Dynamic Wear Simulation of Steps Based on Archard and Numerical Difference Algorithm

In this paper, a dynamic wear multifactor coupling model is proposed, focusing on model construction, typical walking pattern analysis and cross-scale validation. Firstly, based on the theory of wear and elastic mechanics, a single-step wear depth calculation model is established, and the time discretization is carried out by using the explicit difference format, the spatial discretization by using the center difference format, and the two-dimensional discrete numerical simulation is carried out by combining with the adaptive time-step strategy. Secondly, the travel patterns are defined, and the “pattern matrix” framework is constructed by linear superposition, which transforms the pattern distribution into a matrix operation to quantify the incremental wear weights. Finally, the single-step model is extended to the full staircase 3D dataset, and the human flow distribution is inverted using the least squares method and maximum likelihood estimation. The model integrates multi-physical field coupling, and realizes wear prediction with the help of numerical discretization algorithm and matrix superposition, which can accurately reflect the impacts of different walking modes on the structure, and provides a cross-scale quantitative analysis method for the durability assessment of staircases.