Large deformations of gradient elastic beams

TL;DR

This paper develops a fully nonlinear strain-gradient elasticity theory for beams, incorporating large deformations and new degrees of freedom, and demonstrates its application through finite element analysis and magnetic body simulations.

Contribution

It introduces a novel nonlinear strain-gradient elasticity theory for beams and implements a finite element method to analyze large deformations and magnetic effects.

Findings

Strain gradient effects significantly influence large deformation behavior.

Finite element model effectively captures nonlinear geometrical effects.

Magnetic fields impact the deformation of magnetized bodies.

Abstract

Budiansky's nonlinear shell theory is particularized to a 2D setting, and thereupon generalized to a fully nonlinear, statically and kinematically exact, theory of strain-gradient elasticity of beams. The governing equations are displayed in their weak and strong forms. A suitable finite element is used to accommodate the new degrees of freedom emanating from the theory and several numerical examples with large geometrical nonlinearities are displayed showing the relative influence of the strain gradient. The numerical apparatus is then applied to permanently magnetized bodies under the action of external magnetic fields.