Analysis and design of metamaterials and metastructures

The term metamaterials, refers to materials that are micro-architectured, such that their effective properties are primarily controlled by the microstructural geometries rather than by the base materials. Metamaterials are popularly adopted within the broad field of electromagnetics. Mechanical metamaterials are also being developed alongside this process. In particular, mechanical metamaterials refer to materials with enhanced mechanical features due to the designed geometrical properties of the microstructure. Through meticulously designed repeated patterns, metamaterials and metastructures are capable of manipulating waves both at the microscopic and macroscopic scales and lead to the possibility of controlling unique amplitude-dependent behaviours in weakly nonlinear discrete media (e.g. bandgap widening, self-tuning, and sensing). Therefore, metamaterials and metastructures allow for breaking traditional design assumptions where waves are used/controlled in the structural design of linear physical substructures using frequency wavenumber (ω-q) dispersion curves built through finite or spectral elements.

Along these lines, finite locally resonant multiple-degrees-of- freedom (MDoFs) metafoundations were designed and developed for the seismic mitigation of typical storage tanks, where extreme loading conditions have been considered by safe shutdown earthquakes. Nonlinear bistable columns have been employed. In this respect, see Fig. 1. Moreover, the seismic mitigation of a typical nuclear small modular reactor (SMR) was carried out. To protect the reactor from strong earthquakes, finite locally resonant multiple degrees of freedom metafoundations were developed; and resonator parameters were optimized by means of an improved frequency domain multivariate and multiobjective optimization procedure. Also, in this case, additional nonlinear vertical quasi-zero stiffness (QZS) cells were employed. In particular, QZS cells were obtained by horizontally precompressed springs in an unstable state with vertical springs in parallel. This arrangement introduced additional flexibility and dissipation against nonsymmetrical modes of the SMR and vertical seismic loadings. See, Fig. 2.