Numerical analysis of evolutionary mixed variational problems: Applications in modeling asphalt pavements with interlayer frictional contact conditions

Abstract

In this study, we address the numerical approximation of a class of evolutionary mixed variational problems and its application to the modeling of multi-layer viscoelastic contact systems. The specificity of this problem resides in the introduction of a dual multiplier to decouple and describe the nonlinear unilateral constraint, which renders it advantageous in the study and numerical computation of numerous contact problems. By imposing appropriate regularity conditions, we prove the approximation properties of the solution to its corresponding discrete problem and proceed to discuss its application in asphalt pavement mechanics modeling based on multi-layer contact systems. Particularly, the introduction of time-dependent dual constraint conditions realizes the simulation of time-dependent interlayer contact states, making the model more in line with the evolution process of actual pavement. Several numerical experiments conducted in both two and three dimensions illustrate the nonlinear displacement characteristics within the contact zones and validate conclusions related to error convergence. Furthermore, these experiments demonstrate the effectiveness of this approach in modeling pavement mechanics.