Full-field Data Research Articles

Leveraging Full-Field Deformation Measurements in Computational Modeling of Damage

Abstract Advances in sensing and nondestructive evaluation methods have increased the interest in developing data-driven modeling and associated computational workflows for model-updating, in relation also to a variety of emerging digital twin applications. In this context, of particular interest in this investigation are transient effects that lead to or are caused by deformation instabilities, typically found in the cases of complex material behavior or interactions between material and geometry. In both cases, deformation localizations are observed which are typically also related to damage effects. This paper describes a novel framework to incorporate deformation data into a finite element model (FEM) that has been formulated using non-local mechanics and is capable of receiving such data and using it to describe the development of localizations. Specifically, experimentally measured full-field displacement data is used as an input in FEM as an ad-hoc boundary condition at any or every node in the body. To achieve this goal, a plasticity model which includes a spatially averaged non-local hardening parameter in the yield criterion is used to account for associated numerical instabilities and mesh dependence. Furthermore, the introduction of a length scale parameter into the constitutive law allows the connection between material behavior, geometry, and localizations. Additional steps remove the experimental data and evolve the computational predictions forward in time. Both one and three-dimensional boundary value problems are used to present results obtained by the proposed framework, while comments are made in terms of its potential uses.

A Deep Learning Framework to Estimate Elastic Modulus from Ultrasound Measured Displacement Fields.

Ultrasound (US) elastography is a technique that enables non-invasive quantification of material properties, such as stiffness, from ultrasound images of deforming tissue. The displacement field is measured from the US images using image matching algorithms, and then a parameter, often the elastic modulus, is inferred or subsequently measured to identify potential tissue pathologies, such as cancerous tissues. Several traditional inverse problem approaches, loosely grouped as either direct or iterative, have been explored to estimate the elastic modulus. Nevertheless, the iterative techniques are typically slow and computationally intensive, while the direct techniques, although more computationally efficient, are very sensitive to measurement noise and require the full displacement field data (i.e., both vector components). In this work, we propose a deep learning approach to solve the inverse problem and recover the spatial distribution of the elastic modulus from one component of the US measured displacement field. The neural network used here is trained using only simulated data obtained via a forward finite element (FE) model with known variations in the modulus field, thus avoiding the reliance on large measurement data sets that may be challenging to acquire. A U-net based neural network is then used to predict the modulus distribution (i.e., solve the inverse problem) using the simulated forward data as input. We quantitatively evaluated our trained model with a simulated test dataset and observed a 0.0018 mean squared error (MSE) and a 1.14% mean absolute percent error (MAPE) between the reconstructed and ground truth elastic modulus. Moreover, we also qualitatively compared the output of our U-net model to experimentally measured displacement data acquired using a US elastography tissue-mimicking calibration phantom.

A thermodynamics-informed active learning approach to perception and reasoning about fluids

Learning and reasoning about physical phenomena is still a challenge in robotics development, and computational sciences play a capital role in the search for accurate methods able to provide explanations for past events and rigorous forecasts of future situations. We propose a thermodynamics-informed active learning strategy for fluid perception and reasoning from observations. As a model problem, we take the sloshing phenomena of different fluids contained in a glass. Starting from full-field and high-resolution synthetic data for a particular fluid, we develop a method for the tracking (perception) and simulation (reasoning) of any previously unseen liquid whose free surface is observed with a commodity camera. This approach demonstrates the importance of physics and knowledge not only in data-driven (gray-box) modeling but also in real-physics adaptation in low-data regimes and partial observations of the dynamics. The presented method is extensible to other domains such as the development of cognitive digital twins able to learn from observation of phenomena for which they have not been trained explicitly.

Black and gray box learning of amplitude equations: Application to phase field systems.

We present a data-driven approach to learning surrogate models for amplitude equationsand illustrate its application to interfacial dynamics of phase field systems. In particular, we demonstrate learning effective partial differential equationsdescribing the evolution of phase field interfaces from full phase field data. We illustrate this on a model phase field system, where analytical approximate equationsfor the dynamics of the phase field interface (a higher-order eikonal equationand its approximation, the Kardar-Parisi-Zhang equation) are known. For this system, we discuss data-driven approaches for the identification of equationsthat accurately describe the front interface dynamics. When the analytical approximate models mentioned above become inaccurate, as we move beyond the region of validity of the underlying assumptions, the data-driven equationsoutperform them. In these regimes, going beyond black box identification, we explore different approaches to learning data-driven corrections to the analytically approximate models, leading to effective gray box partial differential equations.

Measuring and Predicting the Effects of Residual Stresses from Full-Field Data in Laser-Directed Energy Deposition

This article presents a novel approach for assessing the effects of residual stresses in laser-directed energy deposition (L-DED). The approach focuses on exploiting the potential of rapidly growing tools such as machine learning and polynomial chaos expansion for handling full-field data for measurements and predictions. In particular, the thermal expansion coefficient of thin-wall L-DED steel specimens is measured and then used to predict the displacement fields around the drilling hole in incremental hole-drilling tests. The incremental hole-drilling test is performed on cubic L-DED steel specimens and the displacement fields are visualized using a 3D micro-digital image correlation setup. A good agreement is achieved between predictions and experimental measurements.

Mixed-mode dynamic fracture parameters for soda-lime glass

Dynamic mixed-mode fracture of soda-lime glass (SLG) was experimentally investigated using a full-field optical method - Digital Gradient Sensing (DGS) - in conjunction with ultrahigh-speed photography. Single edge-notched specimens were subjected to reverse impact loading using a modified Hopkinson pressure bar. The specimens were eccentrically loaded at different offset distances relative to the initial notch to achieve a wide range of mode-mixities, from mode-I to nearly mode-II condition, at initiation. Two time-resolved orthogonal angular deflection fields of light rays proportional to the respective full-field stress gradients were optically measured during experiments on different geometries. Mode-I and -II stress intensity factor histories spanning pre- and post-initiation behaviors were evaluated via over-deterministic least-squares error minimization of optically measured full-field data. By considering the critical stress intensity factors at different crack initiation modes, a fracture envelope for SLG encompassing various mode-mixities was developed for the first time for SLG and compared with predictions from prevailing approaches. An empirical fit of data seems to capture the overall trend whereas the prevailing methods do not. Measured crack kink angles are compared with the popular MTS and SED fracture criteria; both predict the kink angles reasonably well. Unlike brittle polymers, the critical effective stress intensity factors for SLG are independent of mode-mixity over a large range of values but show a decreasing trend as mode-II conditions become dominant and an extrapolated critical mode-II stress intensity factor of 0.37 MPa√m, approx. one-half of its mode-I counterpart, is seen.

Novel Characterizations of Effective SIFs and Fatigue Crack Propagation Rate of Welded Rail Steel Using DIC

The fatigue crack growth-rate test of rail head, waist, and bottom material for U71Mn welded rail was carried out. Digital image correlation (DIC) was used to capture the full-field displacement. The crack-tip position was accurately obtained based on the full-field displacement data, and an accurate crack-tip opening displacement (CTOD) measurement point was found. The CTOD values of the welded rail head under overloaded and unloaded condition were extracted, and the area size of elastic CTOD and plastic CTOD was obtained. According to COD data under different experimental conditions, the corresponding crack opening force was extracted, the crack opening function introduced based on the Elber model, and a calculation method of effective stress-intensity factors (SIFs) considering the plasticity-induced crack closure proposed. The results in this paper provide some references for accurately assessing the fatigue life of welded rail.

Graph neural network modeling of grain-scale anisotropic elastic behavior using simulated and measured microscale data

Here we assess the applicability of graph neural networks (GNNs) for predicting the grain-scale elastic response of polycrystalline metallic alloys. Using GNN surrogate models, grain-averaged stresses during uniaxial elastic tension in low solvus high-refractory (LSHR) Ni Superalloy and Ti 7 wt%Al (Ti-7Al) are predicted as example face-centered cubic and hexagonal closed packed alloys, respectively. A transfer learning approach is taken in which GNN surrogate models are trained using crystal elasticity finite element method (CEFEM) simulations and then the trained surrogate models are used to predict the mechanical response of microstructures measured using high-energy X-ray diffraction microscopy (HEDM). The performance of using various microstructural and micromechanical descriptors for input nodal features to the GNNs is explored through comparisons to traditional mean-field theory predictions, reserved full-field CEFEM data, and measured far-field HEDM data. The effects of elastic anisotropy on GNN model performance and outlooks for the extension of the framework are discussed.

Modelling internal structure of differentiated asteroids via data-driven approach

ABSTRACT This paper is devoted to an interdisciplinary method modelling the internal structure of differentiated asteroids via a data-driven approach called invertible neural networks (INNs). The model estimation of the internal structure can be generalized as an inverse problem of estimating internal parameters from a set of observations. Previous works (e.g. Park et al. 2014; Takahashi and Scheeres 2014) used the full gravity field data measures to derive the heterogeneous mass distribution. However, in our method, only the flight state of the spacecraft is adopted as the observation data. Since the internal parameters may not be uniquely determined, typical feedforward neural networks cannot simply be applied to such an inverse problem. The INNs adopted in this paper can ‘read’ the interior information from a flight trajectory of the spacecraft directly. The INNs are employed to establish the two-directional mapping between the group of physical parameters and the set of flight state observations of position and velocity. The INNs are trained in a bi-directional way using four losses. Finally, the performances of the trained networks are shown in both overfit and underfit situations where the internal structure of asteroids can be estimated by this INNs-based method accurately and effectively. The results also show that even when the degeneracy occurs, the true solution still falls inside the estimation distribution.

Comparison of Attachment Types in Maxillary Implant-assisted Obturators using Digital Image Correlation Analysis

The purpose of the study was to evaluate the stress on the implant and to assess the denture displacement for locator and bar and clip attachment types in implant-assisted obturators. A maxillary edentulous experimental model with a maxillectomy defect was made along with an opposing edentulous mandibular model with self-cure acrylic. Two endosseous implants were placed in the maxillary model. Corresponding obturator complete denture was fabricated for the maxillary model and a complete denture for the mandibular. The attachments were positioned on the implants in maxillary model, and their sleeve/clip was placed on intaglio surface of the dentures. The mounted articulator was placed on a loading apparatus, and force was incrementally applied to it. The strain and displacement for both the attachment types were measured and compared using Digital Image Correlation (DIC). Locator attachment showed the least stress and minimal displacement as compared to bar and clip attachment. The stresses around the implants and displacement of the obturator are affected by the attachment type used. It was found that bar and clip (splinted) showed the maximum stresses around the implant and maximum denture displacement. Locator attachment is the better choice over bar and clip because of its additional retentive features. The advantage of using DIC over the conventional strain gauge analysis is that a full-field data of displacement and strain can be obtained instead of getting a mean value on the small surface where the strain gauge is positioned.

Numerical Study of Leakage and Diffusion of Underwater Oil Spill by Using Volume-of-Fluid (VOF) Technique and Remediation Strategies for Clean-Up

An oil spill accident will cause serious harm to marine ecology and the environment. Rapid response and effective prevention methods are required to minimize the damage of oil spill accidents. The critical problems that marine emergency rescue teams face are when the spilled oil reaches the sea surface, the extent of the spilled oil, and how far they are from the drilling platform. However, there is no reliable model to predict the diffusion distance of spilled oil. Accurately predicting the diffusion characteristics of underwater spilled oil can provide timely and accurate information for the treatment of oil spill accidents and guide the correct implementation of emergency treatment. In this paper, the computational fluid dynamics (CFD) method was used to establish a two-phase flow model for the diffusion of a submarine oil spill. The volume-of-fluid (VOF) technique was implemented to track the interface between oil–water phases. The effects of different parameters on leakage and diffusion characteristics were investigated by adjusting spilled oil velocity, ocean current velocity, crude oil density, and crude oil viscosity. The logarithmic velocity profile was adopted for ocean currents to conform to the actual flow near the sea surface. A user-defined function (UDF) was developed and applied for CFD modeling. The focus was on analyzing the diffusion range (rising height Hp and lateral migration distance Wp) from full-field data. The results indicate that the oil spill velocity, ocean current velocity, crude oil density, and crude oil viscosity impact the viscous shear force, the oil spill’s inertia force, and the current shear effect. The formula for calculating the lateral migration distance of spilled oil under different working conditions was obtained by fitting. The results of this study can provide a scientific basis for formulating an emergency treatment plan for offshore oil spill accidents and minimizing the harm to marine ecology and the environment.

TLS and FEM combined methods for deformation analysis of tunnel structures

With the increasing of tunnel mileage, one of the most vital problems of broad-scale structures is the intelligent identification and location of structural defects, which require massive data storage capacity and high data processing efficiency. The full-field point cloud data collected by terrestrial laser scanning (TLS) can be extracted to construct three-dimensional measured models more accurately, therefore, the fusion of TLS and the finite element method (FEM) is particularly beneficial to the deformation analysis of tunnel structures. This paper combines numerical simulation and full-field measurement to interactively verify the reliability of deformation analysis based on FEM simulation and point cloud processing. The innovation of this paper is that a three-dimensional FEM is validated through the measured point cloud data of the tunnel structure. The result of this study indicated that FEM simulation and the structural health monitoring analysis are consistent.

Identification of crack initiation and damage thresholds in sandstone using 3D digital image correlation

In this study, a non-contact image correlation measurement technique, Three-Dimensional Digital Image Correlation (3D-DIC), is employed to identify and quantify the evolution of rock crack initiation and propagation. With the aim of carefully investigating the cracking progress, a uniaxial compression test was conducted on sandstone specimens with a single pre-existing flaw. The surface and internal micro-fracture characteristics of the sandstone specimen were detected by combining 3D-DIC and acoustic emission techniques from both optical and acoustic perspectives. On the basis of the full-field deformation data derived by 3D-DIC, a method for determining the principal strain of cracks was defined, which aids in identifying the spatial propagation characteristics of rock cracks. Additionally, the crack principal strain method (CPSM) was proposed for determining the characteristic stress threshold of rocks based on the crack principal strain. Then, the results obtained from CPSM are compared to the conventional acoustic emission method (AEM) and axial stiffness method (ASM) tests. The research results suggest that AEM is suitable for identifying crack closure stress and crack initiation stress, whereas ASM and CPSM are superior for identifying damage stress. This work provides a novel method and concept for the measurement of non-contact characteristic stress thresholds, as well as has an insight into the detection and evaluation of the evolutionary process of rock damage and fracture.

A comparative study of invariant-based hyperelastic models for silicone elastomers under biaxial deformation with the virtual fields method

Silicone elastomers have been widely used for biomedical applications. A variety of hyperelastic models have been proposed to describe this type of materials in the past few decades. The assessment of the quality of the proposed models is mostly based on stress–strain data obtained from uniform deformation, but very little work has been done to investigate model performances with heterogeneous deformation fields and full-field characterization methods. In this study, thirteen hyperelastic models are evaluated using the virtual fields method combined with full-field deformation data obtained from biaxial tests. The quality of these models is assessed by their capabilities to predict the mechanical responses of silicone elastomers, and the influences of the first and second invariants on modeling of elastomers are investigated through comparative studies between models. The results indicate that for elastomers under finite biaxial deformation, Yeoh model performs the best among selected models; the first invariant plays an important role in constitutive modeling; the second invariant does not have obvious influence on improving the fitting performance. This study provides a full-field method to calibrate and compare hyperelastic models of silicone elastomers under biaxial loading conditions.

Ensemble Kalman method for learning turbulence models from indirect observation data

In this work, we propose using an ensemble Kalman method to learn a nonlinear eddy viscosity model, represented as a tensor basis neural network, from velocity data. Data-driven turbulence models have emerged as a promising alternative to traditional models for providing closure mapping from the mean velocities to Reynolds stresses. Most data-driven models in this category need full-field Reynolds stress data for training, which not only places stringent demand on the data generation but also makes the trained model ill-conditioned and lacks robustness. This difficulty can be alleviated by incorporating the Reynolds-averaged Navier–Stokes (RANS) solver in the training process. However, this would necessitate developing adjoint solvers of the RANS model, which requires extra effort in code development and maintenance. Given this difficulty, we present an ensemble Kalman method with an adaptive step size to train a neural-network-based turbulence model by using indirect observation data. To our knowledge, this is the first such attempt in turbulence modelling. The ensemble method is first verified on the flow in a square duct, where it correctly learns the underlying turbulence models from velocity data. Then the generalizability of the learned model is evaluated on a family of separated flows over periodic hills. It is demonstrated that the turbulence model learned in one flow can predict flows in similar configurations with varying slopes.

Hydrostatic high strain rate loading response of closed-cell polymeric foams as a function of mass density

Closed cell polymeric foams are widely used in naval structures as sandwich core material owing to their lightweight and high energy absorption capabilities. There has been a great push towards understanding their material response under multiple loading scenarios, however, the loading scenarios have been limited to uniaxial or multiaxial in air loadings at different strain rates. Here, the hydrostatic elastic response and yield behavior of PVC foams with varying mass densities under a high strain rate hydrostatic loading state have been investigated. A novel underwater high strain rate loading facility is utilized to subject these foams to near blast strain rate hydrostatic loading. Using the 3-D Digital Image Correlation (DIC) technique in conjunction with ultra-high-speed photography, full-field volumetric deformation data is obtained. The dynamic loading data is obtained using a piezoelectric pressure sensor. This enables the measurement of material yield strength and bulk modulus for these materials under high strain rate hydrostatic loading conditions. The foams demonstrate increment in bulk modulus and yield strength under high strain rate loading. Further, the increment observed is highly sensitive to the material bulk mass density.

MCRE-based parameter identification from full-field measurements: Consistent framework, integrated version, and extension to nonlinear material behaviors

In this paper, we address the effective and robust identification of material behavior parameters from full-field measurements obtained by means of the advanced Digital Image Correlation (DIC) experimental technique. The objective is to optimize the identification procedure by defining an appropriate and flexible numerical methodology that automatically incorporates the limited knowledge on both the used mathematical model (which is always biased, whatever its complexity) and experimental data (which are numerous in the case of DIC, but inevitably noisy). The inverse methodology we propose, denoted DIC-mCRE, is based on the modified Constitutive Relation Error (mCRE) concept which is a convenient tool to deal with reliability of information. In this framework, the designed identification tool is constructed from a hybrid mathematical formulation with a cost function made of weighted modeling and observation error terms. The associated metric thus naturally considers and connects all error and uncertainty sources. We introduce here a consistent setting of the weighting factors with respect to measurement noise, that gives full sense to the quantification of the model quality. Additionally, an integrated version (called mI-DIC) of the methodology is developed, and an extension to nonlinear constitutive models is proposed together with a dedicated solver. The performance of the approach is analyzed and validated on several numerical experiments dealing with linear elasticity or nonlinear models, and using synthetic or real full-field data.

Flow Field Reconstructions With GANs Based on Radial Basis Functions

Nonlinear sparse data regression and generation have been a long-term challenge in the field of aerodynamics, flow field reconstruction is an area of specific interest in this article. The high computational costs of computational fluid dynamics (CFD) make large scale CFD data production expensive, which is the reason why cheaper methods are needed. Traditional reduced-order models were promising but they cannot generate a large amount of full domain flow field data (FFD) to execute high-precision flow field reconstructions. Motivated by the problem of existing approaches, and inspired by the success of generative adversarial networks (GANs) in the field of computer vision, we prove a theorem that shows the optimal approximation to a GAN discriminator is a radial basis function neural network when engaged in with nonlinear sparse FFD regression and generation. Based on this theorem, a radial basis function-based GAN (RBF-GAN) and a RBF cluster-based GAN (RBFC-GAN) are proposed for regression and generation purposes. Three different datasets are applied to verify the feasibility of our models. The results show that the performance of RBF-GAN and RBFC-GAN are better than that of GANs and conditional GANs (cGANs) by both the mean square error and the MSPE measurements. In addition, compared with GANs/cGANs, the stability of the RBF-GAN and the RBFC-GAN are improved by 34.62 and 72.31%, respectively. Consequently, our proposed models can be used to generate full domain FFD from limited and sparse datasets to meet the requirements of high-precision flow field reconstructions.

The Influence of Static Load and Sideways Impact Fall on Extramedullary Bone Plates Used to Treat Intertrochanteric Femoral Fracture: A Preclinical Strength Assessment.

Hip fracture accounts for a large number of hospitalizations, thereby causing substantial economic burden. Majority (> 90%) of all hip fractures are associated to sideways fall. Studies on sideways fall usually involve loading at quasi-static or at constant displacement rate, which neglects the physics of actual fall. Understanding femur resonance frequency and associated mode shapes excited by dynamic loads is also critical. Two commercial extramedullary implants, proximal femoral locking plate (PFLP) and variable angle dynamic hip screw (VA-DHS), were chosen to carry out the preclinical assessments on a simulated Evans-I type intertrochanteric fracture. In this study, we hypothesized that the behavior of the implant depends on the loading types-axial static and transverse impact-and a rigid implanted construct will absorb less impact energy for sideways fall. The in silico models were validated using experimental measurements of full-field strain data obtained from a 2D digital image correlation (DIC) study. Under peak axial load of 3 kN, PFLP construct predicted greater axial stiffness (1.07 kN/mm) as opposed to VA-DHS (0.85 kN/mm), although the former predicted slightly higher proximal stress shielding. Further, with greater mode 2 frequency, PFLP predicted improved performance in resisting bending due to sideways fall as compared to the other implant. Overall, the PFLP implanted femur predicted the least propensity to adverse stress intensities, suggesting better structural rigidity and higher capacity in protecting the fractured femur against fall.

Correction of full-field rigid body rotation and strain using a hybrid peridynamics and digital image correlation approach

Rigid body rotation is difficult to be removed independently while using digital image correlation (DIC) technique for monitoring the displacement and deformation of an object. Furthermore, strain measurement can also become inaccurate due to the presence of displacement caused by rigid body rotation. Common solutions to this problem, such as tracking a single-point's rotation, require additional reference information and only obtain one rigid body rotation angle of the object. In this study, a hybrid computational and experimental mechanics method based on peridynamics (PD) and DIC technique is proposed to measure the full-field rigid body rotation and strain. A DIC-based PD model can be established based on the full-field position data obtained by DIC. The calculation formulas for rigid body rotation and strain are derived in the framework of PD and the calculations of rotation and strain are mutually insensitive and independent. Therefore, without any additional reference information, the rigid body rotation and strain information can be obtained in the presence of simultaneous rigid body rotation and deformation. Different rigid body rotations in various regions of an object, whether large or small rotations, can be calculated by this method. Correspondingly, this method is effective for calculating the local rigid body rotations of objects undergoing local fracture. Numerical simulations and experimental tests were performed to verify the effectiveness of the proposed method. The calculation results show that the proposed method owns the ability to accurately calculate the rotation and strain in the above scenarios.