Response of Graded Miura-Ori Metamaterials to Quasi-Static and Dynamic In-Plane Compression

The non-unique relationship between the density and quasi-static strength of Miura-ori metamaterials was explored for graded materials with respect to quasi-static and dynamic in-plane compression. A lower bound estimate of quasi-static strength and energy absorption was obtained using an analytical method by only considering the deformation mechanism of the rigid origami motion. Graded origami metamaterials were achieved by applying either a variation of the initial folding angle or a variation of the thicknesses of cell walls in the loading direction. It was shown that grading by a moderate increase of the initial folding angle does not notably contribute to the overall material strength and consequently to an improvement of the energy absorption efficiency of the metamaterial under quasi-static compression. Grading by wall thickness variation leads to a notable strength increase and moderately enhanced energy absorption. It is shown that the significant strength gradient leads to a violation of the rigid motion rule and the cells collapse sequentially, which has been validated by test results published in the literature. Different from quasi-static behavior, the response of the Miura-ori metamaterial to relatively high velocity impact is governed by the density gradient values, regardless of the grading technique. Furthermore, the differently graded profiles (positive or negative) affect the force-displacement histories but not the energy absorption efficiency of the examined metamaterials.