A benchmark strain gradient elasticity solution in two-dimensions for verifying computational approaches by means of the finite element method

In elasticity, microstructure-related deviations may be modeled by strain gradient elasticity. For so-called metamaterials, different implementations are possible for solving elasticity problems numerically. Analytical solutions of simple used to verify the numerical approach. We demonstrate such a case in two-dimensional continuum as benchmark computations. As enforces higher regularity conditions displacements, finite element method (FEM), use standard elements is often seen inadequate. piecewise or elementwise continuous elements, we examine remedy correctly simulate implementing two techniques. First, enforce continuity displacement across elements; second, employ mixed where and its solved both unknowns. The results show pros cons each technique. All methods converge monotonically, but more reliable than other one.