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.

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• Presentation Conference Type: Conference Paper (unpublished)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
• 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