Comparison of gradient elasticity models for the bending of micromaterials

[Display omitted] •A modified strain gradient- and micropolar continuum theory is presented.•An analytical and numerical solution is derived from the equilibrium formulations.•The finite element variational formulations are solved within the FEniCS project.•AFM bending experiments with epoxy and SU-8 microbeams show a positive size effect.•The material length scale parameters are fitted in a least square approach. In the context of static elasticity theory for isotropic materials and small deformations, two continuum mechanical theories of higher order are considered. Thinking of generalized continua, a modification/simplification of the strain gradient- and the micropolar theory is shown. An analytical solution strategy is derived for each extended theory using the Euler–Bernoulli beam assumptions. A numerical solution of the resultant differential equations of fourth order, derived from the equilibrium formulation, is realized using a finite element implementation in an open source FE environment. In AFM experiments with microbeams, made of epoxy and of the polymer SU-8, force and deflection data is recorded. As a result, positive size effects depending on thickness are observed and quantified for the microbeams. The material length scale parameters and the elastic moduli are fitted with a least square approach and compared to literature values.