Finite Element Technology for Gradient Elastic Fracture Mechanics

In this paper a unified FE methodology based on gradient-elasticity is presented, including Gauss integration rules and error estimation. Applying the proposed methodology to classical elasticity problems, it has been found that, the linear elements show a convergence rate higher than the theoretical one, for what concerns the stresses. This means that, accepting a small loss in the accuracy of the solution, the use of linear elements, instead of quadratic elements, leads to a solution characterised by a convergence rate higher than the theoretical one along with a sensible reduction in the computational cost. This technology has many possible applications such as the simulation of fatigue failure and bone regeneration.