Geometrically Induced Nonlinearity in Materials and Structural Systems.

摘要

For structural analysis there are three sources of nonlinear behavior. The corresponding nonlinear effects are identified by material, geometry and boundary condition nonlinearities. Here in the present work we focused on nonlinear behavior of structural systems that arises from geometry and specifically tackled three problems: nonlinearity in shell structures, nonlinearity in scale-substrate systems and nonlinearity is cellular solids.;Firstly, we present a new instability that is observed in the indentation of a highly ellipsoidal shell by a horizontal plate. Above a critical indentation depth, the plate loses contact with the shell in a series of well-defined `blisters' along the long axis of the ellipsoid. We characterize the onset of this instability and explain it using scaling arguments, numerical simulations and experiments. We also characterize the properties of the blistering pattern by showing how the number of blisters and their size depend on both the geometrical properties of the shell and the indentation but not on the shell's elastic modulus. This blistering instability may be used to determine the thickness of highly ellipsoidal shells simply by squashing them between two plates.;For the second problem, we investigate the nonlinear mechanical effects of biomimetic scale like attachments on the behavior of an elastic substrate brought about by the contact interaction of scales in pure bending using qualitative experiments, analytical models and detailed finite element analysis. Our results reveal the existence of three distinct kinematic phases of operation spanning linear, nonlinear and rigid behavior driven by kinematic interactions of scales. The response of the modified elastic beam strongly depends on the size and spatial overlap of rigid scales. The nonlinearity is perceptible even in relatively small strain regime and without invoking material level complexities of either the scales or the substrate.;And lastly, we develop a new class of two dimensional (2D) metamaterials with negative Poisson's ratio. This is achieved through mechanical instabilities (i.e., buckling) introduced by structural hierarchy and retained over a wide range of applied compression. This unusual behavior is demonstrated experimentally and analyzed computationally.