An implicit finite wear contact formulation based on dual mortar methods

Abstract

Summary Finite deformation contact problems with frictional effects and finite shape changes due to wear are investigated. To capture the finite shape changes, a third configuration besides the well‐known reference and spatial configurations is introduced, which represents the time‐dependent worn state. Consistent interconnections between these states are realized by an arbitrary Lagrangean–Eulerian formulation. The newly developed partitioned and fully implicit algorithm is based on a Lagrangean step and a shape evolution step. Within the Lagrangean step, contact constraints as well as the wear equations are weakly enforced following the well‐established mortar framework. Additional unknowns due to the employed Lagrange multiplier method for contact constraint enforcement and due to wear itself are eliminated by condensation procedures based on the concept of biorthogonality and the so‐called dual shape functions. Several numerical examples in both 2D and 3D are provided to demonstrate the performance and accuracy of the proposed numerical algorithm. Copyright © 2016 John Wiley & Sons, Ltd.

Algebraic multigrid methods for saddle point systems arising from mortar contact formulations

“…Block matrices usually arise if multiple types of equations are coupled together. In the present context of contact problems in saddle point formulation, two types of equations, namely the balances of linear momentum of the solid bodies and the contact constraints, are connected via the off-diagonal blocks in (5). Similarly, multiphysics problems also yield block matrices where the coupling between different physical fields manifests itself in the off-diagonal blocks of the monolithic system matrix.…”

“…The segregated block transfer operators (7) are put together from the transfer operator blocks for the different physical and mathematical fields. Here, P u and R u describe the transfer operator blocks corresponding to the stiffness matrix block K in (5). The transfer operatorsP andR define the level transfer for the Lagrange multipliers.…”

A mortar finite element approach for point, line, and surface contact

“…One of the main advantages of dual mortar methods in the context of pure surface contact is the nodewise decoupling of the discrete slave side contact virtual work contribution, which results in a diagonal slave mortar matrix D and allows for a computationally efficient elimination of the additional Lagrange multiplier unknowns, see other works. () For this purpose, the third row of is utilized to express the Lagrange multiplier increment in terms of the displacement increments …”

“…As fundamental technique for discretizing the contact constraints, mortar methods are well-established nowadays because they allow for a variationally consistent treatment of contact conditions despite the presence of nonmatching surface meshes, see other works. [6][7][8][9][10][11] These methods have already been successfully extended to resolve complex interface phenomena such as wear, [12][13][14] lubrication, 15 and thermal effects. 16,17 Despite the superior robustness of mortar methods, their applicability is strongly restricted by the requirement of smooth geometries (ie, surface-to-surface contact).…”

A multi-scale FEM-BEM formulation for contact mechanics between rough surfaces

“…Moreover, it is prone to be extended for the solution of nonlinear multi-field problems involved in heat transfer or in reaction-diffusion systems [32,33,34], for which the boundary element method has not been applied so far. Last but not least, new robust contact discretization schemes and solution strategies have been advanced within the framework of the FEM in recent years, including nonlinear thermomechanics and wear [35,36,37,38,39].…”