Interdisciplinary Study on the Wear Mechanism and Service Mode of Stairs Based on Finite Element Fatigue Model

Abstract

The wear trace of stone historical stairs can reflect key information such as its frequency of use, the distribution of people and the repair history, but traditional archaeological methods rely on qualitative observation, so it is difficult to quantify the dynamic fatigue process. The engineering model is difficult to adapt to the complex load environment of historical buildings because it simplifies the homogeneity of materials. In view of the above limitations, this study proposes a finite element fatigue wear model combining finite element analysis (FEA) and material fatigue theory and analyzes the wear mechanism and its historical correlation under periodic load by constructing a three-dimensional simulation model system. Taking typical stone materials (such as gneiss and serpentine) and wood materials (such as begonia and hard maple) as objects, combined with the S-N fatigue curve and wear law, the stress distribution and damage accumulation under different service frequencies are simulated, and multilateral fixed boundary conditions are introduced to approach the actual constraint state. The results show that the material properties play a decisive role in the wear process: stone is significantly better than wood because of its high hardness and shear modulus, and gneiss has the best wear resistance; There is a nonlinear positive correlation between the frequency of use and the wear rate, and the sensitivity of wood under high-frequency trampling is much higher than that of stone. Through long-term simulation and statistical verification (fitting test R² > 0.98), natural wear and artificial repair traces are successfully distinguished, such as judging the existence of renovation when the deviation of the fitting curve exceeds the threshold. The innovation of this study lies in the deep combination of FEA and material fatigue theory, which solves the limitation of traditional archaeological methods relying on qualitative analysis, provides a quantitative tool for the preventive protection of cultural relics, and restores the historical use mode through reverse derivation of wear characteristics. This study also realizes the cross-integration of material mechanics and archaeology and provides a new technical path for the micro-historical research and scientific protection of architectural heritage.