Multigrid solution of the 3D stress field in strongly heterogeneous materials

• Fast solver for 3D elastic materials with strongly heterogeneous/discontinuous properties is proposed.
• Multigrid efficiency is maintained by crucial measures in implementation.
• The large number of points and the CPU times used in the simulations highlight the potential of the method for optimization.
• The method allows dense grids and high accuracy to model highly localized small scale phenomena.

Technology allows the production of advanced (heterogeneous) materials controlling properties on an increasingly local scale, e.g. layered, graded, granular and fiber-reinforced. In this paper the efficiency of the Multigrid method for 3D stress calculation involving such materials is investigated. Results are validated using model problems and the full potential is demonstrated for two representative problems. The developed algorithm facilitates solution of 3D problems with high accuracy and dense grids on standard computers. It has excellent prospects for use in performance prediction, analysis and numerical (local) design optimization in tribology and contact mechanics.