Chapter 4 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 Accelerated Mechanical Behavior Characterization of Structural Materials J. Rathore, A. Imeri, E. Al Amiri, V. Shah, C. O’Brien, B. Wisner, and A. Kontsos Abstract Qualification processes for the mechanical behavior of advanced materials depend heavily on extensive experimental testing needed to also obtain inputs to both physics-based and machine learning models. The use of full-field methods has some inherent advantages towards the direction of accelerating such qualification compared with traditional mechanical testing approaches. To demonstrate an application of this potential, a novel specimen design is produced to obtain all input parameters to a J3-type plasticity model that can characterize the plastic behavior of any type of alloy (in terms of crystallography), while also including the effects of anisotropy and strength differential dependencies. This work presents details on how Digital Image Correlation (DIC) could be used first to obtain mechanical behavior information from tests using standardized geometries which are then used to uniquely define input parameters for the plasticity model. This information is then leveraged to accelerate the plasticity model calibration process by using Finite Element Analysis (FEA) to design a novel test specimen geometry which can produce the same information by a 4-fold reduction of the associated number of experiments. Finally, this presentation concludes with the validation of the results obtained by the use of this novel specimen and by furthermore demonstrating how the FEA model could be used to augment the DIC information by computing the components of the strain tensor that are not measured by DIC while also providing the stress tensor components and related reaction forces. Keywords Mechanical Testing· Digital Image Correlation· Plasticity Introduction Novel developments and performance improvement of advanced materials are hindered by the time involved between discovery and adoption. This is particularly true for the case of advanced manufacturing materials where small changes in the feedstock, process and post-process create unpredictable changes in the resulting mechanical behavior [1, 2]. Thorough understanding of material behavior requires exhaustive testing under various loading and environment conditions[3]. Additionally, testing is also used to develop and calibrate mathematical models (e.g. constitutive laws) to be used, for example, in Finite Element Analysis (FEA). Advanced materials used in engineering applications typically experience complex stress states which cannot be captured by simple specimen geometries, as defined e.g. by common standards[4]. In addition, most conventional and standardized testing methods use point-wise global measurements such as extensometers and strain gauges to provide bulk or global information (typically stress-strain curves). Furthermore, depending on the manufacturing methods used, materials can exhibit anisotropic, differential hardening, damage and other stress-state dependent effects (e.g. triaxiality), which cause non-homogenous stress and strain fields and add difficulty in developing reliable and accurate computational models. J. Rathore · A. Imeri · E. AlAmiri · V. Shah· A. Kontsos( ) Digital Engineering Hub, Department of Mechanical Engineering, Henry M. Rowan College of Engineering, Rowan University, Glassboro, NJ 08028 email: rathor12@students.rowan.edu; imeri@rowan.edu; alamir78@rowan.edu; shahva28@rowan.edu; kontsos@rowan.edu B.Wisner · C. O’Brien Center for Advanced Materials Processing, Department of Mechanical Engineering Russ College of Engineering and Technology, Ohio University, Athens, OH 45701 email: bwisner@ohio.edu © The Author(s), under exclusive license to River Publishers 2025 23 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 4
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