Enhanced finite element formulation incorporating stress jumps and interface behaviour in structures with embedded linear inclusions

When linear inclusions are embedded into a matrix, a perturbation is introduced in the boundary value problem written at the macroscale. Such inhomogeneity can provoke sharp gradients in the solution and a correct evaluation of the interface stress state reveals necessary when localised material degradations can lead to global failure mechanisms. In order to account for such refined description in large scale structural problems, a novel enhanced implicit finite element formulation is presented. The standard displacement approximation is improved by means of a kinematic enrichment aimed at reproducing the local interaction between the matrix and the inclusion. The microscale interface behaviour can then be directly evaluated from the stress jump arising in the bulk. From a computational point of view, this translates in solving an additional local equilibrium equation. The static boundary conditions at the inclusion ends are thus exactly verified and a good precision is achieved with minimal meshing effort and code modifications. The proposed model is applied to elementary and structural examples involving singularities and it is compared to other modelling strategies with focus both on global and local quantities as well on the convergence properties and corresponding CPU times of the approximated solution.