Hereditary Fractional Viscoelastic Thermally Induced Contact-Creep Model for Fractal Surfaces: Materials of Maxwell Type

• A unified model combining fractional viscoelasticity with fractal contact mechanics. • Closed-form solution for thermal contact creep derived using the Meijer G-function. • Cantor-type fractal interface effectively represents multiscale surface roughness. • Two-parameter model demonstrates improved agreement with experimental observations, capturing complex mechanical and thermal behaviors. The main aim of this study is to develop a tribological model describing frictionless thermal-creep contact in a fractional viscoelastic medium with a fractal interface in contact with a rigid foundation. To achieve this, the fractional Maxwell model is employed to represent the material’s constitutive behavior, while the surface roughness of the interface is characterized using a fractal structure based on the middle-third Cantor set, which effectively captures the geometric complexity of asperities at the contact interface. Thermally induced creep is modeled using Arrhenius’s equation, incorporating activation energy to relate temperature to time-dependent deformation. The analytical solution is derived in closed form using the Meijer G-function, a generalized hypergeometric function, enabling the linear creep response under constant load and temperature to be captured with just two model parameters while excluding the tertiary creep phase. Quantitative sensitivity analyses further show that the fractional-order parameter plays a critical role in governing the viscoelastic memory of the material, with α ≈ 0.7 yielding the closest match to experimental creep data and reducing prediction errors by approximately 20–30% compared with α = 0.5 or α = 0.9. Validation against existing experimental results confirms the reliability of the model within the examined deformation regime.