Abstract Classical homogenization is insufficient for finite-sized structures as it does not account for crucial scale-size effects. We develop a thermodynamically consistent model and subsequent two-scale expansion homogenization framework for strain-gradient elasticity that derives scale-dependent effective models complimenting the findings of 58 enabling prediction of finite-size effects in architected metamaterials. Our key result is that the homogenized mechanical properties depend not only on the micro-geometry and volume fraction but also on the absolute size of the underlying constituents. Hence, the homogenized coefficients are not constant (as in classical homogenization) but rather functions of the microstructural size. Numerical validation confirms that the homogenized coefficients converge to the classical ones as the scale-size effects become vanishingly small, providing a critical tool for designing architected materials.
Veluvali et al. (Mon,) studied this question.