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 heterogeneitie

An Efficient 3D Model of Heterogeneous Materials for Elastic Contact Applications Using Multigrid Methods

International audienceAbstract: A 3D graded coating/substrate model based on multigrid techniques within a finite difference frame work is presented. Localized refinement is implemented to optimize memory requirement and computing time. Validation of the solver is performed through a comparison with analytical results for (i) a homogeneous material and (ii) a graded material. The algorithm performance is analyzed through a parametric study describing the influence of layer thickness (0.01 < t/a < 10) and mechanical properties (0.005 < E-c/E-s < 10) of the coating on the contact parameters (P-h, a). Three-dimensional examples are then presented to illustrate the efficiency and the large range of possibilities of the model. The influence of different gradations of Young's modulus, constant, linear and sinusoidal, through the coating thickness on the maximum tensile stress is analyzed, showing that the sinusoidal gradation best accommodates the property mismatch of two successive layers. A final case is designed to show that full 3D spatial property variations can be accounted for. Two spherical inclusions of different size made from elastic solids with Young's modulus and Poisson's ratio are embedded within an elastically mismatched finite domain and the stress field is computed

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

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 mechanic

Multigrid numerical simulation of contact mechanics of elastic materials with 3D heterogeneous subsurface topology

Contact phenomena between deformable bodies are a common problem in engineering. The surface stress distribution and subsurface stresses depend on many parameters. In view of increasingly strict tolerances the effects of local variations in material properties need to be accurately predicted. In this paper a multigrid solution method is presented for contact problems between three dimensional elastic heterogeneous materials. The contact problem is incorporated as boundary condition in the multigrid solution of the displacement equations for the volume. First, validation results are presented. Subsequently a study is presented for soft and hard clusters of inclusions. Finally, results are presented for a contact problem involving a realistic case of a polycrystalline material representative for applications with ceramic materials

Multigrid solution of 2D and 3D stress fields in contact mechanics of anisotropic inhomogeneous materials

Increasing demands on performance of machines lead to severer operating conditions of rolling bearings, i.e. higher loads, less lubricant, thinner lubricant films. Under these conditions, the effects of inhomogeneity and anisotropy on the fatigue life become more important. Accurate prediction of such effects requires detailed surface pressure and subsurface stress calculations. For practically relevant 3D cases with realistic grain sizes, this can only be done with very efficient numerical solution methods. In this paper, multigrid techniques are demonstrated to yield the required performance. The influence of inclusions, crystal orientation and roughness on the Von Mises stress distribution is investigated. The algorithm is suited for subsurface material analysis and optimization as well as for computational diagnostics using image analysis

Three-dimensional Voronoi and multigrid model for microstructure contact problem

International audienceThe prediction of both the tribological behaviour and mechanical analysis of the wear resistance are still of great research interest in order to improve the lifetime of material surfaces. This concerns both bulk and coated materials although coating processes have been often developed in order to protect substrates from tribological solicitations. The wear resistance of coated materials has been the subject of many studies which show that it is possible to protect and improve significantly the durability of substrates. A straightforward discretisation of the multi-scale problem of graded coatings on substrates exceed the memory and CPU capacity of current (and next generation) computers. The authors have proposed an efficient numerical model that can handle this multi-scale problem: using billion points and locally refined grids

A 3D Multigrid solver for elastic contact problems applied to graded materials.

IJTC2011-6103

Detailed modelling of a moving heat source using multigrid methods

International audienceThis paper traces the history of the numerical solutions of the heat equation from the pioneering work of Carslaw and Jaeger, to the current era. The proposed model is based on multigrid techniques within a finite difference frame work. Localised refinement is implemented to optimize memory and computing time costs. The numerical performance of the solver is presented through a comparison with analytical results using different types of boundary conditions. A multisource contact is studied as a first approximation to real asperity interaction