Fractal-Continuum Mechanics for Shear Behavior of Impact-Grown Powdery Layers: Mapping from Fractal to Continuum Spaces

In a powdery layer, the shear mechanical response to impact dictates whether particles roll, slide, deposit. Existing engineering models struggle to balance computational efficiency with physical fidelity, whereas DEM remains computationally prohibitive. To address this challenge, this study develops a macroscopic constitutive model for the shear mechanical response of impact-grown powdery layers based on fractal continuum-based mechanics. Through fractal coordinate transformation, the discrete fractal layer is mapped into an equivalent continuum, from which a linear elastic constitutive relation is derived. In this model, directional codimensions , harmonic index and position-dependent intercept term serve as key links between microstructure and macroscopic response, with their evolution calibrated via DEM simulations. Results show that declines from 0.9 to 0.7 with increasing relative layer height. The harmonic index , calibrated via least-squares optimization, exhibits high sensitivity and decreases with layer height. The intercept term increases with relative layer height and load position factor, reflecting the position-dependent initial shear resistance. Validation against DEM data confirms the model's accuracy in capturing shear force-deflection behavior across varying particle sizes (20–90 ), layer heights, loading positions, and material types (copper and glass). Small particles show near-linear force-deflection relationships, while large particles exhibit rapid initial stiffening followed by nonlinear hardening. This framework provides theoretical and practical tools for macro-scale analysis of ash deposit stability under flue gas shear stress, offering a theoretical basis for predicting crack initiation and spalling.