# Browsing by Subject "Negative stiffness"

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Item 2.5D and conformal negative stiffness honeycombs under static and dynamic loading(2019-05-13) Debeau, David Alexander Robbins; Seepersad, Carolyn; Haberman, Michael R; Kovar, Desiderio; Roach, AllenShow more Negative stiffness honeycombs have been shown to provide nearly ideal impact mitigation with elastically recoverable configuration and mechanical behavior. This capability allows for reliable mitigation of multiple impacts, which conventional honeycombs cannot accommodate because of plastic deformation and collapse. A more in-depth characterization of the mechanical behavior of these negative stiffness honeycombs is presented. The starting point is a 2.5D configuration in which the negative stiffness honeycomb configuration is varied in-plane and extruded out-of-plane. Impact mitigation is investigated by subjecting the 2.5D honeycombs to various drop heights on a purpose-built, drop-test rig. Several embodiments of the 2.5D honeycomb are designed and tested, including nylon versus aluminum, constrained versus unconstrained, and altered configurations with different numbers of rows and columns of negative stiffness elements. While the 2.5D configuration performs well in response to in-plane loading, it is not designed to accommodate out-of-plane loading. A conformal negative stiffness honeycomb design is introduced that conforms to curved surfaces and accommodates out-of-plane loading that is not orthogonal to the load concentrator on top of the honeycomb. Quasi-static mechanical and dynamic mechanical impulse testing of the conformal honeycomb are conducted to characterize the mechanical performance of the conformal design. The final chapter includes a multi-element study that demonstrates how multiple elements perform in an assembly in a more realistic setting. A FEA framework is built to automate the simulation of the 2.5D and conformal negative stiffness honeycomb designs. The framework is built within the commercial Abaqus® FEA package using its Python scripting interface. Automating the design, meshing, loading, and boundary conditions allows for rapid design iteration. Simulations using the FEA framework are compared to experimental quasi-static, impact, and impulse tests. The conformal design was developed to be manufactured additively. The additive manufacturing process introduces sources of potentially significant geometric and material property variability that affect the performance of the honeycombs. The FEA framework is used to conduct a predictability and reliability study that incorporates several sources of variability into the analysis and returns estimates of the expected force threshold and its distribution.Show more Item Application of additively manufactured conformal negative stiffness honeycombs for impact isolation in protective headgear(2018-08-20) Alok, Prashant; Seepersad, CarolynShow more The primary goal of this research is to study the implementation of conformal negatives stiffness elements for impact isolation in baseball helmets. These conformal elements utilize pre-curved beams designed to a specific geometric profile that have been exhibited to have better impact absorption due to their snap-through behavior. A preliminary study is carried out to develop a thorough understanding of pre-curved beams and the negative stiffness elements that utilize this concept. The basic principles and equations of such structures are discussed. Subsequently, the application of the above principles in the context of conformal negative stiffness design is studied. A conformal negative stiffness element is designed and manufactured by SLS using nylon 11. Preliminary tests done on these elements indicated a requirement to improve the effectiveness of the elements so that they are able to absorb impacts of low as well as high magnitude. A novel method to increase the effectiveness by introducing variable force thresholds in these elements is introduced and discussed. The methodology for designing and optimizing an improved element is discussed. The elements are manufactured by SLS using nylon 11. FEA analysis of these elements are carried out in ABAQUS under quasi-static conditions and dynamic conditions. The elements are subjected to physical quasi-static and impact testing as well. Finally, the performance of these elements is compared to a conventional padding used in baseball helmets under one-dimensional impacts using a drop test rig. The results obtained from physical tests are also compared with those obtained from FEA analysis.Show more Item Coextrusion : a feasible method to manufacture negative stiffness inclusions(2013-08) Hook, Daniel Taylor; Kovar, DesiderioShow more This work demonstrates the effectiveness of coextrusion as a method to manufacture negative stiffness inclusions for use in vibrational damping applications. The theory and mechanics of negative stiffness and coextrusion are introduced and the process of creating and extruding a feed rod with negative stiffness architecture explained. Coextrusion is shown to be a viable method to create negative stiffness inclusionsShow more Item Design and evaluation of negative stiffness honeycombs for recoverable shock isolation(2015-05) Correa, Dixon Malcolm; Seepersad, Carolyn; Haberman, Michael RShow more Negative stiffness elements are proven mechanisms for shock isolation. The work presented in this thesis investigates the behavior of negative stiffness beams when arranged in a honeycomb configuration. Regular honeycombs consisting of cells such as hexagonal, square, and triangular absorb energy by virtue of plastic deformation which is unrecoverable. The major goal of this research is to investigate the implementation of negative stiffness honeycombs as recoverable shock isolation so as to better the performance of regular honeycombs.To effectively model the honeycomb behavior, analytical expressions that define negative stiffness beam behavior are established and finite element analysis (FEA) is used to validate them. Further, the behavior of negative stiffness beams when arranged in rows and columns of a honeycomb is analyzed using FEA. Based on these findings, a procedure for the optimization of negative stiffness honeycombs for increased energy absorption at a desired force threshold is developed. The optimization procedure is used to predict trends in the behavior of negative stiffness beams when its design parameters are varied and these trends are compared to those observed in regular honeycombs. Additionally, experimental evaluations of negative stiffness honeycombs under quasi-static loading are carried out using prototypes built in nylon 11 material manufactured by selective laser sintering (SLS). Energy absorption calculations conclude that optimization of negative stiffness honeycombs can yield energy absorption levels comparable to regular honeycombs. A procedure for dynamic testing of negative stiffness honeycombs is discussed. Results from dynamic impact testing of negative stiffness honeycombs reveal excellent shock absorption characteristics. FE models are developed for static and dynamic loading and the results show strong correlation with experiments. Further, temperature dependency of nylon 11 is investigated using impact tests on honeycomb prototypes. Finally, example applications utilizing negative stiffness honeycombs are discussed and recommendations are made for their refinement.Show more Item Energy dissipation and stiffness of polymeric matrix composites with negative stiffness inclusions(2016-08) Cortes, Sergio Andres; Kovar, Desiderio; Seepersad, Carolyn C.; Haberman, Michael R.; Bourell, David L.Show more Typical structural materials have high stiffness to support a static load but offer low damping capacity. These materials easily transmit vibrations that can propagate through the structure, inducing fatigue and premature failure. Thus, structural materials with enhanced damping would increase the operating life of the structure and improve its performance. Here, we study a new class of metamaterials that exhibits simultaneously high damping and stiffness through the use of negative stiffness structures (NSS) embedded into a polymer matrix. Traditional materials have positive stiffness behavior, meaning that the stress increases monotonically with the strain. Similarly, structures made from traditional materials exhibit a positive stiffness, so that the load increases monotonically with displacement applied. NSS structures, however, exhibit a region of negative slope in the force versus displacement response. It has been predicted that the incorporation of these mechanically activated NSS into a polymer matrix would improve the damping behavior, but this has not previously been demonstrated experimentally. A significant part of this work was aimed at determining the geometry of the NSS and the material properties of the NSS and matrix required to achieve high damping. Thus several combinations of NSS geometries, matrix stiffnesses and NSS properties were considered. Analytical and numerical models were developed to guide the design of specimens. Experiments were aimed at producing specimens where damping performance was measured for NSS embedded in a polymer matrix. To conduct these experiments, macro-scale NSS were produced from stainless steel 17-4PH and the properties of the NSS and the NSS embedded in matrices were measured. Results showed that both the design of the NSS and the ratio of the stiffness of the NSS to that of the matrix are important for producing composites that offer simultaneously high damping capacity and high stiffness. Another key challenge is producing NSS at a fine enough scale so that they can be incorporated into a polymer matrix to produce a composite damping material. Amongst potential manufacturing techniques, the multi-filament co-extrusion (MFCX) was selected because it has the potential to produce ceramic, metal or polymer micro-configured geometries in large quantities, quickly and at low cost. This process uses combinations of ceramic-polymer or metal-polymer compounds to reduce an initially macroscopic structure to the microscale while preserving the geometry of the cross-section. When the viscosities of the compounds are ideally matched, co-extrusion is capable of reducing the cross-section by a factor of up to 1000 times (e.g. well into the microscale). However, extensive characterization of the rheology of the compounds is required to achieve very large reductions for complex cross-section such as these. Preliminary results with co-extruded materials were presented to demonstrate the feasibility of this approach.Show more Item Evaluation of Negative Stiffness Elements for Enhanced Material Damping Capacity(2010-05) Kashdan, Lia Beatrix; Seepersad, Carolyn; Haberman, Michael R.Show more Constrained negative stiffness elements in volume concentrations (1% to 2%) embedded within viscoelastic materials have been shown to provide greater energy absorption than conventional materials [Lakes et al., Nature (London) 410, 565–567 (2001)]. This class of composite materials, called meta-materials, could be utilized in a variety of applications including noise reduction, anechoic coatings and transducer backings. The mechanism underlying the meta-material's behavior relies on the ability of the negative stiffness element to locally deform the viscoelastic material, dissipating energy in the process. The work presented here focuses specifically on the design of the negative stiffness elements, which take the form of buckled beams. By constraining the beam in an unstable, S-shaped configuration, the strain energy density of the beam will be at a maximum and the beam will accordingly display negative stiffness. To date, physical realization of these structures has been limited due to geometries that are difficult to construct and refine with conventional manufacturing materials and methods. By utilizing the geometric freedoms allowed by the Selective Laser Sintering (SLS) machines, these structures can be built and tuned for specific dynamic properties. The objective of this research was to investigate the dynamic behavior of SLS-constructed meso-scale negative stiffness elements with the future intention of miniaturizing the elements to create highly absorptive meta-materials. This objective was accomplished first through the development and analysis of a mathematical model of the buckled beam system. A characterization of the Nylon 11 material was performed to obtain the material properties for the parts that were created using SLS. Applying the mathematical model and material properties, a tuned meso-scale negative stiffness structure was fabricated. Transmissibility tests of the meso-scale structure revealed that the constrained negative stiffness system was able to achieve overall higher damping and vibration isolation than an unconstrained system. Quasistatic behavior of the system indicated that these elements would be ideal for implementation within meta-materials. Based on the results of the meso-scale system, a method to test a representative volume element for a negative stiffness meta-material was developed for future completion.Show more Item Evaluation of systems containing negative stiffness elements for vibration and shock isolation(2012-05) Fulcher, Benjamin Arledge; Haberman, Michael R. (Michael Richard), 1977-; Seepersad, Carolyn; Wilson, Preston S.Show more The research presented in this thesis focuses on the modeling, design, and experimentation of systems containing negative stiffness mechanisms for both vibration and shock isolation. The negative stiffness element studied in this research is an axially compressed beam. If a beam is axially compressed past a critical value, it becomes bistable with a region of negative stiffness in the transverse direction. By constraining a buckled beam in its metastable position through attaching a stiff linear spring in mechanical parallel, the resulting system can reach a low level of dynamic stiffness and therefore provide vibration isolation at low frequencies, while also maintaining a high load-carrying capacity. In previous research, a system containing an axially compressed beam was modeled and tested for vibration isolation [7]. In the current research, variations of this model were studied and tested for both vibration and shock isolation. Furthermore, the mathematical model used to represent the compressed beam in [7] was improved and expanded in current research. Specifically, the behavior exhibited by buckled beams of transitioning into higher-mode shapes when placed under transverse displacement was incorporated into the model of the beam. The piecewise, nonlinear transverse behavior exhibited by a first-mode buckled beam with a higher-mode transition provides the ability of a system to mimic an ideal constant-force shock isolator. Prototypes manufactured through Selective Laser Sintering were dynamically tested using a shaker table. Vibration testing confirmed the ability of a system containing a constrained negative stiffness element to provide enhanced vibration isolation results with increasing axial compression on a beam. However, the results were limited by the high sensitivity of buckled beam behavior to geometrical and boundary condition imperfections. Shock testing confirmed the ability of a system containing a buckled beam with a higher-mode transition to mimic the theoretically ideal constant-force shock isolator.Show more Item Experimental study of impact loading on negative stiffness structures(2015-05) Bostwick, Kenneth Stanley; Seepersad, Carolyn; Haberman, Michael R. (Michael Richard), 1977-; Wilson, Preston SShow more This work outlines the design of a drop testing apparatus and the use of the apparatus to perform impact tests on negative stiffness honeycomb structures. Negative stiffness beams are non-linear spring elements that can be used to absorb energy. When prefabricated negative stiffness beams are arranged together in a periodic pattern they create an energy absorbing honeycomb material that can recover from large deformations. Negative stiffness honeycombs have been shown to function similarly to regular honeycombs during quasi-static loading, but are largely untested for impact loading. Two types of honeycomb designs--referred to as vertical and horizontal arrays--have been designed and fabricated to experimentally determine their performance when subjected to impact loading. The performance of each array is compared using finite element models (FEM), quasi-static tests, and drop tests. A drop test apparatus is constructed to perform the impact testing, by measuring the acceleration profile of a mass released from variable drop heights. Results indicate that vertical and horizontal honeycombs reduce accelerations by at least 85 percent when compared to impact without the presence of a honeycomb.Show more Item Exploration and visualization of design spaces with applications to negative stiffness metamaterials(2018-08) Morris, Clinton Benjamin; Seepersad, Carolyn; Haberman, Michael R; Crawford, Richard; Aughenbaugh, JasonShow more Engineering design problems are commonly hierarchical and multilevel which requires coordination between models at each scale. If the models are computationally expensive or highly nonlinear, such as many materials design applications, identification of an optimal design may be exceptionally difficult. Alternatives to optimization-based methods include set-based methods that classify and track sets or ensembles of high performance designs. By relaxing the requirement for an optimal design, it is often possible to identify promising, high performance regions of the design space efficiently. Bayesian network classifiers (BNCs) are such an approach that can identify these regions of promising designs in the presence of nonlinear relationships and mixed variables. When manufacturing the promising designs identified by the BNC approach, the intended design may not match the physical embodiment due to manufacturing variations. These variations may alter the performance of the design leading to unsatisfactory results and products. To facilitate selection of not only high performance but reliably manufacturable designs, a method for incorporating manufacturing variation, modeled as a joint probability distribution is presented for the BNC approach. The approach utilizes a dual classification strategy that identifies regions of design that are likely to perform well within statistical confidence. These design regions can be high dimensional in which it becomes very difficult to identify and visualize clusters of promising designs. This leads to a lack of understanding of the design space. To enhance the designer’s knowledge of the design space, this work presents a method, based on spectral clustering, that can identify high performance regions in a high dimensional space. Furthermore, a method for visualizing each individual design region is presented that is accomplished by incorporating t-Distributed Stochastic Neighbor Embedding. Through the accomplishment of these three tasks—incorporating manufacturing variation, clustering, and visualizing—a novel design methodology will be developed which will then be applied to identify satisfactory designs for a negative stiffness metamaterials design problem which will be manufactured and tested.Show more Item Extreme energy absorption : the design, modeling, and testing of negative stiffness metamaterial inclusions(2013-08) Klatt, Timothy Daniel; Seepersad, Carolyn; Haberman, Michael R. (Michael Richard), 1977-Show more A persistent challenge in the design of composite materials is the ability to fabricate materials that simultaneously display high stiffness and high loss factors for the creation of structural elements capable of passively suppressing vibro-acoustic energy. Relevant recent research has shown that it is possible to produce composite materials whose macroscopic mechanical stiffness and loss properties surpass those of conventional composites through the addition of trace amounts of materials displaying negative stiffness (NS) induced by phase transformation [R. S. Lakes, et al., Nature, 410, pp. 565-567, (2001)]. The present work investigates the ability to elicit NS behavior without employing physical phenomena such as inherent nonlinear material behavior (e.g., phase change or plastic deformation) or dynamic effects, but rather the controlled buckling of small-scale structural elements, metamaterials, embedded in a continuous viscoelastic matrix. To illustrate the effect of these buckled elements, a nonlinear hierarchical multiscale material model is derived which estimates the macroscopic stiffness and loss of a composite material containing pre-strained microscale structured inclusions. The nonlinear multiscale model is then utilized in a set-based hierarchical design approach to explore the design space over a wide range of inclusion geometries. Finally, prototype NS inclusions are fabricated using an additive manufacturing technique and tested to determine quasi-static inclusion stiffness which is compared with analytical predictions.Show more Item Shock isolation performance of a negative stiffness honeycomb with an integrated fluid damping system(2015-05) Kershisnik, Mark C., Jr.; Seepersad, Carolyn; Wilson, Preston SShow more In this thesis, the design, modeling, and shock testing of a monolithic curved beam negative stiffness honeycomb with an integrated air damping system is presented. The purpose of this research was to explore the potential to introduce one way damping into negative stiffness honeycombs by exploiting the geometry changes of the honeycomb during deformation. By adhering an elastomeric diaphragm to the open ends of the honeycomb, the volume of air displaced by the beams during compression is exhausted to the atmosphere from the interior of the honeycomb reservoir through a direction biased check valve system. During rebound, the extension of the honeycomb causes air to be drawn in through an orifice resulting in a damping force. A mathematical model of the system was derived using the theory of compressible flow through an orifice and the constitutive force-displacement relationship of the negative stiffness honeycomb was obtained through quasi-static compression testing of a sample negative stiffness honeycomb. A prototype integrally-damped negative stiffness honeycomb was created using the Selective Laser Sintering additive manufacturing process. A latex rubber diaphragm with a differential check valve system was adhered to the open ends of the honeycomb. The honeycomb was subjected to shock loadings using a drop-test apparatus, and the flow control orifice diameter was varied to observe the effect of orifice size on both compressive, or snap-through accelerations, and rebound or snap-back accelerations. By decreasing the rebound flow control orifice diameter, the snap-back accelerations were reduced, but not as effectively as predicted in the mathematical model, providing an incentive to further investigate the concept of integrated damping systems for negative stiffness honeycombs.Show more