Finite-element analysis of polyhedra under point and line forces in second-strain gradient elasticity

In this paper, a finite-element implementation of linear second-strain gradient elasticity is introduced based on a HellingerReissner variational principle in order to use standard finite-element methods. Displacement boundary conditions are applied to one or more vertices of different polyhedrons. As a result, a smooth deformation around deformed vertices of the polyhedrons can be observed, in contrast to the appearance of singularities in the first-order theory, i.e., a Cauchy continuum, where strain singularities appear in such cases.