A novel progressive filamentary model for simulating the coupled shearing-indentation mechanism in elliptical vibration texturing of nano-gratings

Elliptical vibration texturing (EVT) has emerged as a promising technique for fabricating functional nano-gratings for optical applications, yet accurately predicting their nanoscale topography remains a critical challenge. Traditional models fail to capture the coupled shearing-indentation mechanism inherent in the EVT process or suffer from prohibitive computational costs. This paper presents a novel progressive filamentary model to accurately and efficiently simulate nano-grating formation in EVT. The model discretizes the 3D diamond tool into filamentary elements and incorporates parallel surface updating strategy to handle the significant scale mismatch between grating cross-sectional features and grating width. The mathematical expressions for all six characteristic cases of resultant cutting trajectories are firstly derived, followed by detailed model development for the coupled shearing-indentation mechanism in nano-grating formation. The model is validated through extensive machining experiments on multiple metallic materials using tools with different clearance angles. Results show that the proposed model successfully predicts nano-grating topography across various cutting conditions and all six classified types of resultant cutting trajectories, demonstrating its generality and robustness. This work provides a computationally efficient and high-fidelity simulation framework for nano-grating topography prediction, paving the way for deterministic fabrication of diffractive nano-gratings via EVT.