Gradient-enriched finite element methodology for axisymmetric problems

Due to the axisymmetric nature of many engineering problems, bi-dimensional axisymmetric finite elements play an important role in the numerical analysis of structures, as well as advanced technology micro/nano-components and devices (nano-tubes, nano-wires, micro-/nano-pillars, micro-electrodes). In this paper, a straightforward (Formula presented.)-continuous gradient-enriched finite element methodology is proposed for the solution of axisymmetric geometries, including both axisymmetric and non-axisymmetric loads. Considerations about the best integration rules and an exhaustive convergence study are also provided along with guidances on optimal element size. Moreover, by applying the present methodology to cylindrical bars characterised by a circumferential sharp crack, the ability of the present methodology to remove singularities from the stress field has been shown under axial, bending, and torsional loading conditions. Some preliminary results, obtained by applying the proposed methodology to notched cylindrical bars, are also presented, highlighting the accuracy of the methodology in the static and fatigue assessment of notched components, for both brittle and ductile materials. Finally, the proposed methodology has been applied to model the unit cell of the anode of Li-ion batteries showing the ability of the methodology to account for size effects.