An augmentation technique for large deformation frictional contact problems

Abstract

SUMMARYThe present work deals with a new approach to frictional large deformation contact problems. In particular, a new formulation of the frictional kinematics is introduced that is based on a specific augmentation technique used for the introduction of additional variables. This augmentation technique substantially simplifies the formulation of the whole system. A size reduction of the resulting system of algebraic equations is proposed. Consequently, the augmentation technique does not lead to an increase in size of the algebraic system of equations to be ultimately solved. The size reduction retains the simplicity of the formulation and preserves important conservation laws such as conservation of angular momentum.

A Higher Order Phase-Field Approach to Fracture for Finite-Deformation Contact Problems

“…Contact contribution The underlying contact description is based on the description given in [10]. Note, as mentioned earlier, the phase-field and the contact boundaries do not depend on each other.…”

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

“…If such a static condensation is not desired or not feasible (e.g., when choosing a standard basis rather than dual basis functions for the Lagrange multipliers, see, e.g., References 24,26), the linear system remains in its generalized saddle point format arising from the contact constraint equations. Both the standard and the dual mortar approach have become increasingly popular in recent years, with new contributions focusing for example on higher-order finite element interpolation, 27,28 isogeometric mortar methods, [29][30][31][32][33] or improved robustness of the solution algorithms, [34][35][36] to name only a few particularly active research directions.…”

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

“…[47,81]), the linear system remains in its generalized saddle point format arising from the contact constraint equations. Both the standard and the dual mortar approach have become increasingly popular in recent years, with new contributions focusing for example on higher-order finite element interpolation [49,83], isogeometric mortar methods [16,60,62,63,86], or improved robustness of the solution algorithms [21,30,51], to name only a few particularly active research directions.…”

“…As one can see from (21), SIMPLE does not affect the terms that operate on the primary displacement variables, but it perturbs the Lagrange multipliers. Choosing S = αZ + αC 2 K −1 C T 1 , the error matrix reduces to…”