Dynamic Response of Tunable Phononic Crystals and New Homogenization Approaches in Magnetoactive Composites

This research investigates dynamic response of tunable periodic structures and homogenization methods in magnetoelastic composites (MECs). The research on tunable periodic structures is focused on the design, modeling and understanding of wave propagation phenomena and the dynamic response of smart phononic crystals. High-amplitude wrinkle formation is employed to study a one-dimensional phononic crystal slab consists of a thin film bonded to a thick compliant substrate. Buckling induced surface instability generates a wrinkly structure triggered by a compressive strain. It is demonstrated that surface periodic pattern and the corresponding large deformation can control elastic wave propagation in the low thickness composite slab. Simulation results show that the periodic wrinkly structure can be used as a smart phononic crystal which can switch band diagrams of the structure in a transformative manner. A magnetoactive phononic crystal is proposed which its dynamic properties are controlled by combined effects of large deformations and an applied magnetic field. Finite deformations and magnetic induction influence phononic characteristics of the periodic structure through geometrical pattern transformation and material properties. A magnetoelastic energy function is proposed to develop constitutive laws considering large deformations and magnetic induction in the periodic structure. Analytical and finite element methods are utilized to compute dispersion relation and band structure of the phononic crystal for different cases of deformation and magnetic loadings. It is demonstrated that magnetic induction not only controls the band diagram of the structure but also has a strong effect on preferential directions of wave propagation. Moreover, a thermally controlled phononic crystal is designed using ligaments of bi-materials in the structure. Temperature difference is used to generate large deformations and affect the elastic moduli tensor of the structure. Phononic characteristics of the proposed structure are controlled by the applied temperature difference. The effect of temperature difference on the band diagrams of the structure is investigated.;Homogenization methods in periodic and random MECs are also investigated. A finite element method (FEM)-based homogenization approach is presented to simulate the nonlinear behavior of MECs under a macroscopic deformation and an external magnetic field. Micro-scale formulation is employed on a characteristic volume element, taking into account periodic boundary conditions. Periodic homogenization method is utilized to compute macroscopic properties of the MEC at different mechanical and magnetic loadings. A new efficient numerical scheme is used to develop the magnetoelastic tangent moduli tensors. In addition, the effective response of a random MEC under applied magnetic fields and large deformations is computed. The focus is on the spatially random distribution of identically circular inclusions inside a soft homogenous matrix. A FEM-based averaging process is combined with Monte-Carlo method to generate ensembles of randomly distributed MECs. The ensemble is utilized as a statistical volume element in a scale-dependent statistical algorithm to approach the desired characteristic volume element size.