Implicit gradient elasticity

A new formulation of gradient elasticity is derived and implemented. Padé approximations are used to introduce an implicit relation between non-local strains and displacements. As a result, the finite element interpolation requires only C0-continuous (rather than C1-continuous) shape functions. The underlying energy functional is presented and it is found that the present formulation is of the mixed type, whereby the non-local strains act as the primary unknowns and the displacements as the auxiliary unknowns. The implications on the interpolation are studied. Finally, the influence of the additional length scale parameter on the global response is assessed