Full-field Displacement Research Articles

Research on full-field vibration displacement measurement based on grid CCD moiré method

The development of full-field, accurate vibration testing techniques has been vastly valued by the academic and engineering community. However, due to the limited data transmission speed of digital cameras, the contradiction between speed and resolution remains in the traditional full-field vibration measurement systems based on image measurement, failing to acquire high-resolution images at high-speed simultaneously. In this paper, a high-speed and high-resolution full-field vibration displacement measurement system is established based on the grid CCD moiré method. A periodic grid is arranged on the surface of the sample as a deformation carrier, and the periodic pixel of the digital camera is used as a reference grating that ‘enlarges’ the grid on the surface of the sample to form a grid CCD moiré with a geometry significantly larger than the original, capturing images for deformation analysis. This approach lowers the requirement of digital image resolution for high-resolution deformation measurement, reducing the contradiction between speed and resolution in full-field vibration measurement. In this paper, the principle and implementation of full-field vibration measurement using the CCD moiré method are introduced, and the experiment results of full-field in-plane vibration displacement measurement are included, verifying the effectiveness and reliability of the system.

Discrete data-adaptive approximation of hyperelastic energy functions

Phenomenological constitutive modeling is prone to uncertainty and results in loss of information as data coming from experiments are not used directly in calculations. Data-driven approaches are a promising alternative to constitutive modeling. We present a new data-adaptive approach to model hyperelastic rubber-like materials at finite strains. Our proposed modeling procedure combines the advantages of phenomenological hyperelasticity with the data-driven paradigm of directly including experimental data in calculations. We suggest formulating a finite-element-like approximation of the strain energy function as a sum of basis functions expanded over a set of invariants multiplied by unknown parameters. The parameters are determined by an optimization algorithm to match measured experimental data (full-field displacements and global reaction forces) in a least-squares sense. We verify our approach and show that computation times are similar compared to those of phenomenological models. By numerical examples, we demonstrate the ability of our approach to re-identify O(10) parameters.

Measurement of surface-checking in sliced lamellae-based engineered wood flooring using digital image correlation

The lack of quantitative methods for surface-checking measurements may hinder improving the product characteristics of engineered wood flooring products built with sliced top-layer lamellae. This study evaluated the digital image correlation method for its applicability to surface checking measurements in engineered wood flooring elements with the top-layer comprising the plain sliced lamellae of oak (Quercus spp.) species with nominal thicknesses of 1.5–4.5 mm. The method involves observing full-field surface displacements of the sliced lamellae-based wood flooring specimens subjected to an accelerated sorption/desorption cycle. Detection of surface checks relates to discontinuities in surface displacements which can be interpreted from the output strain data as strain peak regions. Additionally, a surface-checking index was defined to describe the extension of surface-checking. Exposure tests were performed on a combination of coating presence and a different number of testing cycles. The main findings provide insight into the method procedure parameters, such as exposure duration, climate conditions, analysis parameters and recommendations regarding the digital image correlation setup settings and specimen manufacturing.

Automated discovery of interpretable hyperelastic material models for human brain tissue with EUCLID

We propose an automated computational algorithm for simultaneous model selection and parameter identification for the hyperelastic mechanical characterization of biological tissue and validate it on experimental data stemming from human brain tissue specimens. Following the motive of the recently proposed computational framework EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery) and in contrast to conventional parameter calibration methods, we construct an extensive set of candidate hyperelastic models, i.e., a model library including popular models known from the literature, and develop a computational strategy for automatically selecting a model from the library that conforms to the available experimental data while being represented as an interpretable symbolic mathematical expression. This computational strategy comprises sparse regression, i.e., a regression problem that is regularized by a sparsity promoting penalty term that filters out irrelevant models from the model library, and a clustering method for grouping together highly correlated and thus redundant features in the model library. The model selection procedure is driven by data stemming from mechanical tests under different deformation modes, i.e., uniaxial compression/tension and simple torsion. The data is acquired through conventional mechanical tests that deliver labeled one-dimensional data pairs, and thus the method can be interpreted as a supervised counterpart to the originally proposed EUCLID that is informed by full-field displacement data and global reaction forces. The proposed method is verified on synthetical data with artificial noise. In addition, we present for the first time an experimental investigation of the EUCLID framework by validating the proposed method on experimental data acquired through mechanical tests of human brain specimens, proving that the method is capable of discovering hyperelastic models that exhibit both high fitting accuracy to the data as well as concise and thus interpretable mathematical representations.

Uncertainty quantification for 3D digital image correlation displacement measurements using Monte Carlo method

Three-dimensional digital image correlation (3D-DIC) is a leading optical measurement technique for measuring full-field shape, displacement, and deformation of solid materials and structures. However, compared with the well-developed and well-accepted measurement technique, uncertainty quantification (UQ) of 3D-DIC measurements is less advanced and less widely practiced. There still lacks a simple and effective method for quantifying the uncertainty of displacements measured by a specific 3D-DIC system for a specific speckle pattern. This is because the 3D-DIC practice involves a complex and long measurement chain and the propagation of uncertainty is highly nonlinear, which makes the uncertainty quantitation tricky. This work proposes a Monte Carlo-based method to quantify the uncertainty of 3D-DIC displacement measurements. The method is based on a theoretical analysis of random error in image matching and theoretical estimation of camera calibration uncertainty. It can estimate the uncertainty in 3D-DIC displacement measurements without additional experimental procedures. Validation experiments reveal that the estimated uncertainty agrees well with the actual situation. Based on the proposed method, the effects of the speckle pattern quality, subset size, and camera calibration quality on 3D digital image correlation displacement measurement uncertainties are also examined. The results reveal that, compared with image matching, camera calibration has a more pronounced influence on the uncertainty of displacement measurements. The proposed method can be integrated with existing 3D-DIC software to quantify the metrological performance of 3D-DIC measurements and therefore better interpret the measurement results.

Characterizing the Adhesion Between Thin Films and Rigid Substrates Using Digital Image Correlation-Informed Inverse Finite Elements and the Blister Test

Abstract Characterizing the adhesion between thin films and rigid substrates is crucial in engineering applications. Still, existing standard methods suffer from issues such as poor reproducibility, difficulties in quantifying adhesion parameters, or overestimation of adhesion strength and fracture energy. Recent studies have shown that the blister test (BT) is a superior method for characterizing adhesion, as it provides a quantifiable measurement of mix-mode fracture energy, and it is highly reproducible. In this paper, we present a novel method to characterize mechanical mix-mode adhesion between thin films and rigid substrates using the BT. Our method combines the full triaxial displacement field obtained through digital image correlation with inverse finite element method simulations using cohesive zone elements. This approach eliminates the need for making any mechanistic or kinematic assumptions of the blister formation and allows the characterization of the full traction-separation law governing the adhesion between the film and the substrate. To demonstrate the efficacy of this methodology, we conducted a case study analyzing the adhesion mechanics of a polymeric pressure-sensitive adhesive on an aluminum substrate. Our results indicate that the proposed technique is a reliable and effective method for characterizing the mix-mode traction-separation law governing the mechanical behavior of the adhesive interface and could have broad applications in the field of materials science and engineering. Also, by providing a comprehensive understanding of the adhesion mechanics between thin films and rigid substrates, our method can aid in the design and optimization of adhesively bonded structures.

Optimized super-resolution promote accuracy for projection speckle three-dimensional digital image correlation

The camera resolution and electronic noise limit the accuracy of the projection speckle three-dimensional digital image correlation (3D-DIC) which is a non-invasive method to detect the reliability of electronic packaging structure. In this study, a measurement method of super-resolution (SR) reconstruction coupled with projection speckle DIC is proposed. The algorithm based on the maximum a posteriori model for DIC measurement systems was also optimized, and a speckle-specific bimodal prior was proposed to adapt to speckle images. By using optimized SR technology as an image pre-processing technique to enhance the resolution of captured images, the accuracy of measurements is improved. Full-field displacement measurement experiments show that, with suitable magnification and speckle size, the use of SR technology reduces the range of displacement errors from 8 μm to 2 μm. Experiments on step block topography measurements show that the use of SR technology reduces the error between DIC measurements and Moiré interferometry from 5 μm to within 2 μm. Therefore, SR technology can be effectively paired with projection speckle DIC measurements to adapt to various measurement scenarios in the field of electronic packaging reliability testing.

Monocular vision based 3D vibration displacement measurement for civil engineering structures

Vibration displacement of civil structures are crucial information for structural health monitoring (SHM). However, the challenges and costs associated with traditional physical sensors make displacement measurement difficult. In recent years computer vision (CV) techniques have been employed for measuring vibration displacement in civil structures. There has been a growing interest in CV-based three-dimensional (3D) displacement measurement, as it provides comprehensive information for structural health assessment. Most existing methods use multi-view geometry, requiring multiple cameras for depth measurement. This paper proposes a new system for measuring the 3D vibration displacement utilising a single camera. Instead of using multi-view geometry, deep neural networks are utilised to learn the depth of scenes from monocular images. Compared with the multi-view methods, the proposed 3D measurement system with monocular vision is more cost-effective and much more convenient to set up and use in practice, avoiding the complicated calibration and object matching between multiple cameras. Experimental tests are conducted in the laboratory to investigate the feasibility of the proposed system. Physical displacement sensors are equipped with the testing structure to provide the ground truth data. The results demonstrate that the proposed monocular 3D displacement system is able to produce reasonable 3D full-field displacement measurement, which makes monocular image based CV system a promising approach to achieve 3D displacement measurement, with its obvious advantages in cost and convenience compared to the traditional sensor-based or multi view CV-based methods.

Analysis of the shear behavior of reinforced recycled aggregate concrete beams based on shear transfer mechanisms

This study aims to contribute to a more rational understanding of the shear behavior of reinforced recycled (concrete) aggregate concrete beams. Twelve reinforced concrete beams - six with natural aggregate concrete (NAC) and six with 100% coarse recycled concrete aggregates (RAC) - with same concrete compressive strength (38 MPa) and proportions of cement and aggregates per volume, varying the longitudinal (1.15%, 1.75%, and 2.50%) and transverse (0%, 0.086%, and 0.114%) reinforcement ratios, were tested under a 4-point bending setup with a full-field displacement monitoring. A thorough examination of the failure span along the tests, associating critical crack shape and kinematics with an investigation of the shear transfer mechanisms provided by mechanical models from the literature was conducted. Direct shear tests on push-off specimens followed by analyses of their failure surface evaluated the characteristics of shear crack surfaces and a proper modeling of the aggregate interlock contribution. The results showed a 28% average reduction in the shear strength of RAC beams with no stirrups in comparison with their reference beams (NAC), whereas beams with stirrups of same characteristics showed a similar shear strength, regardless of the type of coarse aggregate. The evaluation of the shear transfer mechanisms enabled an understanding of the reasons for those behaviors. Experimental results were also compared with those predicted in design codes. They were conservative for beams with stirrups, and, in general, less accurate than those obtained by the shear transfer mechanisms.

Inferring displacement fields from sparse measurements using the statistical finite element method

Nowadays, strain and displacement can be measured using techniques such as electronic speckle pattern interferometry and digital image correlation. However, usually, only some part of the domain of interest is accessible for measurement devices. In order to assess also inaccessible areas of the structure, a fundamental task for structural health monitoring is the inference of full-field displacements from sparse measurements. Another important task is the inference of mechanical stress from displacement or strain data. In computational mechanics, the link between such data and stress is established via constitutive models.A well-established approach for inferring full displacement and stress fields from possibly sparse data is to calibrate the parameter of a given constitutive model using a Bayesian update. After calibration, a (stochastic) forward simulation is conducted with the identified model parameters to resolve physical fields in regions that were not accessible to the measurement device. A shortcoming of model calibration is that the model is deemed to best represent reality, which is only sometimes the case, especially in the context of the aging of structures and materials. While this issue is often addressed with repeated model calibration, a different approach is followed in the recently proposed statistical Finite Element Method (statFEM). Instead of using Bayes’ theorem to update model parameters, the displacement is chosen as the stochastic prior and updated to fit the measurement data more closely. For this purpose, the statFEM framework introduces a so-called model-reality mismatch, parametrized by only three hyperparameters. This makes the inference of full-field data computationally efficient in an online stage: If the stochastic prior can be computed offline, solving the underlying partial differential equation (PDE) online is unnecessary. Compared to solving a PDE, identifying only three hyperparameters and conditioning the state on the sensor data requires much fewer computational resources. Computational efficiency is an essential requirement for online applications. It is noted that conditioning a model-based prior field on sensor data represents a variant of physics-based regression.This paper presents two contributions to the existing statFEM approach: First, we use a non-intrusive polynomial chaos method to compute the prior, enabling the use of complex mechanical models in deterministic formulations. Second, we examine the influence of prior material models (linear elastic and St.Venant Kirchhoff material with uncertain Young’s modulus) on the updated solution. We present statFEM results for 1D and 2D examples, while an extension to 3D is straightforward.

Full-field displacement and strain reconstruction for beam structures based on the extended inverse finite element method

The inverse finite element method (iFEM) is a superior shape sensing methodology in the field of structural health monitoring. However, the standard iFEM for beams yields only displacements at iFEM nodes whose spatial resolution is limited by the number of strain measurements. This study presented an extended iFEM that renders high-quality full-field displacement and strain fields by interpolating the displacements and strains at all locations on the beam using elemental shape functions. A series of numerical studies were implemented to verify the extended iFEM algorithm for various sensor and mesh configurations under different boundary and loading conditions. It showed that the extended iFEM gives smoother and more accurate results using far fewer inverse elements than the standard iFEM.

Extracting high-precision full-field displacement from videos via pixel matching and optical flow

Accurate sensing of full-field displacements plays a significant role in dynamic testing for structural health monitoring (SHM). Recently, video camera has become a more promising tool in displacement sensing due to advantages such as low price, agility, simultaneous measurement, and high spatial sensing resolution. Traditional target tracking approaches (e.g., digital image correlation, template matching, etc.) typically require clear targets on the structure surface and thus only provide sparse displacement. Phase-based motion extraction enables full-field displacement measurement at subpixel precision without the need of markers as tracking targets, which has achieved great success in structural modal identification among many other SHM applications. However, the phase-based approach in a Eulerian framework fails to deal with large motions. To tackle these challenges, an enhanced phase-based method, that synergistically combines the developed local amplitude supplemented pixel matching algorithm and optical flow processing, is proposed for full-field displacement sensing with subpixel precision meanwhile capable of dealing with large motions. In particular, the pixel matching estimates the integer-pixel motion vectors of pixels which have sufficient texture contrast determined by local amplitude. The optical flow, represented by the first order Taylor series, is then employed to approximate the rest subpixel motion associated with the integer-pixel motion vectors. The proposed technique is validated by processing a field-test videos with LVDT reference and then applied to other several lab/field recorded videos of different vibrational objects for displacement extraction and modal identification.

New Plastic Crack-Tip Opening Displacement Tool Based on Digital Image Correlation for Estimating the Fatigue-Crack-Growth Law on 316L Stainless Steel.

This work presents a new approach for studying crack growth resulting from fatigue, which utilizes the plastic contribution of crack-tip opening displacement (CTODp). CTODp is used to predict austenitic stainless-steel crack propagation. Unlike linear elastic fracture mechanics analysis, the method presented here is also helpful for tasks other than small-scale yielding. The approach was based on correlating full-field displacement information with post-processing digital images. This work describes a detailed post-processing protocol that can be used to calculate CTODp. The results for steel compact-tension specimens were especially promising. Of note, there was a linear relationship between the propagation rate of fatigue cracks and the CTODp range.

An electrochemical-mechanical coupled multi-scale modeling method and full-field stress distribution of lithium-ion battery

The rapid development of lithium-ion batteries has made the market more and more concerned about their lives. A large number of studies have shown that the alternating diffusion-induced stress caused by the cyclic charging and discharging processes can significantly shorten the service life of a battery. In recent years, scientists have tried to reveal the distributions and evolutions of the internal stress in lithium-ion batteries during operation by means of experiments and simulations, so as to propose guidance for their design and application. However, the existing numerical simulation framework is still limited to the particles, electrodes and battery units, rather than a battery cell. It is urgent to develop a method that can obtain the full-field stress distributions in commercial lithium-ion battery cells during working, so as to reveal the influence of stress on their lives, and further improve the efficiency of design and optimization. In this paper, an electrochemical-mechanical coupled multi-scale modeling method for lithium-ion batteries is proposed, which solves the technical problem of cross-scaled modeling and simulation from battery units to battery cells. Taking a pouch lithium-ion cell as an example, the lithium concentration distribution, potential distribution, and current density distribution of the battery unit, as well as the full-field displacement distribution, strain distribution and stress distribution of the battery cell during charging are obtained and analyzed. And the assumption, adaptability and potential applications of the method are discussed. It provides a new technical means and insight into the properties of lithium-ion batteries, and even solid-state batteries in the future.

Coarse and Fine Two-Stage Calibration Method for Enhancing the Accuracy of Inverse Finite Element Method.

The inverse finite element method (iFEM) is a novel method for reconstructing the full-field displacement of structures by discrete measurement strain. In practical engineering applications, the accuracy of iFEM is reduced due to the positional offset of strain sensors during installation and errors in structural installation. Therefore, a coarse and fine two-stage calibration (CFTSC) method is proposed to enhance the accuracy of the reconstruction of structures. Firstly, the coarse calibration is based on a single-objective particle swarm optimization algorithm (SOPSO) to optimize the displacement-strain transformation matrix related to the sensor position. Secondly, as selecting different training data can affect the training effect of self-constructed fuzzy networks (SCFN), this paper proposes to screen the appropriate training data based on residual analysis. Finally, the experiments of the wing-integrated antenna structure verify the efficiency of the method on the reconstruction accuracy of the structural body displacement field.

A materials data framework and dataset for elastomeric foam impact mitigating materials

The availability of materials data for impact-mitigating materials has lagged behind applications-based data. For example, data describing on-field helmeted impacts are available, whereas material behaviors for the constituent impact-mitigating materials used in helmet designs lack open datasets. Here, we describe a new FAIR (findable, accessible, interoperable, reusable) data framework with structural and mechanical response data for one example elastic impact protection foam. The continuum-scale behavior of foams emerges from the interplay of polymer properties, internal gas, and geometric structure. This behavior is rate and temperature sensitive, therefore, describing structure-property characteristics requires data collected across several types of instruments. Data included are from structure imaging via micro-computed tomography, finite deformation mechanical measurements from universal test systems with full-field displacement and strain, and visco-thermo-elastic properties from dynamic mechanical analysis. These data facilitate modeling and design efforts in foam mechanics, e.g., homogenization, direct numerical simulation, or phenomenological fitting. The data framework is implemented using data services and software from the Materials Data Facility of the Center for Hierarchical Materials Design.

Physics-guided identification of Euler–Bernoulli beam PDE model from full-field displacement response with SimultaNeous basis function Approximation and Parameter Estimation (SNAPE)

Full-field measurements of the continuous spatiotemporal response of the physical processes such as structural vibration or fluid flow generate large datasets. In many scientific fields, such continuous spatiotemporal dynamic models are represented by partial differential equations (PDEs). In the past, attempts have been made to identify the PDE models from the measured response by inferring its parameters by the use of either regression or deep learning-based techniques. But the previously presented regression-based methods fail to estimate the parameters of the higher-order PDE models in the presence of moderate noise. Likewise, the deep learning-based methods lack the much-needed property of repeatability and robustness in the identification of PDE models from the measured response. The authors introduced the method of SimultaNeous Basis Function Approximation and Parameter Estimation (SNAPE) in a recent paper which addresses such drawbacks by fitting basis functions to the measured response and simultaneously infer the parameters of the PDE model. In this paper the theory and formulation of SNAPE is presented to perform physics-guided identification of the Euler–Bernoulli beam PDE model which is widely applied in the modeling of large scale infrastructures to nanoscale structures.The domain knowledge of the physics is used as a constraint in the formulation of the optimization framework. The alternating direction method of multipliers (ADMM) algorithm is used to simultaneously optimize the loss function over the parameter space of the PDE model and coefficient space of the basis functions. The proposed method not only infers the parameters but also estimates a continuous function that approximates the solution to the PDE model. The efficacy of the method is both numerically and experimentally validated on noise corrupted full-field vibration response. The method neither requires the knowledge of the initial or boundary conditions of the beam nor comprises of model discretization error as in the case of finite element model updating. SNAPE demonstrates its applicability on various homogeneous and time-varying nonhomogeneous boundary conditions.

Research on the mechanical properties of polyvinyl alcohol-modified waste rubber-filled cement paste using digital image correlation technology

The incorporation of waste rubber into concrete has significant environmental value. However, a hydrophobic waste rubber surface results in poor adhesion to concrete, which damages the mechanical properties of concrete. In this paper, polyvinyl alcohol (PVA) is used to modify the waste rubber and the mechanical properties of PVA-modified waste rubber-filled cement paste are examined using digital image correlation (DIC) technology. According to the results, the addition of PVA increases the compressive strength and flexural strength of waste rubber-filled cement paste by 7.9%-15.4% and 12.7%-25.0% at the different curing ages with the content of waste rubber is 25%, respectively. In addition, the specimen exhibits higher integrity after complete destruction in the compressive strength and flexural strength tests as the waste rubber content increases. More importantly, DIC provides a good analysis of the full field displacement and strain in the compressive strength and flexural strength tests of PVA-modified waste rubber-filled cement paste. At the same time, DIC can accurately capture the generation and development of surface cracks on the specimen. The calculated results of the displacement and strain fields visually demonstrate the strengthening effect of PVA on the waste rubber-filled cement paste, especially the inhibition of crack development by PVA.

BUILDING COMPONENT DEFORMATION TRACKING USING STRUCTURED LIGHT TECHNIQUE

Abstract. It is crucial to fully master the mechanical properties of building components for ensuring the safety of infrastructures during service. The laboratory deformation test is an important way to study the mechanical properties of building components. At present, there is still a lack of a combination of high-efficiency, high-accuracy, and low-cost measurement methods for laboratory deformation tests. To address the issue, a method is proposed to measure the deformation of building components by using the structured light technique in this paper. It is applied to the axial tensile test of the dog-bone specimen, and the 3D full-field displacement of the dog-bone specimen is obtained by calculating the established deformation tracking model. The experimental results demonstrate the deformation measurement accuracy is at the millimeter level and can meet the accuracy requirement in the laboratory. Furthermore, the results are consistent with the way of force and the deformation mechanism of the dog-bone specimen. This paper presents a novel method for the deformation measurement, which provides a reliable analysis basis for studying the mechanical properties of building components.

Phase-based vibration imaging for structural dynamics applications: Marker-free full-field displacement measurements with confidence measures

Inspired by the concept of thermal imaging, we develop a phase-based vibration imaging technique using marker-free full-field displacement measurements, which aims to determine vibrational energy distribution and possibly vibration parameters as the thermal imaging determining thermal energy distribution using colormap. In this study, accurate full-field measurements are conducted at the sub-pixel level by performing a full-field phase-based optical flow with three novel progresses. First, an image-preprocessing Gaussian smoothing gradient is applied to reduce the nonlinear phase caused by homogenous patterns and image noise. Second, two confidence measures (phase nonlinearity and filter response) are adopted to obtain reliable displacement measurements estimated from the multi-scale and multi-direction phases. Third, the combination of vector average and the intersection of constraints ensure the accuracy of integrating every pixel’s displacement components. The vibrations can then be imaged by analyzing the acquired full-field displacements using techniques such as mean absolute deviation and frequency analyses. The capability of the proposed technique is demonstrated through numerical experiments using artificial patterns. After then, experimental validation is performed, which includes full-field operational deflection shape extraction on a 5-story structure and vibration imaging of an in-service hydrogen charging station, further proving the effectiveness of the proposed vibration imaging technique.