On the efficiency of the iterative coupling FEM–BEM for solving the elasto-plastic problems

• An iterative coupling FEM–BEM for solving elastoplastic problems has been developed.
• This coupling approach preserves the nature of FEM and BEM.
• Several elastoplastic problems have been analyzed to establish their accuracy.
• A good agreement has been found between the coupled FEM–BEM and the other solutions.

In this paper an interface relaxation finite element-boundary element coupling method has been developed to analyze the non-linear elastoplastic problems of solid mechanics. While finite element method (FEM) is used to model the nonlinear sub-region, the remainder which is linear elastic is discretized with boundary element method (BEM). In order to perform the coupling of the two numerical methods, separate computing for each sub-region and successive renewal of the variables on the interface between the two sub-regions is performed through an iterative procedure until the final convergence is achieved. To speed up the rate at which the algorithm converges, a relaxation of the displacement data at the interface is employed. This iterative scheme preserves the nature of the FEM and the BEM and there is no need to combine their coefficient matrices, which allows us to use different software packages for solving respective sub-problems. Hence, it is a physically based method and easy to implement. Furthermore, since the analysis of elastoplastic problems are non-linear and involves iterative solution, the reduced size of the final system of equations introduced by combining the two methods is very advantageous. The coupling FEM–BEM approach was implemented by using readily computer programs for an elastoplastic analysis using the FEM and an elastic analysis using the BEM and was tested through several examples. The obtained results were compared to the experimental data, the conventional methods FEM and BEM and, if available, analytical solutions to establish their accuracy.