Advanced modeling of the mechanical behavior of natural fiber-reinforced earthen bricks: A second-order gradient theory approach

Flax fiber-reinforced earthen bricks offer a sustainable alternative to conventional masonry but exhibit complex mechanical behavior due to their heterogeneous microstructure. This study addresses this challenge by combining experimental three-point bending tests with a multiscale numerical framework based on gradient elasticity theory. We first implement first-order gradient elasticity using Code_Aster and an in-house FFT-based code to compute the effective stiffness tensor A0,0. This approach yields relative errors of 3% and 4% for bricks reinforced with 16 and 64 long fibers, respectively, compared to experimental data. To improve accuracy, we extend the framework to second-order gradient elasticity, incorporating size effects and non-local interactions through higher-order tensors B0,1 and C0,0. The refined model reduces relative errors to below 0.1%, demonstrating its robustness in capturing microstructural phenomena. Our findings confirm that second-order gradient theory significantly enhances predictive accuracy for fiber-reinforced composites and validate the potential of flax-reinforced earthen bricks as eco-friendly construction materials.