A Temperature-Dependent Discrete Contact Model for Linear Viscoelastic Bodies

A temperature-dependent discrete contact model for linear viscoelastic bodies is developed to predict normal contact forces at different prescribed temperatures. The formulation combines the Lee–Radok contact theory, the equivalent contact concept, the time–temperature superposition principle, and a generalized Maxwell representation. A global fitting procedure is employed to represent the equivalent contact relaxation modulus over specified time and temperature ranges, allowing for the fitted parameters to be reused without separate identification at each temperature. For two viscoelastic bodies at different temperatures, a best fit equivalent temperature is introduced to approximate their combined temperature-dependent relaxation response. Based on the resulting equivalent relaxation modulus, a discrete contact force expression is obtained through numerical evaluation of the hereditary convolution. The framework covers contact between dissimilar or identical viscoelastic bodies and between elastic and viscoelastic bodies. Numerical comparisons are conducted using finite element simulations of PTFE-based material pairs and steel–viscoelastic pairs over 0–50 °C. The maximum fitting error of the equivalent contact relaxation modulus is 2.62%, and the maximum error associated with the equivalent temperature approximation is 10.6% over the investigated domain. The calculated force histories show good agreement with the finite element results during loading. These results demonstrate that the proposed framework provides a unified representation of temperature-dependent viscoelastic contact while avoiding repeated fitting of equivalent contact parameters over the prescribed temperature range.