Multigrid Solution of the 3D Elastic Subsurface Stress Field for Heterogeneous Materials in Contact Mechanics

The need to increase efficiency, stimulates the development of new materials tailored to specific applications and thermal/mechanical loading conditions, e.g. by controlling the property variations on a local scale: layered, graded, granular, porous and fibre-reinforced. For design and optimization of such materials the response to specific load conditions must be predicted which requires computer simulations. For applications in contact mechanics and lubrication failure criteria need to be developed which require the stress fields inside the (strongly heterogeneous) material induced by surface loading. The geometrical complexity of the subsurface topography and the need of an accurate solution require the use of a very fine discretization with a large number of elements, especially for three-dimensional problems. This requires optimally efficient numerical algorithms. In this paper the authors demonstrate the capability of Multigrid techniques to compute displacement and stress fields with great detail in strongly heterogeneous materials subject to surface loading, and in a contact mechanics application. Results are presented for a ceramic application and a contact problem of material with multiple inclusions. The efficiency of the method will allow extensive parameter studies with limited computational means. Moreover, it can efficiently be used to derive macroscopic stress-strain relations by simulations of microscopic problems. Also the method can be used for computational diagnostics of materials with specific heterogeneities