UC San Diego

Periodic composites (PCs) are artificial materials with specially designed microstructure to manage stress waves. The objective of this dissertation is to study various techniques for microstructural design of PCs for a desired elastodynamic response. A mixed variational formulation is studied for band structure calculation of PCs. Dynamic homogenization is studied for calculation of the frequency dependent effective properties of PCs. Optimization techniques are used together with mixed variational formulation and dynamic homogenization to make a computational platform for microstructural design of PCs. Several PCs are designed and fabricated, and various tests are performed for experimental verification.

First, band-gap in one- and two-dimensional PCs is investigated experimentally. Mixed variational formulation is used to design samples with band-gaps at frequencies convenient to conduct experiment. Samples are fabricated and their transmission coefficient is measured. Experimental data are compared with theoretical results for evaluation of the band structure. Using constituent materials with temperature dependent material properties, it is also shown that band structure of PCs can be tuned by changing the ambient temperature. Furthermore, dynamic homogenization is used to design a one-dimensional PC for acoustic impedance matching. As a result, the reflection of stress waves at the interface of two impedance matched media becomes zero. Samples are fabricated and ultrasound tests are performed to measure the reflection coefficient for experimental verification. In addition, a one-dimensional PC with metamaterial response is designed to achieve a composite with both high stiffness-to-density ratio and high attenuation at low frequency regime. Samples are fabricated and the attenuation coefficient is measured for experimental verification.

Moreover, optimal design of PCs for shock wave mitigation is investigated. A genetic algorithm is used to design the microstructure of a one-dimensional PC for maximum band-gap bandwidth. To verify the theoretical calculation, samples are fabricated and Hopkinson bar experiments are performed. In addition, negative refraction in two-dimensional PCs is investigated. Equifrequency surface of a two-dimensional PC are calculated together with vectors of group velocity. Dynamic homogenization is used to find overall elastodynamic properties of the two-dimensional PC. Energy refraction at the interface of a homogenous half-space and the two-dimensional PC is investigated.