Chapter 3 Chapter 1 On the Detection and Quantification of Nonlinearity via Statistics of the Gradients of a Black-Box Model Georgios Tsialiamanis and Charles R. Farrar Abstrac t Detection and identification of nonlinearity is a task of high importance for structural dynamics. On the one hand, identifying nonlinearity in a structure would allow one to build more accurate models of the structure. On the other hand, detecting nonlinearity in a structure, which has been designed to operate in its linear region, might indicate the existence of damage within the structure. Common damage cases which cause nonlinear behaviour are breathing cracks and points where some material may have reached its plastic region. Therefore, it is important, even for safety reasons, to detect when a structure exhibits nonlinear behaviour. In the current work, a method to detect nonlinearity is proposed, based on the distribution of the gradients of a data-driven model, which is fitted on data acquired from the structure of interest. The data-driven model selected for the current application is a neural network. The selection of such a type of model was done in order to not allow the user to decide how linear or nonlinear the model shall be, but to let the training algorithm of the neural network shape the level of nonlinearity according to the training data. The neural network is trained to predict the accelerations of the structure for a time-instant using as input accelerations of previous time-instants, i.e. one-step-ahead predictions. Afterwards, the gradients of the output of the neural network with respect to its inputs are calculated. Given that the structure is linear, the distribution of the aforementioned gradients should be unimodal and quite peaked, while in the case of a structure with nonlinearities, the distribution of the gradients shall be more spread and, potentially, multimodal. To test the above assumption, data from an experimental structure are considered. The structure is tested under different scenarios, some of which are linear and some of which are nonlinear. More specifically, the nonlinearity is introduced as a column-bumper nonlinearity, aimed at simulating the effects of a breathing crack and at different levels, i.e. different values of the initial gap between the bumper and the column. Following the proposed method, the statistics of the distributions of the gradients for the different scenarios can indeed be used to identify cases where nonlinearity is present. Moreover, via the proposed method one is able to quantify the nonlinearity by observing higher values of standard deviation of the distribution of the gradients for lower values of the initial column-bumper gap, i.e. for “more nonlinear” scenarios. Keyword s Structural health monitoring (SHM) · Structural dynamics · Nonlinear dynamics · Machine learning · Neural networks 1.1 Introduction In the pursuit of making everyday life safer, humans have extensively tried to model the environment around them. Structures are an important part of the environment, in which humans live. They are man-made and should be safe throughout their lifetime. Structures are exposed to numerous environmental factors, which may cause them to fail. Moreover, during operation, structures are subjected to dynamic loads, which, in time, may cause failure. Such failures will most probably result in economic damage to society and may even result in loss of human lives. Therefore, for the purpose of maintaining structures safe, the field of structural health monitoring (SHM) [1] has emerged. G. Tsialiamanis ( ) Dynamics Research Group, Department of Mechanical Engineering, University of Sheffield, Sheffield, UK e-mail: g.tsialiamanis@sheffield.ac.uk C. R. Farrar Engineering Institute, MS T-001, Los Alamos National Laboratory, Los Alamos, NM, USA e-mail: farrar@lanl.gov © The Society for Experimental Mechanics, Inc. 2024 M. R. W. Brake et al. (eds.), Nonlinear Structures & Systems, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-031-36999-5_1 1 Interfacial Characterization of Metal Wire Inlays for 3D Printed FDMParts Vereesh Ayyagari, Hugh A. Bruck, Amir H. Ohadi, and Michael M. Ohadi Abstract A novel process for creating 3D printed parts with metal wire inlay has been developed at the University of Maryland. By using metal wire inlay, parts can retain the properties of drawn metal wires that can be either embedded in polymer or fully exposed. As a result, the mechanical integrity of the metal wire interface with the FDM polymer can be controlled through the printing conditions and preparation of the wire surface. In this investigation, we develop a novel test specimen for characterizing the mechanical integrity of the metal wire/polymer interface. In particular, the test specimen is designed to quantify the ability of the interface to provide hermetic sealing when loaded by pressurized fluids. The effects of the processing and preparation conditions on the interfacial strength are also investigated via single fiber pullout tests. As a result, it is possible to design new 3D-printed metal-polymer composite structures with free standing metal wires that can be utilized in a a variety of different applications ranging from integrated flow sensing to enhanced thermal control. Keywords Metal-polymer composites · Polymer-metal interface · Failure characterization· Adhesion · Interfacial strength Introduction Polymer matrix-metal wire composite structures are increasingly being developed for strengthening polymer structures [1], heat exchangers [2], and conductive path tracing for electronic components [3]. For a mechanistic point of view, there could be two variants of the composites. In the first, the metal wire is wholly embedded in the polymer. In the second composite, the metal wires are partially exposed, resulting in a partially free-standing metal wire. The two variants of the composites are shown in Figure 1, where Figure 1a shows the polymer-metal composites where the metal wires are completely embedded into the polymer, and 1b shows the composites where metal wires are partially free-standing. While the fabrication of the composite can be achieved through conventional manufacturing techniques, additive manufacturing, commonly referred to as 3D Printing, has become popular choice of fabrication, primarily due to the complex nature of the composite. For 3D printing of the composites, Fused Filament Fabrication (FFF) has been widely used for depositing the polymer, and metal wires are thermally embedded. In FFF, thermoplastic materials, such as polycarbonates, acrylonitrile butadiene styrene (ABS), Polylactic Acid (PLA), and Poly Amides (PA), are used as feedstocks due to their favorable properties such as low melting temperature and appropriate melt viscosities [4]. Recently, we have developed a 3D printing process for metal wire-inlay to create cross-media heat exchangers [5–8] which contains an array of free-standing metal wires embedded into the polymer structure. The failure mechanisms of the polymer-metal composites are critical to understanding their limitations in the applications. In particular, to estimate how much pressure can be applied to the structure before the wires start pulling out i.e. interfacial strength between metal and polymer, wire push out tests are applied [1, 9–11]. While a few studies exist on the characterization of composites where metal fibers that are embedded continuously in a polymer matrix, very few have studied 3D-printed polymer-metal composites fundamentally, where the metal wires are partially exposed. The current study focuses on the failure characterization of the partially free-standing metal fibers in polymer-metal composites. Vereesh Ayyagari · Hugh A. Bruck· Amir H. Ohadi · Michael M. Ohadi Department of Mechanical Engineering, A. James Clark School of Engineering, University of Maryland, College Park, MD 20742 e-mail: veeresha@umd.edu; bruck@umd.edu; amir@umd.edu; ohadi@umd.edu © The Author(s), under exclusive license to River Publishers 2025 13 Emily Retzlaff et al. (eds.), Mechanics of Additive & Advanced Manufacturing, Inverse Methods and Machine Learning, Vol. 5, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.13052/97887-438-0831-2 3
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