A novel hereditary viscoelastic Fractional-Fractal creep model for the contact of rough Surfaces: Maxwell medium

The main goal of this work is to develop a tribological model for frictionless creep-contact in a fractional viscoelastic medium with a fractal interface in contact with a rigid foundation. The research is motivated by the limitations of traditional models and seeks to offer a more accurate representation of time-dependent and memory effects. These effects are especially critical in materials with rough surfaces. To accomplish this, the fractional Maxwell law is used to approximate the constitutive equation. Furthermore, the interface topography is modeled using fractal geometry to capture asperities. To analyze the interface roughness, a Cantor fractal structure is created based on the middle third Cantor set. This method provides an analytical solution represented by the Meijer G-function, which is also referred to as the generalized hypergeometric function. The Meijer G-function is applied specifically to describe the creep compliance response of Maxwell viscoelastic materials under a constant load on a rough surface. By employing a limited number of model parameters, this framework effectively captures the fundamental creep characteristics with high accuracy.

The model presented in this study is designed to represent the linear segment of creep behavior, excluding the nonlinear creep domain associated with the tertiary phase. This methodology remains valid as long as the deformation of the viscoelastic medium’s surface topography is smaller than the peak asperity heights. Comparisons with experimental datasets from scientific literature show strong consistency, validating the accuracy and reliability of the proposed fractional Maxwell-based model.