A Finite Element Formulation of Contact Problems for Viscoelastic Structures, Based on the Generalized Maxwell Relaxation Model

The objective of this study is to develop a general finite element formulation associated with an incremental adaptive procedure established for the calculation of contact pressure distributions in viscoelastic structures. A generalized Maxwell model has been used to model the viscoelastic constitutive equations in which bulk and shear relaxation functions are represented by 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. The viscoelastic contact behavior has been studied through an improved augmented Lagrangian approach, based on kinematical conditions of contact bodies. The proper convergence caused by the numerical examples with those obtained from analytical results shows the applicability of presented finite element formulation.