A geometrically-exact Finite Element Method for micropolar continua with finite deformations

O'Hare, Ted J.; Gourgiotis, Panos A.; Coombs, William M.; Augarde, Charles E.

A geometrically-exact Finite Element Method for micropolar continua with finite deformations

O'Hare, Ted J.; Gourgiotis, Panos A.; Coombs, William M.; Augarde, Charles E.

Authors

Ted O'Hare ted.o'hare@durham.ac.uk
PGR Student Doctor of Philosophy

Panos A. Gourgiotis

Professor William Coombs w.m.coombs@durham.ac.uk
Professor

Professor Charles Augarde charles.augarde@durham.ac.uk
Head Of Department

Abstract

Micropolar theory is a weakly non-local higher-order continuum theory based on the inclusion of independent (micro-)rotational degrees of freedom. Subsequent introduction of couple-stresses and an internal length scale mean the micropolar continuum is therefore capable of modelling size effects. This paper proposes a non-linear Finite Element Method based on the spatial micropolar equilibrium equations, but using the classical linear micropolar constitutive laws defined in the reference configuration. The method is verified rigorously with the Method of Manufactured Solutions, and quadratic Newton-Raphson convergence of the minimised residuals is demonstrated.

Citation

O'Hare, T. J., Gourgiotis, P. A., Coombs, W. M., & Augarde, C. E. (2023, April). A geometrically-exact Finite Element Method for micropolar continua with finite deformations. Paper presented at UKACM 2023, University of Warwick, Coventry, UK

Presentation Conference Type	Conference Paper (unpublished)
Conference Name	UKACM 2023
Conference Location	University of Warwick, Coventry, UK
Start Date	Apr 19, 2023
End Date	Apr 21, 2023
Deposit Date	Jul 3, 2023
Publicly Available Date	Jul 4, 2023
Public URL	https://durham-repository.worktribe.com/output/1133673
Publisher URL	https://sites.google.com/view/ukacm2023conference

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For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising.