An augmented lagrangian finite element approach for the tribological analysis of frictional contact problems in viscoelastic systems

The tribological aspects of contact systems are greatly affected by the friction and contact pressure distribution throughout the surface of the contact interface. Generally the contact of deformable bodies is a nonlinear problem and for the viscoelastic bodies it has a time-dependent response, since their viscous characteristics depends on time. The introduction of friction with its irreversible characteristic in contact surface makes the contact problem more difficult. The objective of this study is to develop a general augmented Lagrangian finite element formulation associated with an incremental adaptive procedure which established for analysis of frictional contact problems in viscoelastic systems. The contact behavior has been studied through an improved augmented Lagrangian approach. A generalized Maxwell model has been used to model the viscoelastic constitutive equations in which bulk and shear relaxation functions are represented by the sum of a series of decaying exponential functions of time. Based on the principle of virtual work, an effective finite element formulation associated with an incremental relaxation procedure has been developed. As an application of formulation, the numerical example has been presented to evaluate the numerical approach.