Work

Saint-Venant torsion of exponentially graded micropolar circular and annular bars

Year: 2026

Type: article

Abstract: In this paper, we consider Saint-Venant torsion of a functionally graded micropolar (Cosserat) beam, where the elastic moduli vary within the plane of the beam cross-section. We state a well-posedness result for the corresponding Neumann boundary-value problem in the weak Sobolev-space setting and show the existence and uniqueness of the solution up to the natural rigid micropolar mode. In view of symmetry, the circular and annular cases reduce to an ordinary differential equation for the radial amplitude. Numerical examples are presented for the stress and couple-stress fields and for the torsional rigidity. The characteristic micropolar length associated with the chosen material parameters is compared with the size of the cross-section, and the classical limit is recovered as a special case.

Source: Mathematics and Mechanics of Solids

DOI: 10.1177/10812865261446546

Authors: Jivan Garcha, Stanislav Potapenko

Institution: University of Waterloo

Language: English

Topic: Nonlocal and gradient elasticity in micro/nano structures

Subfield: Materials Chemistry

Field: Materials Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,150

Funder: Natural Sciences and Engineering Research Council of Canada