Spectral entropy and strain energy trends in composite mechanical metamaterials

The strain energy and spectral (Shannon) entropy distributions in composite lattices made of core and reinforcement components are investigated by conducting numerical experiments on a set of indefinitely tall lattice strips subjected to a point surface load. The spectral entropy measures the complexity of the strain energy spectrum as it transforms with distance from the loaded surface. The spectral entropy behavior is tailored by adjusting the degree of anisotropy in the lattices. Isotropic continuum-like responses exhibited enhanced spectral entropy decay near the loaded surface and were associated with dispersion of strain energy over a wide spatial area of the lattice. Highly anisotropic responses showed a slow entropy decay at the surface and the localization of strain energy. Interestingly, with sufficient distance from the loaded surface, all lattice designs exhibited the same asymptotic rate of entropy decay, and this rate also was similar to an isotropic continuum material behavior. This implies in practice that any exotic properties of metamaterials determined by their modal selectivity are generally better pronounced in the vicinity of loads, and that they tend to diminish on the periphery of these interesting material systems.