English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This study undertakes the mathematical modelling and numerical analysis ofdislocations within the framework of differential geometry. The fundamentalconfigurations, i.e. reference, intermediate and current configurations, areexpressed as the Riemann-Cartan manifold, which equips the Riemannian metricand Weitzenb\"ock connection. The torsion 2-form on the intermediateconfiguration is obtained through the Hodge duality of the dislocation densityand the corresponding bundle isomorphism is subjected to the Helmholtzdecomposition. This analysis introduces the boundary condition for plasticdeformation. Cartan first structure equation and stress equilibrium equationare solved numerically using weak form variational expressions and isogeometricanalysis. The numerical analysis carried out for this study reveals thedistribution of plastic deformation fields around screw and edge dislocationsfor the first time. It also demonstrates stress fields around dislocations ofwhich the distant fields show full agreement with the classical Volterratheory, while at the same time eliminating the singularity otherwise introducedat the dislocation by classical methods. The stress fields include severalcharacteristic features due to the geometrical nonlinearity included therein.We also demonstrate that free surfaces affect both plastic and elasticdeformation, but in different ways. The mathematical framework of this study isapplicable to an arbitrary configuration of dislocations.

Geometrical Modelling and Numerical Analysis of Dislocaion Mechanics