Thermo-mechanical bending of architected functionally graded cellular beams

This article investigates the effect of cell architecture on the bending behavior of architected cellular beams subjected to a thermo-mechanical load. The architected functionally graded cellular (FGC) beam is made of porous cells whose properties vary across the thickness or length of the beam. The FGC beam is modeled according to Reddy's third-order shear deformation theory (TSDT), and the effective thermo-mechanical properties are obtained by standard mechanics homogenization. The governing equations are solved by a finite element method, and deflection curves are presented for the architected cellular beams with relative density gradients, subjected to thermal and mechanical loads. Numerical results demonstrate that tailoring relative density through the thickness of an FGC beam can reduce the lateral deflection of lightweight beams to less than half; consequently, tuning the flexural stiffness of cellular structures without changing their total weight. Interestingly, numerical results reveal that the flexural deformation of an FGC beam subjected to a thermo-mechanical load can be controlled by means of the variation function of cell architectures. We also present the optimized architectural variation and cell topologies leading to the least flexible architected cellular beams for alternative thermo-mechanical loading conditions. This paper sheds light on the application of cellular-based mechanical metamaterials for programming the multifunctional behavior of lightweight meta-structures.