Two dimensional mortar contact methods for large deformation frictional sliding

Abstract

SUMMARYThis paper presents a mortar-based formulation for the solution of two dimensional frictional contact problems involving finite deformation and large sliding. As is widely recognized, traditional node-tosurface contact formulations have several drawbacks in solution of deformable-to-deformable contact problems, including lack of general patch test passage, degradation of spatial convergence rates, and robustness issues associated with the faceted representation of contacting surfaces. The mortar finite element method, initially proposed as a technique to join dissimilarly meshed domains, has been shown to preserve optimal convergence rates in tied contact problems (see (Discretization Methods and Iterative Solvers Based on Domain Decomposition, Springer-Verlag, Heidelberg, 2001) for a recent review), and is examined here as an alternative spatial discretization method for large sliding contact. In particular, a novel description for frictional sliding conditions in large deformation mortar formulations is proposed in this work.In recent years, the mortar element method has already been successfully implemented to solve frictional contact problems with linearized kinematics (see (Int. J. Numer. Meth. Engng 1993; 36: 3451)). However, in the presence of large deformations and finite sliding, one must face difficulties associated with the definition and linearization of contact virtual work in the case where the mortar projection has a direct dependence on the tangential relative motion along the interface. In this paper, such a formulation is presented, with particular emphasis on key aspects of the linearization procedure and on the robust description of the friction kinematics. Some novel techniques are proposed to treat the non-smoothness in the contact geometry and the searching required to define mortar segments. A number of numerical examples illustrate the performance and accuracy of the proposed formulation.

A mortar method for energy‐momentum conserving schemes in frictionless dynamic contact problems

“…Originally, contact segments have been introduced by Simo et al [22] to take into account the kinematics of the contact between two discretized bodies. Similar segmentation procedures have been devised by Papadopoulos and Taylor [23], Zavarise and Wriggers [24], McDevitt and Laursen [6] and Yang et al [9].…”

“…It is worth noting that in previous works on mortar contact formulations (see [7,9,12,13]) additional simplifying assumptions are commonly incorporated into the contact virtual work. These simplifications typically sacrifice conservation of the angular momentum.…”

2d Frictional B-Spline Smoothed Mortar Contact Problems Part I: Matching Phase

“…Discretizing with mortar approach, part of the STS method family, is stable and passes the patch test but its implementation is difficult and requires a lot of technical expertise. This technique has been successfully applied for normal contact problems [3,8,9] and for contact problems with friction [2,11,13,53,[54][55][56][57].…”

Structural contact problems for large deformations ‐ Comparison of steady and non steady normal field

“…Continuously averaged non-mortar side normal vectors ( Figure 1b) Yang presented in his paper [3] (see also [4], [5], [6]) a new method on defining the normal vectors. Those methods have in common that there is an averaged unit normal defined on start and end nodes of the contact edges (mostly non-mortar side edges).…”