Error estimation and mesh adaptation for Signorini–Coulomb problems using E-FEM

An error estimator for modeling contact and friction problems is presented in this paper. This estimator is obtained by solving two contact with friction problems: the first problem is formulated, as classically, in terms of displacement fields, and the second one is obtained using a stress field formulation. With this approach, it is necessary to develop a stress (equilibrium) finite element method such as that presented in previous studies. This estimator is similar to that discussed in [11]. The efficiency of the error estimator is tested by applying it to some examples. Due to the non-associativity of the friction problem, the present estimator is not strictly a majorant of the error. However, in the case of the examples studied here, the value of the estimator was approximately that of a given reference error. A refinement strategy was therefore developed. This strategy is very robust, even in the presence of stress singularities. With a sufficiently fine initial mesh, this method was found to be very efficient.