A Numerical Solution for Quasistatic Viscoelastic Frictional Contact Problems

Abstract

The tribological aspects of contact are greatly affected by the friction throughout the contact interface. Generally, contact of deformable bodies is a nonlinear problem. Introduction of the friction with its irreversible character makes the contact problem more difficult. Furthermore, when one or more of the contacting bodies is made of a viscoelastic material, the problem becomes more complicated. A nonlinear time-dependent contact problem is addressed. The objective of the present work is to develop a computational procedure capable of handling quasistatic viscoelastic frictional contact problems. The contact problem as a convex programming model is solved by using an adaptive incremental procedure. The contact constraints are incorporated into the model by using the Lagrange multiplier method. In addition, a local-nonlinear nonclassical friction model is adopted to model the friction at the contact interface. This eliminates the difficulties that arise with the application of the classical Coulomb’s law. On the other hand, the Wiechert model, as an effective model capable of describing both creep and relaxation phenomena, is adopted to simulate the linear behavior of viscoelastic materials. The resulting constitutive integral equations are linearized; therefore, complications that arise during the integration of these equations, especially with contact problems, are avoided. Two examples are presented to demonstrate the applicability of the proposed method.

Effect of the Material Parameters on Layered Viscoelastic Frictional Contact Systems

“…The model adopted the Wiechert model to simulate the linear response of viscoelastic materials and the incremental convex programming method to manipulate contact events. This model is then extended to handle the frictional contact problems [17].…”

“…All ingredients, modules and solution procedure of the model are presented in [16,17]. In the general framework of the FEM, the space domain of the contact system is discretized into finite elements.…”

“…where Δt c and Δt r are the consumed and remaining time step, respectively, which can be defined as Δt Δt − Δt j c where α j is the minimum scale factor within the increment j [17].…”

“…Three material parameters will be considered: the layer/contact solid stiffness ratio E eqv /E c , the delayed/ instantaneous elasticity ratio E 1 /E ∞ , and the material relaxation time of the layer ρ. The results are obtained by using a two-dimensional time-dependent nonlinear FE model, developed by Mahmoud et al [16,17], that modified to account for the layering effect. The model adopts the Wiechert model, presented by Williams [35], to simulate the linear response of viscoelastic materials.…”

“…The position vector of the contact point P can be expressed in terms of the position vectors of the nodes K 1 and K 2 , which are connecting the target segment S l using the interpolation shape function. The position vector of the physical contact point P is defined by the parameter t ξ P [17] …”