Exploring interesting effects of symmetric functionally graded unit cells for the design of nonlinear mechanical metamaterials

Elastic waves at high frequencies (MHz) interact with microscopic imperfections, showing harmonic generation—where frequencies are multiples of the original wave. Elastic wave scattering by material imperfections was studied using theoretical models of circular and 1D strip-like nonlinear inclusions. Researchers (Tang et al., 2012; Kube, 2017–18; and Achenbach & Wang, 2017–18) aimed to understand how the properties of these imperfections influence the scattered waves. Expanding on this understanding, Ghodake (2023) devised a novel unit cell comprising three nonlinear layers. This metamaterial mimics nonlinear light scattering, showing ‘Raman Scattering’ effects and exhibits tunable wave manipulation. Expanding on these findings, a functionally graded nonlinear unit cell is defined by establishing a spatially continuous distribution of the nonlinear parameter in the first and last layers, symmetrically centered around the central layer. Our novel approach manipulates the spatial distribution of nonlinear parameters, central layer intensity, and unit cell width to achieve unprecedented control over the harmonic response of scattered waves. Numerical experiments reveal non-intuitive behaviors in forward and backscattered harmonics. These harmonics can mysteriously emerge or vanish entirely due to complex interactions between the scattered waves. The proposed unit cell design empowers the inverse design of nonlinear metamaterials for tailored wave harmonic control.