Studies on the effect of internal geometry in the macroscopic deformation of solids

Abstract

A comprehensive understanding of the arrangements of internal geometries in solids is essential to predict their macroscopic response which evolves with time and space under external loading and ultimately leads to their failure. The internal geometries may vary over a wide range of length scales (from nanometer to meter) and at times can be highly complex, and heterogeneous and can exhibit nonlinear constitutive re lations. Altering the internal geometries of a solid in an appropriate manner can enhance the overall macroscopic response leading to an efficient design. As a part of this thesis, we study the effect of internal geometry in the form of heterogeneity arising from periodic inclusions. Towards this, we borrow ideas from the analysis of mechanical metamaterials. However, large-scale implementation of metamaterial de signs is rather a recent and less explored phenomenon. One such implementation is seismic metamaterials (length-scale of meter-Order) used to shield earthquake forces. But most of the works are on the experimental front and lack on the modeling front. Another interesting implementation is a metamaterial-based design of armor (length scale of millimeter-Order) which remained largely unexplored to date. The basic idea is similar to a crystal lattice with periodic structure, when local resonators are placed in the form of stiffer inclusions, they collectively show nonintuitive behavior such as large attenuation of elastic waves. This thesis uses such a concept of metamaterials to design efficient solids with specific applications to seismic metamaterials and armor design. Initially, the effect of internal geometries (in the form of inclusion shapes and orientations) on modulating frequency bandgap is studied. This is shown with specific application to seismic metamaterials which can be deployed to shield/divert earthquake waves.