| Abstract: |
| Classical homogenization is insufficient for finite-sized structures as it does not account for crucial scale-size effects. We will present a thermodynamically consistent model and subsequent two-scale expansion homogenization framework for strain-gradient elasticity that derives effective models with scale-dependent homogenized coefficients. 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 micro-architected materials. |
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