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 Fracture Properties Identification using Full-field Measurements: Some Important Concepts and Validation Joa˜o Carlos A. D. Filho, Lukas Wittevrongel, Amar Peshave, Pascal Lava, and Fabrice Pierron Abstract This article studies the effect of Digital Image Correlation uncertainties on fracture parameters obtained from a CT test specimen. It uses synthetic image deformation from finite element simulations to identify such errors. The paper looks at systematic errors from the DIC process as well as the effect of image noise. Keywords Fracture mechanics · Synthetic image deformation· Uncertainty quantification· Digital image correlation Introduction Fracture mechanics is a widely used tool in academia and industry to predict the failure of materials. An important parameter to such models is the fracture toughness in the different modes of fracture, I, II and III. Many techniques have been developed over the years to obtain such parameters, and it is beyond the scope of the present paper to review them. They mostly use the load recorded by the load cell of the test machine together with some (semi-) analytical solutions to derive the fracture properties. In the last twenty years, full-field optical measurements have gradually spread in the experimental mechanics community, providing very dense sets of kinematic data (typically tens of thousands or more), hence the term ‘full-field’. Digital Image Correlation (DIC) is the most widespread [1], with many commercial systems providing turnkey solutions. It is therefore not surprising that many studies have used DIC data to extract fracture parameters, as reviewed in [2]. There are generally two main families of approaches: either fitting the crack-tip displacement field with a Williams series [3] to obtain the stress concentration factor; or using the J-integral [4]. DIC is a complex measurement chain, highly nonlinear and subject to many potential sources of error. As a consequence, while it is easy to process DIC data for stress concentration factors or toughness, it is hard to establish realistic error bars on these quantities. This is the objective of the present contribution. It relies on the technology of synthetic image deformation developed initially in [5, 6] to perform uncertainty quantification in material constitutive model identification with the Virtual Fields Method. It is extended here to the determination of stress concentration factors and J-integrals. Simulation of DIC measurements on CT specimen A finite element (FE) model of a Compact Tension (CT) specimen was developed using Abaqus v.6.6, based on the ASTM standard E399 [7]. Plane stress CPS4R linear elements were used. The dimensions and the mesh are reported in Fig. 1. The bottom and top holes were constrained in all translational degrees of freedom, except the top hole vertical displacement which was left free while a vertical load of 35 N was applied. Large transformations were enabled. The material selected for this study is PMMA with a Young’s modulus of 3260 MPa and Poisson’s ratio of 0.36. The material thickness is 1 mm. Based on the FE model displacements, a numerically-generated speckle pattern was deformed according to the procedure described in [6]. The pattern was generated with the internal speckle pattern generator in the MatchID software. It consists of Joa˜o Carlos A.D. Filho· Lukas Wittevrongel · Amar Peshave · Pascal Lava · Fabrice Pierron MatchID NV, Leiekaai 25A, 9000 Ghent, Belgium e-mail: joao.filho@matchid.eu; lukas.wittevrongel@matchid.eu; amar.peshave@matchid.eu; pascal.lava@matchid.eu; fabrice.pierron@matchid.eu © The Author(s), under exclusive license to River Publishers 2025 15 Garrett Pataky et al. (eds.), Fracture, Fatigue, Failure, Damage Evolution and Thermomechanics & Infrared Imaging, Vol. 4, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.13052/97887-438-0830-5 3
RkJQdWJsaXNoZXIy MTMzNzEzMQ==