Adaptive cellular structures and devices with internal features for enhanced structural performance

This dissertation aims to develop a family of cellular and repeatable devices that exhibit a variety of force-displacement behaviors. It is envisioned that these cellular structures might be used either as stand-alone elements, or combined and repeated to create multiple types of structures (i.e. buildings, ship hulls, vehicle subfloors, etc.) with the ability to passively or actively perform multiple functions (harmonic energy dissipation, impact mitigation, modulus change) over a range of loading types, amplitudes, and frequencies. To accomplish this goal, this work combines repeatable structural frameworks, such as that provided by a hexagonal cellular structure, with internal structural elements such as springs, viscous dampers, buckling plates, bi-stable von Mises trusses (VMTs), and pneumatic artificial muscles (PAMs). The repeatable framework serves to position damping and load carrying elements throughout the structure, and the configuration of the internal elements allow each cell to be tuned to exhibit a desired force-displacement response. Therefore, gradient structures or structures with variable load paths can be created for an optimal global response to a range of loads.;This dissertation focuses on the development of cellular structures for three functions: combined load-carrying capability with harmonic energy dissipation, impact mitigation, and cell modulus variation. One or more conceptual designs are presented for devices that can perform each of these functions, and both experimental measurements and simulations are used to gain a fundamental understanding of each device. Chapter 2 begins with a presentation of a VMT model that is the basis for many of the elements. The equations of motion for the VMT are derived and the static and dynamic behavior of the VMT are discussed in detail. Next, two metrics for the energy dissipation of the VMT - hysteresis loop area and loss factor - are presented. The responses of the VMT to harmonic displacement and force inputs are contrasted in relation to these metrics.;The key innovation to the early structural elements presented here is the combination of the VMT with the pin-jointed hexagonal cell. Chapter 3 explores several prototypes of repeatable structural elements for simultaneous load-carrying capability and energy dissipation that are based on this innovation. The final demonstration prototype presented in this chapter is a column-like element that is based on a hexagonal cell containing two horizontal springs and one vertical damper. The unit is enclosed by a pair of buckling plates that serve to give the prototype a high initial stiffness and load carrying capability. The prototype is tested in both displacement and force input and its behavior is compared to simulation.;Chapter 4 builds on the conceptual designs of Chapter 3 with the introduction of a plate-like element, that contains two compact VMTs connected by a horizontally oriented damper. Pre-loaded springs are used in the prototype to perform the same load carrying function as the buckling plates in the column-like prototype with increased predictability. The plate-like prototype is studied under impact to demonstrate its effectiveness as a protective layer. It is shown to reduce peak impact loads transmitted to the base of the device by over 60%. In most cases, the prototype compares well with a conventional protective rubber layer, and in cases of extreme impact loads, it exceeds the performance of the rubber layer. In addition to impact testing, the prototype is also experimentally tested under harmonic displacement input, and is simulated under both harmonic displacement and force input. The experiments illustrate that while the VMT parameters of a single layer can be optimized to a particular harmonic load amplitude, having two layers with softer and stiffer VMTs allows the system to show good energy dissipation characteristics at different harmonic load amplitude levels.;Chapter 5 examines using PAM inclusions within planar hexagonal cells as variable stiffness springs to create a variable modulus cellular structure. The proposed concept is envisioned as a first step toward a structural unit cell whose in-plane modulus in a given direction can be tuned based on the orientation of PAMs within the cell and the pressure supplied to the individual muscles. To begin, a pin-jointed cell is considered, loaded in the horizontal direction, with three PAMs (one vertical PAM and two horizontal PAMs) oriented in an "H" configuration between the vertices of the cell. A method for calculation of the hexagonal cell modulus is introduced, as is an expression for the balance of tensile forces between the horizontal and vertical PAMs. An aluminum hexagonal unit cell is fabricated and simulation of the hexagonal cell with PAM inclusions is then compared to experimental measurement of the unit cell modulus in the horizontal direction over a pressure range up to 682 kPa. An increase in cell modulus of 200% and a corresponding change in cell angle of 1.53 degrees are demonstrated experimentally. A design study via simulation predicts that differential pressurization of the PAMs up to 1992 kPa can increase the cell modulus in the horizontal direction by a factor of 6.66 with a change in cell angle of only 2.75 degrees. Additionally, simulation predicts that variation of unpressurized cell equilibrium angle and vertical wall length coefficient can result in changes in cell modulus greater than 1000%.;A drawback of the pin-jointed cell with PAM inclusions is that it is inherently underconstrained. To solve this problem, the pin-jointed cell walls are replaced with a continuous Delrin hexagon which gives the cell kinematic stability and allows for experimental measurement of modulus in both the horizontal and vertical directions. The Delrin cell is designed to have a modulus on the same order as that of the pin-jointed cell at zero pressure and is experimentally measured without the PAM inclusions. These measurements validate the use of a combined flexural/hinging analytical model that accurately simulates the cell modulus. This analysis is then combined with the PAM force equations to model the complete hexagonal cell with PAM inclusions. Simulation and experimental measurement of the cell modulus with the PAM inclusions are compared in both the horizontal and vertical directions over an expanded pressure range up to 1302 kPa. The interplay between the contraction ratio and pressure in orthogonal sets of PAMs is highlighted as the primary driver of overall cell modulus.