ADAPTIVE FINITE ELEMENT ANALYSIS OF NONLINEAR FRICTIONAL CONTACT WITH MIXED EULERIAN-LAGRANGIAN COORDINATES

This work is concerned with new computational methods for the analysis of frictional contact problems. Several new computational techniques are employed. The new techniques are first presented in their generic form, before specialization to the problem of contact analysis. A new finite element model based on a mixed Eulerian-Lagrangian kinematic description is reviewed. The mixed kinematic model treats both initial and deformed nodal coordinates as unknowns. This feature enables the element mesh to adaptively adjust to moving boundary conditions. A consistent finite element technique for the recovery of surface tractions and distributed reactions is reviewed. This technique is combined with the adaptive capability of the Eulerian-Lagrangian model to formulate the sensitivity of computed surface tractions to changes in the finite element grid geometry.; A new topological description of the frictional contact problem is introduced, in which criteria involving the contact stresses are used to define the locations of transition contours separating zones of different contact behavior (stick, slip, separation). A solution to the contact problem is obtained by determining transition contour locations and an associated displacement solution that simultaneously satisfy the transition stress criteria, the special contact boundary conditions and the usual equilibrium, compatibility and material behavior constraints.; The new computational techniques and the topological contact problem definition are combined to create novel finite element solution algorithms. Contact analysis is treated as a bi-level programming problem. The upper-level problem involves the determination of contour locations that minimize residuals associated with the transition stress criteria. The subordinate problem involves satisfaction of the equilibrium and kinematic requirements by minimization of an energy functional or an equivalent weighted residuals problem.; Two frictional contact algorithms are presented. The first algorithm determines the contact zone topology and geometry by means of a heuristic iterative analysis. The second algorithm uses adaptive Eulerian-Lagrangian remeshing to determine precise transition contour locations for a predetermined contact zone topology. The two algorithms can be applied in sequence to obtain automatic and accurate contact solutions. Example problems involving large deformations, curved contact surfaces and cyclic loading are included.