Semi-Analytical Results for the Linear Nonaging Viscoelastic Contact Behaviors

Abstract

This paper investigates the importance of creep and relaxation functions in modeling the Hertzian contact problem between linear nonaging viscoelastic materials and viscoelastic rough surfaces. We provide novel analytical and semi-analytical solutions to these functions for various materials, including Generalized Maxwell, Generalized Kelvin, and Burgers’ rheological materials. Closed-form and semi-analytical solutions are developed for several specific cases with high practical applications, such as the contact between incompressible solids, a rigid material and an incompressible material, and two solids with no volumetric viscous strain. They are extensions of existing solutions given in the literature. A simple computation procedure based on the discretized integral technique is proposed for the general case of contact between linear nonaging viscoelastic materials. This proposed method is easy to implement in practical applications such as the interpretation of viscoelastic indentation tests for material characterization and the implementation of viscoelastic contact in finite/discrete element simulations.