-mechanical theories of the type initiated in rudimentary form by the Cosserats [1], which admit in addition to ordinary stresses the presence of couple-stresses, have—for several and diverse reasons—attracted a renewed and growing interest during recent years. A particularly comprehensive study of the linearized Cosserat theory with constrained rotations for elastic solids was published by Mindlin and Tiersten [2]² in 1962. Since that time various related broader generalizations of conventional elasticity theory have been proposed in investigations that introduce, beyond ordinary and couple-stresses, hyper-stresses of ever increasing complexity and physical elusiveness.

This paper was prepared under Contract Nonr-220 (58) with the Office of Naval Research in Washington, D.C., for presentation at the IUTAM Symposium on the Generalized Cosserat Continuum and the Continuum Theory of Dislocations in Stuttgart and Freudenstadt, August 1967.