Stress distribution in a multi-layer soft viscoelastic material under sliding motion of a spherical indenter tip

Modeling stress distributions in multi-layer soft viscoelastic materials has great importance for evolving robotics and mechanism of machines, where soft viscoelastic materials are increasingly replacing traditional rigid materials. Nevertheless, tackling this problem remains a challenge, particularly when considering the viscoelastic properties of soft materials. This research presents a theoretical model for stress distribution in a two-dimensional sliding contact between a spherical rigid indenter tip and a plane composed of multi-layer soft viscoelastic material. The material is characterized using the viscoelastic Kelvin–Voigt model, where the viscosity coefficient defines the viscoelastic behavior. Explicit mathematical formulas for stress and strain determination in the multiple soft layers are derived using mathematical transformations based on the Fourier transformation. The system of third-order nonlinear differential equations of the contact model is tackled using the finite difference method, within the given boundary conditions. Then, a numerical algorithm is proposed to effectively solve the finite difference equations, considering various parameters of soft viscoelastic material’s properties and sliding velocity. The effectiveness of our proposed model is validated by numerical simulations and the machine learning method. The developed contact model is expected to be a platform for modeling and analyzing the sliding-spherical contact in novel mechanism designs, such as soft robotics, soft tactile sensors, and intelligent integration in soft bodies.