Mechanical Homogenization of Biochar Porous Structures Using Two-Dimensional RVE: A Study of Finite Element Methods on the Relationship of Actual Porosity and Effective Elastic Modulus

This study analyzes the mechanical response of porous biochar using a 2D FEM–RVE homogenization approach to investigate the effect of mesh-based actual porosity and microstructural arrangement on stiffness and stress concentration. Three types of RVEs (regular, shifted, and random) were simulated at several porosity levels for five biochar types (wood, bamboo, grass, RHB, and sludge) under the assumption of linear elastic material. Loading was applied using kinematic uniform boundary conditions (KUBC), and the effective elastic modulus ( ) was extracted from the homogenization response, while the maximum stress ( ) was recorded as an indicator of stress localization. Results show that decreases nonlinearly with increasing , and at the same porosity, more continuous microstructures retain higher stiffness. Normalization into relative modulus (E_rel) reveals overlapping trends across biochar types for the same RVE, allowing the influence of solid-phase properties to be separated from pore shape effects. These findings underscore the importance of using actual porosity and simultaneously evaluating global stiffness and local stress indicators in interpreting the mechanics of porous biochar.