A FAST ALGORITHM FOR DISPLACEMENT-DRIVEN ELASTIC CONTACT MODELING GRADINARU Dorin, SPINU Sergiu University “Stefan cel Mare” of Suceava, ROMANIA gradinaru@fim.usv.ro, sergiu.spinu@fim.usv.ro Keywords: elastic contact, numerical simulation, iteration, displacement-driven, conjugate gradient Abstract: A variation of elastic contact problem is approached in this paper, considering the case when the loading is not known, but the normal displacement is. The algorithm for modeling the classical load-driven elastic contact problem is modified to allow for the new input. Interference equation in the original algorithm is completed with the rigid-body displacement, and pressure correction instruction is removed. Guess values for load and initial pressure are required for iteration of pressure distribution and contact area. Predictions of the numerical program newly advanced are compared with analytical results, for three types of technologically important, axisymmetric contacts, and a good agreement is found. 1. INTRODUCTION When force is transmitted through a contact between two bodies, assessment of contact area and pressure distribution can provide valuable information concerning the strength of the contact. Stress state induced in subsurface by surface tractions is responsible for plastic yielding and finally for contact failure. With analytical solutions lacking the mathematical support for solving the complex equations which arise (Lamé), numerical approaches have found great applicability to various situations of contact geometry or material response. Great efforts were conducted lately towards increasing the computational efficiency of these methods, as the currently available computational power is easily surpassed by the complexity of the models to be solved. The search for refined numerical methods capable of handling fine meshes and complex patterns of material behavior remains one of the major challenges to be met. While most algorithms are centered on the load-driven formulation, the displacement- driven elastic contact problem has received little attention. Boucly, Nélias and Green, [1], have included a displacement driven elastic contact solver in their elastic-plastic contact algorithm. Gallego, [3], advanced an extended elastic contact solver, with both normal and tangential loading, capable of modeling both load and displacement driven variations. 2. LOAD-DRIVEN ELASTIC CONTACT PROBLEM The framework for the elastic contact solver consists of the following assumptions / limitations: 1. Contact area is small compared to dimensions of the contacting bodies, so the half- space approximation holds. 2. Only small strains and small displacements are considered. 3. The contact is dry and friction is not accounted for. Numerical resolution of elastic contact problem relies on considering continuous distributions as piecewise constant on the elements of a mesh including the contact area. This approach allow for transforming the integral contact equation, which accepts analytical solutions only in a few cases, in a linear system of equations in pressure. Its solution can be found by numerical means; however, only fast iterative algorithms are suitable for implementation. Only a small domain, which is expected to include the contact area and the subsurface, needs to be considered. This is an important advantage of this method over finite element analysis (FEA), where the entire bulk has to be meshed. In order to keep the ANNALS of the ORADEA UNIVERSITY. Fascicle of Management and Technological Engineering, Volume IX (XIX), 2010, NR1 1.35