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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.

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Suspension systems in running vehicles keep the occupants comfortable and isolated from road noise, disturbances, and vibrations and consequently prevent the vehicle from damage and wearing. To attain comfortable and vibration isolation conditions, both material flexibility and damping should be considered in the considered suspension model. This paper presents an incremental finite element model to study and analyze the dynamic behavior of double wishbone suspension systems considering both material flexibility and damping effects. The flexibility of the suspension links are modeled with plane frame element based on Timoshenko beam hypothesis (TBH). On the other hand, the flexibility of joints connecting the suspension links together and with the vehicle chassis is modeled with the revolute joint element. To incorporate the damping effect, viscoelastic, viscous and proportional damping are considered. An incremental viscoelastic constitutive relations, suitable for finite element implementation, are developed. The developed finite element equations of motion are solved using the Newmark technique. The developed procedure is verified by comparing the obtained results with that obtained by the developed analytical solution and an excellent agreement is found. The applicability and effectiveness of the developed procedure are demonstrated by conducting parametric studies to show the effects of the road irregularities profiles, the vehicle speed, and the material damping on the transverse deflection and the resultant stresses of suspension system. Results obtained are supportive in the mechanical design, manufacturing processes of such type of structural systems.