Unified finite element methodology for gradient elasticity

•Finite elements for gradient elasticity.•Removal of singularities.•Optimal element size for gradient elasticity.

In this paper a unified finite element methodology based on gradient-elasticity is proposed for both two- and three-dimensional problems, along with some considerations about the best integration rules to be used and a comprehensive convergence study. From the convergence study it has emerged that for both two and three-dimensional problems, the implemented elements show a convergence rate virtually equal to the corresponding theoretical values. Recommendations on optimal element size are also provided. Furthermore, the ability of the proposed methodology to remove singularities in statics has been demonstrated through a couple of examples, in both two and three dimensions.