3D strain gradient elasticity: Variational formulations, isogeometric analysis and model peculiarities

This article investigates the theoretical and numerical analysis as well applications of three-dimensional theory first strain gradient elasticity. The corresponding continuous discrete variational formulations are established with error estimates stemming from continuity coercivity within a Sobolev space framework. An implementation isogeometric Ritz–Galerkin method is provided open-source software package GeoPDEs. A thorough convergence accomplished for confirming verifying implementation. Lastly, set model comparisons presented revealing demonstrating some essential peculiarities: (1) 1D Timoshenko beam essentially closer to 3D than Euler–Bernoulli model; (2) models agree on strong size effect typical microstructural microarchitectural structures; (3) stress singularities reentrant corners disappear in computational homogenization methodologies applied examples beams shown possess disadvantages that future research should focus on.