Discretization of Gradient Elasticity Problems Using C1 Finite Elements

Strain-gradient theories have been used to model a variety of problems (such as elastic deformation, fracture behavior and plasticity) where size effect is of importance. Their use with the finite element method, however, has the drawback that specially designed elements are needed to obtain correct results. This work presents an overview of the use of elements with C-1 continuous interpolation for strain-gradient models, using gradient elasticity as an example. After showing how the C-1 requirement arises and giving details concerning the implementation of specific elements, a theoretical comparison is made between elements based on this approach and elements resulting from the use of some alternative formulations.