Finite element analysis of plane strain solids in strain-gradient elasticity

In the current contribution, plane strain deformation of the strain-gradient solids is addressed using the finite element method. To this end, 4-node quadrilateral elements based on the Hermite shape functions explicitly are developed for predicting the response of two-dimensional solids in small scales. The principle of virtual work is applied to derive the weak form of the equilibrium static equations. In addition, the geometry and variables are interpolated adopting different shape functions resulting in the subparametric elements. For showing the performance and accuracy of the novel elements, some known problems in plane strain elasticity are solved, and there is a comparison between the classical and strain-gradient solutions.