Numerical simulations of classical problems in two-dimensional linear second gradient elasticity

A two-dimensional solid consisting of a linear elastic isotropic material is considerd in this talk. The strain energy is expressed as a function of the strain and of the gradient of strain. The balance equations and the boundary conditions have been used and numerically simulated for those classical problems for which an analytical solution is available in the literature. Numerical simulations have been developed with a commercial code and a perfect overlap between the results and the analytical solution has been found. The role of external edge double forces and external wedge forces has also been analysed. We finally investigate a mesh-size independency of second gradient numerical solutions with respect to the classical first gradient one.