Inverse design method for tailoring the deflection of beams with functionally graded metamaterials

Functionally graded metamaterials represent a cutting-edge approach to designing structures with cellular materials. By manipulating parameters in specific regions, a customized mechanical response is achieved, optimizing material utilization. Despite various proposed methods to generate functionally graded structures, the challenge of high computational costs persists. This study introduces a novel and computationally efficient inverse design method for beams featuring segment-wise graded metamaterials. Using a semi-analytical approach based on Castigliano's second theorem, this method significantly reduces computational demands. The approach leverages prior experimental and computational characterizations of the transverse deflection in rectangular, reentrant, and hexagonal honeycombs. Validation through finite element models and experimental tests on additively manufactured beams confirms the adequate performance of the method. The proposed framework successfully generates beams with targeted deflections, demonstrating the method's capability for inverse design under specific loading and boundary conditions. This approach not only optimizes material utilization but also broadens the application scope of functionally graded metamaterials in structural design.