Three-layer RVE-based homogenization approach for elasticity and strength analysis of natural fiber composites

Abstract

Natural fiber composites (NFCs) are widely used in lightweight structures, but their heterogeneous multilayered nature complicates strength prediction, necessitating multiscale homogenization to link micro- and macro-scale behavior. This study presents a mathematical approach to solve the elasticity problem of natural fiber composites (NFCs) using homogenization theory by integrating micro-scale variables into macro-scale analysis. A micro-mechanical stress analysis is conducted on an effective three-layer Representative Volume Element (RVE) of flax fiber-reinforced epoxy composite to evaluate composite performance and determine peak allowable deformation using a homogenized strength criterion. Six boundary conditions including uniaxial displacements along x , y , and z axes, in-plane shifts, and bending in orthogonal planes—yield maximum fiber stresses ranging from 61.94 to 618.66 MPa. The investigation highlights boundary layer effects in nine-layer NFC plates, revealing thinner boundary layers than individual structural layers and distinct behavior at plate surfaces compared to homogeneous composites. The three-layer RVE model accurately captures multi-layer composite behavior, offering detailed insights into local stress-strain distributions while reducing computational complexity. Further analysis was conducted by varying the middle fiber orientation from 30 to 90° for flax, coir, pineapple, and hemp composites under different boundary conditions. The results indicate that flax fiber composites oriented between 45 and 60°, particularly at 45° under x -axis displacement loading, exhibit superior mechanical strength compared to the other configurations.