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DOE OSTI2023

Additively Manufactured Strain Sensing for Nuclear Reactor Applications

Real-time monitoring of materials in harsh environments is a crucial technique towards reducing innovation time in nuclear systems. The successful measurement of real time, in-situ strain measurements during nuclear reactor operation requires innovative sensing solutions, including novel sensing strategies as well as advanced sensor design, manufacturing, and materials selection. In this paper, we will discuss two primary strategies for in-situ strain measurement strategies: additively manufactured (AM) capacitive strain gauges (CSGs) and digital image correlation (DIC). Current commercial strain gauges have limited applications in reactors due to the harsh operating conditions and non-trivial attachment strategies (i.e., welding, epoxy-adhesive) that can affect both the sensing performance and the underlying substrate under testing. AM CSGs are a viable solution as they have a low profile, low hysteresis, and wireless sensing integration capabilities that will enhance nuclear sensing technologies. In this work, the mechanical and thermal performance of the AM CSGs were tested up to 300 °C using ASTM standardized testing procedures to simulate the temperatures found in existing light water reactors. The AM CSGs had a similar performance across multiple samples which correlates to analytical models. This work leads towards the development of CSGs designed for higher temperatures and additional environmental factors found in Generation-IV reactors. Non-contact sensors, such as DIC, offer a less destructive way to measure deformation of materials when compared to alternative methods of in-situ strain determination, such as weldable strain gauges. However, DIC requires high contrast surfaces, which often relies on the implementation of artificial patterns. Using traditional splatter techniques to fabricate these patterns have limitations, including poor surface adhesion and reproducibility. In this work, AM fabrication techniques were implemented to avoid such limitations. Accordingly, aerosol jet printing (AJP) was used to print small scale periodic patterns of silver on stainless steel and aluminum tensile specimens. DIC was employed to monitor strain (up to 1100 µe) during temperature cycling from 23-600 °C. The results validated the use of AJP to better control pattern parameters for small fields of view applications at high temperatures.

36 MATERIALS SCIENCE↗

DOE OSTI2020

A complete grain-level assessment of the stress-strain evolution and associated deformation response in polycrystalline alloys

Polycrystalline alloys are used pervasively across structural applications contingent upon extensive experimental testing. A statistically representative number of tests are required to expose the variability in the material's performance, as a result of non-uniform microstructures and associated micromechanical fields. In a more direct means of capturing this pertinent information, multi-modal experimental techniques are presented to measure and track the complete micromechanical state, evolving during loading, of each and every grain within the regions of interest. Specifically, a combination of high-energy X-ray diffraction microscopy and digital image correlation coupled with electron backscatter diffraction are conducted on a specimen for each of the alloys, Haynes 282 and Ti7Al. The results of the multi-modal analysis definitively demonstrate that the degree of heterogeneity increases with deformation level and is used to assess the number of grains necessary for a representative volume element description of the stress state for each of these materials. Moreover, higher resolution imaging is used for identification of the slip system activity and subsequently used to study slip transmission events. An accurate knowledge of the resolved shear stress in adjacent grains (grain interactions) is demonstrated to be a key descriptor of the slip transmission events.

36 MATERIALS SCIENCE↗

DOE OSTI2020

A method for characterization of multiple dynamic constitutive parameters of FRCs

We propose a method to measure multiple dynamic material constitutive parameters of unidirectional fiber reinforced composites (FRCs) in a single experiment. Dynamic short-beam shear (DSBS) experiments were performed on a modified Kolsky compression bar, with integration of high-speed imaging and digital image correlation (DIC). The unidirectional FRCs investigated were S-2 glass fiber reinforced matrix of TGDDM-Jeffamine® D230 with monoamine functionalized partially reacted substructures (mPRS) and commercially available SC-15. Analytical solutions of normal and shear strains of a composite beam were derived based on Timoshenko beam theory, assuming material to be transversely isotropic and have different moduli in tension and compression in each principle material orientation. Tensile and compressive moduli were inversely computed through monitoring normal strain slope when specimen was constantly loaded at a speed of ~7.3 m/s within a small deflection. Non-linear shear stress-strain behavior of the composite was described via Ramberg–Osgood equation. Finite element (FE) analysis was conducted in ABAQUS, simultaneously defining via user subroutine UMAT the transverse isotropy of material, bi-modulus constitutive model, and non-linear shear stress-strain relation. The method proposed in this work was validated by comparing strain distributions computed by FE model and DIC measurements. Comparing with traditional dynamic tensile, compressive, and shear experiments on FRCs, this method significantly simplifies the specimen preparation and design of complicated gripping fixtures for multiple experiments. Here, systematic errors resulting from variations of specimen geometry and dimension, loading direction, and instrumentation are reduced, thereby providing compatible data for numerical studies on impact behavior of composites.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Full-Field Strain Measurement Integrated with Two Dimension Regression Analysis to Evaluate the Bi-Modulus Elastic Properties of Isotropic and Transversely Isotropic Materials

Background: Measuring the physical properties of shale is critical for optimizing engineering activities such as geothermal energy generation and hydraulic fracturing. Shale is a transversely isotropic material. Furthermore, this material can also include micro and macro cracks at different locations and orientations that cause it to behave differently under tensile or compressive loading. Objective: In this work, a combined experimental–numerical approach is proposed to evaluate the bi-modulus elastic properties of isotropic and transversely isotropic materials. Methods: Full-field strain measurements for a circular disk under diametral compression are integrated with a regression analysis technique to evaluate the elastic properties of bi-modulus materials subjected to tensile and compressive loads using two loading configurations on the same specimen. Digital Image Correlation (DIC) is used to measure the full-field strains. Subsequently, in the case of an isotropic material, a linear least-squares approach is utilized to process the experimentally determined strains in conjunction with analytical expressions of the stress fields (in terms of far-field loading) to determine the elastic modulus E, the shear modulus G, and the Poisson’s ratio $v$. In the case of a transversely isotopic material, such as shale, a finite element model is implemented to determine the stress fields (again in terms of far-field loading), which is followed by repeating the previous regression analysis in an iterative process to estimate the elastic parameters. Results: The results show that the proposed technique successfully provides a complete set of elastic properties as a function of both the loading condition and the principal material directions. The technique is validated by measurements on a known isotropic material and then applied to determine the properties of shale. Conclusion: In this work, the proposed approach is successfully used to calculate the bi-modulus elastic response of poly(methyl meth- acrylate) (PMMA) and shale. As expected, PMMA exhibits an isotropic response with no bi-modulus effect, however, shale exhibits both transverse isotropy and a bi-modulus effect. Therefore, this approach holds promise for investigating the elastic properties of materials like rocks and fiber-reinforced composite laminates as functions of the principal material directions and the loading conditions.

42 ENGINEERING↗

DOE OSTI2022

Development of grain-scale slip activity and lattice rotation fields in Inconel 718

Using a combination of in-situ high-resolution digital image correlation (HR-DIC), Heaviside-DIC method (H-DIC), and crystal plasticity finite element (CPFE), we investigate the evolution of intragranular lattice rotations and slip activity during monotonic and cyclic loading in a high performance, polycrystalline face centered cubic material. The CPFE employs a quasi-3D model microstructure, which is a highly resolved mirror representation of the experimental in-situ test sample. In agreement, the measurements and calculations reveal that most grains, regardless of their size and lattice orientation, develop intragranular lattice rotation gradients that span the grain. For a small cluster of grains on the deformed material, we perform HR-DIC analysis of slip lines to demonstrate agreement in the active slip systems and changes in this local slip activity across the individual grains. The combined analysis reveals that deforming grains are divided into sub-granular regions of uniform lattice rotation and these regions are most often associated with only one or two active slip systems. The gradient lines that divide them correspond to changes in the predominant slip system. The model is used to examine the evolution of intragranular lattice rotation in a single fully reversed tension-compression cycle. The calculations indicate that intragranular gradients intensify during the reverse loading path as nearest neighboring regions appear to shed lattice rotation, increasing the lattice rotation in some regions, while shutting down rotation in neighboring regions. So these findings provide insight into the irreversible changes that develop within deforming grains at the scale of the grain, particularly the heterogeneous development of intragranular lattice rotation in early stages of deformation, which could serve as precursors to localization.

36 MATERIALS SCIENCE↗

NASA NTRS2020

Change of Exposure Time Mid-test in High Temperature DIC Measurement

Performing digital image correlation (DIC) at extreme temperatures has been greatly challenging due to the radiation which saturates the camera sensor. At such high temperatures, the light intensity emitted from an object is occasionally so powerful that the acquired images are overwhelmingly saturated. This induces data loss, potentially ruining the test, thus requiring the user to restart the test. For this reason, selection of an appropriate camera sensitivity plays a crucial role prior to beginning the test. Exposure time is a factor contributing to camera sensitivity and it is the easiest setting to manipulate during the test since it introduces minimal errors when comparing to other factors, especially in quasi-static tests. This paper examines the influence of changing exposure time mid-test on DIC measurement uncertainty. The investigation was conducted by rigid body motion experiments at room temperature and 1600 ◦C, respectively. Thereby, some recommendations are given to help DIC users assess their images at room temperature to extrapolate the exposure at extreme temperatures along with accompanying solutions to salvage data at high temperature.

Digital Image Correlation↗

DOE OSTI2024

Geophysical Signatures of Crack Network Coalescence in Rocks at Multiple Length Scales

The main goal of the research project was to identify the geophysical signatures of fracture growth in natural rocks by utilizing novel geophysical techniques. The research objectives were to (a) investigate the potential for geophysical methods to determine when cracks initiate, the types and locations of propagated cracks, and the coalescence of networks of cracks in natural rocks at multiple scales, (b) determine how damage at the microscale evolved into damage at the macroscale and then link the microscopic and macroscopic observations, (c) quantify crack coalescence in rocks under realistic stress conditions using coupled mechanical-geophysical-optical visualization, and (d) identify the precursors in geophysical signals to crack coalescence. The following research thrusts were explored to achieve the research objectives: (1) uniaxial compression testing of rock specimens with and without a set of pre‐existing flaws and (2) triaxial compression testing of natural rock specimens. These thrusts allowed for exploring fracturing in rocks under realistic in situ environments and at multiple scales. This project provided educational opportunities for nine graduate and undergraduate students and resulted in 27 peer-reviewed publications. This first research thrust focused on investigating the micromechanics of fractures in rocks through uniaxial compression testing combined with advanced geophysical and imaging techniques, specifically acoustic emission (AE) monitoring, ultrasonic imaging, and 2-dimensional Digital Image Correlation (2D-DIC). By examining damage processes under time-independent and time-dependent loading conditions, insights into damage localization, crack initiation, and fracturing mechanisms were gained. It was observed that the AE signals and the strain-based measurements directly reflect the state of damage in the rock specimen and could be used to identify the cracking levels, such as the crack initiation (CI) and crack damage (CD), and the mode of deformation. A novel calibration apparatus was developed to enhance the accuracy of AE sensors, allowing for the estimation of key parameters such as magnitude, source dimension, stress drop, and radiated seismic energy associated with the fractures. The findings highlighted significant variations in the temporal evolution of AE source parameters during the primary, secondary, and tertiary stages of creep, identifying tensile cracking as the primary deformation mode. The second research thrust focused on enhancing the understanding of fracturing processes in natural rocks through triaxial compression testing, real-time AE monitoring, and ultrasonic monitoring. We investigated the impact of various factors such as fracture propagation regimes, injection parameters, rock types, and pre-existing conditions on the hydraulic fracture (HF) behavior using scaled true-triaxially loaded specimens of Barre granite and Lyons sandstone. Custom sensor housing facilitated concurrent active and passive monitoring to analyze hydro-mechanical responses and microseismicity associated with different HF scenarios. A coupled investigation of passive microseismicity and active signal attributes permitted a detailed comprehension of the various HF processes (aseismic deformation, fracture initiation and propagation, fluid permeation, and leak-off) and their dependence on the specific rock type. The findings of this research demonstrated the effectiveness of AE monitoring techniques in providing valuable insights into the impact of various factors on the behavior and dynamics of HF processes. The advancements in monitoring techniques, offering a more thorough and precise approach, represent a significant step towards optimizing HF practices and ensuring sustainable resource extraction.

58 GEOSCIENCES↗

DOE OSTI2024

Intern Poster

Digital Image Correlation (DIC) is an optical technique that combines image registration and tracking methods for accurate two-dimensional and three-dimensional changes in images. DIC software can be used to track the contour, deformation, and strain of a sample. In the Advanced Test Reactor (ATR) at INL (Idaho National Laboratory) there exists a small working window of samples that can become irradiated. Hundreds of graphite disks called piggybacks have undergone this irradiation as part of the Advanced Reactor Technologies (ART) program. After irradiation, it is desirable to understand the change in tensile strength as a function of dose. Due to the limited space in the ATR, typical dog bone tensile tests reduce the number of graphite samples from hundreds to tens. However, there does exist an ASTM standard, D8289, which uses disc compression of graphite to estimate the tensile strength of the specimen with the Brazilian Disk test fixture. While only used as an estimate, which is typically off by a third, it is the purpose of this study to identify how to amend D8289 to remove the word "estimate" with the help of DIC.

36 MATERIALS SCIENCE↗

NASA NTRS1972

Digital image registration by correlation techniques.

This study considers the translation problem associated with digital image registration and develops a means for comparing commonly used correlation techniques. Using suitably defined constraints, an optimum and four suboptimum registration techniques are defined and evaluated. A computational comparison is made and Gaussian image statistics are used to compare the selected techniques in terms of radial position location error.

Popp, D. J.↗

NASA NTRS2015

Correlation of Electrical Resistance to CMC Stress-Strain and Fracture Behavior Under High Heat-Flux Thermal and Stress Gradients

Because SiCSiC ceramic matrix composites (CMCs) are under consideration for use as turbine engine hot-section components in extreme environments, it becomes necessary to investigate their performance and damage morphologies under complex loading and environmental conditions. Monitoring of electrical resistance (ER) has been shown as an effective tool for detecting damage accumulation of woven melt-infiltrated SiCSiC CMCs. However, ER change under complicated thermo-mechanical loading is not well understood. In this study a systematic approach is taken to determine the capabilities of ER as a relevant non-destructive evaluation technique for high heat-flux testing, including thermal gradients and localized stress concentrations. Room temperature and high temperature, laser-based tensile tests were conducted in which stress-dependent damage locations were determined using modal acoustic emission (AE) monitoring and compared to full-field strain mapping using digital image correlation (DIC). This information is then compared with the results of in-situ ER monitoring, post-test ER inspection and fractography in order to correlate ER response to convoluted loading conditions and damage evolution.

electrical resistance↗

NASA NTRSDate not supplied

Local Analysis-Test Correlation Of Tow-Steered Composite Shells With Small Cutouts

The prebuckling and postbuckling behavior of two composite tow-steered shells with small cutouts is assessed using nonlinear dynamic finite element analyses and compared in detail with experimental measurements. The cylindrical shells were manufactured without cutouts using an automated fiber placement system, where the shells’ fiber orientation angles vary continuously around the shell circumference from ±10 degrees on the axially stiff crown and keel, to ±45 degrees on the shear-stiff sides. The first shell with overlaps has laminate thickness variations on the crown and keel that result from application of all 24 tows during each pass of the fiber placement system. The second shell without overlaps uses the fiber placement system’s tow drop/add capability to achieve a more uniform shell wall thickness. An unreinforced cutout representing a passenger door on a commercial aircraft fuselage is machined into the side of each of the two shells. These shells with cutouts were tested in axial compression and buckled elastically in previous work. Detailed nonlinear finite element analysis results are compared with their corresponding measured local load-displacement and load-strain responses in prebuckling, at global buckling, and into a stable postbuckled state. Test data from displacement transducers, strain gages, and digital image correlation are extracted at the centers of the crown and keel, and at the middles of the top and left edges of the cutout. The overall agreement between these measured and analytical responses is excellent in prebuckling through global buckling, and very good from global buckling through postbuckling. As such, the excellent correlation observed here increases confidence in applying tow-steered composites in operational vehicles.

Composites↗

NASA NTRSDate not supplied

Local Analysis-Test Correlation Of Tow-Steered Composite Shells With Small Cutouts

Composites↗

NASA NTRS2013

Common Practice Lightning Strike Protection Characterization Technique to Quantify Damage Mechanisms on Composite Substrates

To support FAA certification airworthiness standards, composite substrates are subjected to lightning direct-effect electrical waveforms to determine performance characteristics of the lightning strike protection (LSP) conductive layers used to protect composite substrates. Test results collected from independent LSP studies are often incomparable due to variability in test procedures & applied practices at different organizations, which impairs performance correlations between different LSP data sets. Under a NASA supported contract, The Boeing Company developed technical procedures and documentation as guidance in order to facilitate a test method for conducting universal common practice lightning strike protection test procedures. The procedures obtain conformity in future lightning strike protection evaluations to allow meaningful performance correlations across data sets. This universal common practice guidance provides the manufacturing specifications to fabricate carbon fiber reinforced plastic (CFRP) test panels, including finish, grounding configuration, and acceptable methods for pretest nondestructive inspection (NDI) and posttest destructive inspection. The test operations guidance elaborates on the provisions contained in SAE ARP5416 to address inconsistencies in the generation of damage protection performance data, so as to provide for maximum achievable correlation across capable lab facilities. In addition, the guidance details a direct effects test bed design to aid in quantification of the multi-physical phenomena surrounding a lightning direct attachment supporting validation data requirements for the development of predictive computational modeling. The lightning test bed is designed to accommodate a repeatable installation procedure to secure the test panel and eliminate test installation uncertainty. It also facilitates a means to capture the electrical waveform parameters in 2 dimensions, along with the mechanical displacement and thermal heating parameters which occur during lightning attachment. Following guidance defined in the universal common practice LSP test documents, protected and unprotected CFRP panels were evaluated at 20, 40 and 100KAmps. This report presents analyzed data demonstrating the scientific usefulness of the common practice approach. Descriptions of the common practice CFRP test articles, LSP test bed fixture, and monitoring techniques to capture the electrical, mechanical and thermal parameters during lightning attachment are presented here. Two methods of measuring the electrical currents were evaluated, inductive current probes and a newly developed fiberoptic sensor. Two mechanical displacement methods were also examined, optical laser measurement sensors and a digital imaging correlation camera system. Recommendations are provided to help users implement the common practice test approach and obtain LSP test characterizations comparable across data sets.

Szatkowski, George N.↗

DOE OSTI2024

The Toughness of Interlocking Metasurfaces

Interlocking metasurfaces (ILMs) are arrays of autogenous latching unit cells patterned across a surface. These create structural joints similar to bioinspired suture joints but patterned over a 2D surface rather than a 1D seam. This enables ILMs to be an alternative to conventional joining technologies such as bolts, welds, and adhesives. However, compared to conventional joining methods, relatively little is known of the engineering considerations for designing structural ILMs. Herein, the interfacial toughness of an archetypal ILM is examined for the first time. Under the conditions studied here, the ILM is substantially tougher than the material from which it is made, in this case, exhibiting up to a 50% increase in interfacial crack initiation energy over the solid base material, a photocured 3D‐printed polymer. Through experimental tests using in‐situ digital image correlation along with complementary computational analyses, the mechanism of toughening in the ILM structure and the origins of toughness anisotropy are revealed. The increase in toughness is associated with cross‐cell interactions, that is, load‐sharing across unit cells, which give rise to a finite process zone length with different effective material properties. In this way, ILM toughening is analogous to crack blunting in ductile materials or fiber bridging in composites; yet here, the ILM is composed of a single‐phase base material and so the architected toughening is geometric in nature and hence amenable to future topological optimization.

fracture↗

DOE OSTI2023

The Role of Transition Metals on Chemo-Mechanical Instabilities in Prussian Blue Analogues For K-Ion Batteries: The Case Study on KNHCF Versus KMHCF

Prussian blue analogues (PBAs) cathodes can host diverse monovalent and multivalent metal ions due to their tunable structure. However, their electrochemical performance suffers from poor cycle life associated with chemo-mechanical instabilities. This study investigates the driving forces behind chemo-mechanical instabilities in Ni- and Mn-based PBAs cathodes for K-ion batteries by combining electrochemical analysis, digital image correlation, and spectroscopy techniques. Capacity retention in Ni-based PBA is 96% whereas it is 91.5% for Mn-based PBA after 100 cycles at C/5 rate. During charge, the potassium nickel hexacyanoferrate (KNHCF) electrode experiences a positive strain generation whereas the potassium manganese hexacyanoferrate (KMHCF) electrode undergoes initially positive strain generation followed by a reduction in strains at a higher state of charge. Overall, both cathodes undergo similar reversible electrochemical strains in each charge–discharge cycle. There is ~0.80% irreversible strain generation in both cathodes after 5 cycles. XPS studies indicated richer organic layer compounds in the cathode-electrolyte interface (CEI) layer formed on KMHCF cathodes compared to the KNHCF ones. Faster capacity fades in Mn-based PBA, compared to Ni-based ones, is attributed to the formation of richer organic compounds in CEI layers, rather than mechanical deformations. In conclusion, understanding the driving forces behind instabilities provides a guideline to develop material-based strategies for better electrochemical performance.

25 ENERGY STORAGE↗

DOE OSTI2021

The impact of alkali‐ion intercalation on redox chemistry and mechanical deformations: Case study on intercalation of Li, Na, and K ions into FePO 4 cathode

Abstract Batteries made of charge carriers from Earth‐crust abundant materials (e.g., Na, K, and Mg) have received extensive attention as an alternative to Li‐ion batteries for grid storage. However, a lack of understanding of the behavior of these larger ions in the electrode materials hinders the development of electrode structures suitable for these large ions. In this study, we investigate the impact of alkali ions (Li, Na, and K) on the redox chemistry and mechanical deformations of iron phosphate composite cathodes by using electrochemical techniques and in situ digital image correlation. Na‐ion and Li‐ion intercalation demonstrate a nearly linear correlation between electrochemical strains and the state of charge and discharge. The strain development shows nonlinear dependance on the state of charge and discharge for K ions. Strain rate calculations show that K ion intercalation results in a progressive increase in the strain rate for all cycles. Li and Na intercalation induce nearly constant strain rates with the exception of the first discharge cycle of Na intercalation. When the same amount of ions are inserted into the electrode, the electrode shows the lowest strain generation upon Li intercalation compared to larger alkali ions. Na and K ions induce similar volumetric changes in the electrode when the state of charge and discharge is around 30%. Although the electrode experiences larger absolute strain generation at the end of the discharge cycles upon Na intercalation, strain rates were found to be greater for K ions. Potential‐dependent behaviors also demonstrate more sluggish redox reactions during K intercalation, compared to Li and Na. Our quantitative analysis suggests that the strain rate, rather than the absolute value of strain, is the critical factor in amorphization of the crystalline electrode.

25 ENERGY STORAGE↗

DOE OSTI2022

Experimental study of compaction localization in carbonate rock and constitutive modeling of mechanical anisotropy

Abstract Sedimentary rocks are inherently anisotropic and prone to strain localization. While the influence of rock anisotropy on the brittle/dilative regime has been studied extensively, its influence on the ductile/compactive regime is much less explored. This paper discusses the anisotropic behavior of a high‐porosity carbonate rock from central Europe (the Maastricht Tuffeau). A set of triaxial tests with concurrent x‐ray tomography has been performed at different confining pressures. The anisotropic characteristics of this rock have been investigated by testing samples cored at different inclinations of the bedding, thus revealing non‐negligible effects of the coring direction on yielding and compaction behavior. Specifically, samples cored perpendicular to bedding display higher strength and longer stages of post‐yielding deformation before manifesting re‐hardening. Despite such alterations of the inelastic response, Digital Image Correlation has revealed that the strain localization mode is independent of the coring direction, thus being primarily affected by the confinement level. To capture the observed interaction between material anisotropy and compaction behavior at the continuum‐scale, an elastoplastic constitutive law has been proposed. For this purpose, a set of tensorial bases has been introduced to replicate how the oriented rock fabric modulates the yielding and plastic flow characteristics of the material. The analyses show that the impact of the coring direction on yield function and plastic flow rule is fundamentally different, thus requiring the use of distinct projection strategies (a strategy here defined heterotopic mapping). The performance of the model, studied through parametric analyses and by calibrating the experimental results, illustrates the improved capability of the proposed constitutive approach when applied to strongly anisotropic porous rocks.

Shahin, Ghassan↗

DOE OSTI2021

Calibration of elastoplastic constitutive model parameters from full-field data with automatic differentiation-based sensitivities

Here, we present a framework for calibration of parameters in elastoplastic constitutive models that is based on the use of automatic differentiation (AD). The model calibration problem is posed as a partial differential equation-constrained optimization problem where a finite element (FE) model of the coupled equilibrium equation and constitutive model evolution equations serves as the constraint. The objective function quantifies the mismatch between the displacement predicted by the FE model and full-field digital image correlation data, and the optimization problem is solved using gradient-based optimization algorithms. Forward and adjoint sensitivities are used to compute the gradient at considerably less cost than its calculation from finite difference approximations. Through the use of AD, we need only to write the constraints in terms of AD objects, where all of the derivatives required for the forward and inverse problems are obtained by appropriately seeding and evaluating these quantities. We present three numerical examples that verify the correctness of the gradient, demonstrate the AD approach's parallel computation capabilities via application to a large-scale FE model, and highlight the formulation's ease of extensibility to other classes of constitutive models.

42 ENGINEERING↗