Deformation Measurement Research Articles

Normal Values for Atrial Deformation Measured by Feature-Tracking Cardiac MRI: A Meta-Analysis.

A consensus on normal atrial deformation measurements by feature-tracking cardiac MRI remained absent. Provide reference ranges for atrial strain parameters in normal subjects, evaluating the influence of field strength and analysis software on the measurements. Meta-analysis. 2708 subjects from 42 studies undergoing cardiac MRI. A systematic search was conducted from database (PubMed, Web of Science, ScienceDirect, and EMBASE) inception through August 2023. The random-effects model was used to pool the means of biatrial strain parameters. Heterogeneity and clinical variable effects were assessed. Strain measurements among different field strengths and analysis software were compared. The inverse-variance method, Cochrane Q statistic, and I2 value, meta-regression analysis, and ANOVA were used; P < 0.05 was considered statistically significant. The pooled means of left atrial (LA) total strain (εs), passive strain (εe), and active strain (εa) were 37.46%, 22.73%, and 16.24%, respectively, and the pooled means of LA total strain rate (SRs), passive strain rate (SRe), and active strain rate (SRa) were 1.66, -1.95, and -1.83, indicating significant heterogeneity. The pooled means of right atrial (RA) εs, εe, and εa were 44.87%, 26.05%, and 18.83%. RA SRs, SRe, and SRa were 1.66, -1.95, and -1.83, respectively. The meta-regression identified age as significantly associated with LA εs, εe and SRe, field strength was associated with LA SRa (all P < 0.05). ANOVA revealed differences in LA εa and SRa among different analysis software and in LA εs and all LA strain rates (all P < 0.05) among field strengths. No significant differences were identified in RA strain across analysis software (RA strain: P = 0.145-0.749; RA strain rates: P = 0.073-0.744) and field strengths (RA strain: P = 0.641-0.794; RA strain rates: P = 0.204-0.458). This study demonstrated the pooled reference values of biatrial strain. Age, analysis software, and field strength were attributed to differences in LA strain, whereas RA strain showed consistency across different field strengths and analysis software. Limited study subjects may account for the absence of influence on RA strain. Stage 5.

Residual stress determination by blind hole drilling and local displacement mapping in aluminium alloy aerospace components

The determination of residual stresses by combining blind hole drilling and optical interferometric measurement of relief deformation is re-visited to evaluate its applicability to aerospace structures. The experimental methodology involves drilling a deep blind hole and evaluating the hole diameter increments in the principal strain directions using electronic speckle-pattern interferometry (ESPI). This is followed by the determination of the principal residual stress components via the solution of the inverse correlation problem. The study presents the pathway to overcoming one of the primary obstacles in residual stress determination, namely, the optimization of the measurement and interpretation procedures to obtain reliable results. It can be concluded from the analysis of the problem that the formulae connecting the raw experimental data and to the sought residual stress component values lead to a well-posed inverse problem. This makes it possible to obtain estimations of the measurement uncertainty. High density fringe patterns from ESPI provide a rapid and reliable method for residual stress determination, as illustrated using examples of approximately 160 MPa stresses in irregular zones of thick-walled structures.

Effect of formulation method for plastic deformation rate on topology optimization considering elastic-plastic behavior

In continuum mechanics the deformation rate is a crucial tensor that drives deformation evolution. It plays an important role in the formulation of elastic and plastic deformations, and makes a distinction between Lagrangian and Eulerian formulations. Furthermore, because plastic deformation measure is not uniquely determined, the modeling method adopted has a bearing on topology optimization and structural design. However, research on this aspect has been scarce. The objective of this study was to investigate the effect of the formulation method chosen for the plastic deformation rate on topology optimization by considering both Lagrangian and Eulerian formulations. In this work, the Lagrangian framework adopted both phenomenological and crystal plasticity, while the Eulerian framework used microstructural vector theory. For the sake of brevity, the phenomenological plasticity in the Lagrangian framework has been denoted as classical plasticity in this work. The Eulerian formulation was the first to be implemented for topology optimization in this study. The plastic deformation rates from the three models were applied to the topology optimization with the finite element (FE) method. The Messerschmitt–Bölkow–Blohm beam problem, a widely known example in this regard, was considered in this study for comparison purposes. While classical and crystal plasticity models exhibited similar overall trends in terms of optimization, the Eulerian deformation rate presented distinctly different optimization results compared with the other two approaches. All the three models aimed to minimize free energy in the topology optimization loop. However, ultimately, differences in the constitutive equations affected the resultant values of the free energy leading to different optimization outcomes. The results of this study were validated through comparisons between experimental and FE analysis results for each design. The results clearly demonstrate that the plastic deformation rate significantly affects the topology optimization, and hence needs to be appropriately adapted based on the design objectives.

Visiting experience of digital museum interior design based on virtual reality and sensor networks

China's computer technology and image sensor technology are both rapidly developing, and the related advantages of digital holography technology are gradually expanding. These technologies have been applied in many fields. For example, three-dimensional measurement, deformation measurement, and anti-counterfeiting fields. This article combines holographic technology and virtual reality technology, and applies them to the interior design of digital museums and the optimization of auxiliary visits. A corresponding mathematical calculation model is established for digital holographic images, and in-depth research is conducted on this mathematical calculation model. Relevant personnel have also conducted relevant research on commonly used digital holography technology, and provided a detailed introduction to the principles of virtual reality technology. They have also conducted in-depth research on the specific working principles of VR technology and the application technology of virtual reality systems. Finally, an analysis and research were conducted on the development of Chinese museums, and a new perspective was proposed on the indoor space of museums under the new digital concept, which has certain reference significance. Currently, Chinese museums are thriving, so deepening the interior space of museums is very important. This article hopes to provide some guidance and practical value for the development of Chinese museums.

Effects of environmental humidity on the gap of mortise-tenon joints: Experimental and numerical investigations

Mortise-tenon (MT) joints play a vital role in the lateral deformability and seismic performance of traditional timber structures. However, moisture exposure can cause shrinkage-induced gaps and then affect the durability of MT joints. Limited knowledge exists on the humidity response of MT joints. To investigate the effect of environmental humidity on the gaps between mortise and tenon, multiple measurements of moisture content (MC) and shrinkage deformation were conducted on straight MT joints that were subjected to humidity variations. Different ambient conditions and exposure levels were taken into account. Three-dimensional numerical models were established to simulate the humidity response of MT joints. Model validation was then performed by comparing the simulation and experimental results in terms of moisture distribution and gaps. On this basis, quantitative analysis was made to reveal the development mechanism and main influence factors of moisture-induced gaps. Results show that straight MT joints are vulnerable to environmental humidity changes. The observed gap is estimated to cause a decrease of up to 23.1% in the initial elastic stiffness. Although only contributed by the shrinkage deformation of tenons, the vertical gap is theoretically larger than the horizontal one which is attributed to a combination of both mortise and tenon. A clear linear relationship is found between the vertical gaps and the MC decrease, with the product of the radial shrinkage coefficient and tenon height as the theoretical ratio. Controlling the moisture exposure is considered the most effective way to reduce moisture-induced gaps in MT joints.

A continuum model for granular materials exhibiting a smooth transition between inelastic flow and elastic jamming

A continuum model for granular materials, which transitions from an elastic jammed phase to rapid flows, is developed using a large deformation Eulerian formulation for compressible elastic-viscoplastic response. The model incorporates constitutive functions capturing μ(I) rheology, the value of the solid fraction developed for steady-state shearing, and the transient response for shear reversal based on experiments and simulations of interacting particles using the Discrete Element Method (DEM). The present model exhibits hyperelastic response with the stress determined by measures of elastic dilatation and elastic distortional deformations. This causes the stress to naturally have a direction different from the rate of deformation tensor for transient response. Examples examine pure dilation, steady-state simple shear, transient shearing with shear reversal for constant volume and constant non-shearing components of stress, and the transient transition to jamming.

Temporary hemi-epiphysiodesis with tension band plates in skeletally immature patients with genu valgum: Faster correction in patients with more than 2 years of expected time of growth remaining.

Hemi-epiphysiodesis procedures in skeletally immature patients are commonly done to correct genu valgum over time. This study seeks to demonstrate the average rate of deformity correction for genu valgum using hinged tension band plates, while examining different age groups and sex-related differences. A retrospective chart review of patients who underwent hemi-epiphysiodesis with hinged tension band plates for valgus knee deformity from 2012 to 2022 by one pediatric orthopaedic surgeon was performed. Expected time of growth remaining was calculated as the difference between age of skeletal maturity and bone age at time of surgery. The mechanical lateral distal femoral angle, mechanical medial proximal tibial angle, mechanical femoral tibia angle, screw divergence angle, and hinge angle were measured immediately after implant placement and prior to implant removal. 54 skeletally immature patients were treated for pathologic genu valgum. The mean age at time of surgery was 12.5 ± 1.9 years. The radiographic measurement of the valgus deformity between the beginning and end of treatment showed significant correction (p = 0.002). The lower limb axis of the younger cohort corrected significantly faster (7.5 ± 4.6°/year) than the older cohort (5.3 ± 2.8°/year) (p = 0.030). The mechanical lateral distal femoral angle correction rate was also significantly different between the two cohorts (7.0 ± 4.7°/year vs. 4.8 ± 2.8°/year, respectively (p = 0.002)). The group with greater expected time of growth remaining demonstrated a significantly faster rate of correction than the group with less than 2 years of growth remaining (p < 0.001). This study reaffirms the finding that timing is essential when performing temporary hemi-epiphysiodesis for valgus knee deformity in skeletally immature patients.

On the sound velocity bound in neutron stars

It has been suggested in the literature that the sound velocity of the nuclear matter vs exceeds the so-called sound velocity bound vs≤c/3 at high density, where c is the speed of light. In this paper, we revisit the issue of neutron star properties, comparing current measurements of mass, radius, and tidal deformability with 105 different equations of state. These equations are parametrized at low density and saturate the sound velocity bound beyond twice the saturation density. This allows us to conservatively determine the maximum mass compatible with observed neutron star properties and the sound velocity bound. We find that majority of the models are eliminated by the incompatibility with the observations and, especially, the recently detected massive pulsar (2.35±0.17M⊙) is hardly realized by our simulations. Our study strongly supports that the sound velocity bound is not satisfied in nature.

Standard PSInSAR approach: Experimental study on the sensitivity of different bounds change on the deformation

Abstract. An experimental study conducted on standard PSInSAR technique to check the sensitivity of different bounds on the deformation results. This study is motivated by the results obtained from employment of different parameter ranges, with the assumption of the linear behavior of the deformation. despite implementation of slight parameter change shows similarity in most of the PS points. However, significant PS points display slightly different deformation measurements and trends. This change in the PS points motivated an experimental study to evaluate, analyze and assess the results from each different bounds through searching the solution space to find the best fitting to the estimated model, besides assessing of the temporal coherence estimator as quality and fitting indicator. A high-resolution TerraSAR-X (TSX) dataset is used to estimate the deformation using linear model and check the behavior over time. These dataset cover Wuhan city as a case study within two years to avoid non-linearity in the deformation. The main part of this experiment is the descriptive of the statistics across all trials of different bounds. Then, assessing the measurement results of the trials, and the coherence estimator that used as a quality indicator to assess the quality of the PS points in comparison with the standard deviation. The results of the measurements indicate that while the coherence estimator select the PS points based on their stability and fitting to estimated model but does not provide a big difference as function of different bounds through searching the solution space. The results are confirmed with the available global Positioning system (GPS) station in our study area and displays similar trends and patterns over all the trials with slight differences with the different parameters range. The statistical analysis and assessment reveals differences in the velocity results and erroneous during changing the parameters range.

Real-Time Deformation Measurement of Long-Span Bridge using Multi-Inertial Camera System

Abstract. Monitoring the deformation of long-span bridges is essential for assessing structural health and safety. The existing single-camera deformation measurement method is unable to meet the high-precision measurement requirement for the deformation of large-span bridges. This paper proposes a real-time deformation measurement method for the long-span bridge using multi-inertial camera system. The method is based on visual measurement which the target deformation is measured by multiple cameras. Meanwhile, inertial measurement is used to estimate the relative pose of the camera to compensate for camera motion errors. It is applied to the health monitoring system of a long-span bridge. The experimental results show that the method proposed in this paper is highly consistent with the hydrostatic leveling measurement, with a RMSE of 4.83mm. The method can accurately and real-time measure the deformation of large-span bridges with a promising engineering value.

An Optimization Approach for Creating Application-specific Ultrasound Speckle Tracking Algorithms

ObjectiveUltrasound speckle tracking enables in vivo measurement of soft tissue deformation or strain, providing a non-invasive diagnostic tool to quantify tissue health. However, adoption into new fields is challenging since algorithms need to be tuned with gold-standard reference data that are expensive or impractical to acquire. Here, we present a novel optimization approach that only requires repeated measurements, which can be acquired for new applications where reference data might not be readily available or difficult to get hold of. MethodsSoft tissue motion was captured using ultrasound for the medial collateral ligament (MCL) of three quasi-statically loaded porcine stifle joints, and medial ligamentous structures of a dynamically loaded human cadaveric knee joint. Using a training subset, custom speckle tracking algorithms were created for the porcine and human ligaments using surrogate optimization, which aimed to maximize repeatability by minimizing the normalized standard deviation of calculated strain maps for repeat measurements. An unseen test subset was then used to validate the tuned algorithms by comparing the ultrasound strains to digital image correlation (DIC) surface strains (porcine specimens) and length change values of the optically tracked ligament attachments (human specimens). ResultsAfter 1500 iterations, the optimization routine based on the porcine and human training data converged to similar values of normalized standard deviations of repeat strain maps (porcine: 0.19, human: 0.26). Ultrasound strains calculated for the independent test sets using the tuned algorithms closely matched the DIC measurements for the porcine quasi-static measurements (R > 0.99, RMSE < 0.59%) and the length change between the tracked ligament attachments for the dynamic human dataset (RMSE < 6.28%). Furthermore, strains in the medial ligamentous structures of the human specimen during flexion showed a strong correlation with anterior/posterior position on the ligaments (R > 0.91). ConclusionAdjusting ultrasound speckle tracking algorithms using an optimization routine based on repeatability led to robust and reliable results with low RMSE for the medial ligamentous structures of the knee. This tool may be equally beneficial in other soft-tissue displacement or strain measurement applications and can assist in the development of novel ultrasonic diagnostic tools to assess soft tissue biomechanics.

3D deformation measurement of rotating blades based on concentric ring calibration and GPU-SIFT feature point searching

Image grayscale matching and camera calibration are two key technologies for measuring the three-dimensional deformation of rotating blades. To address the issues of low accuracy in extracting corresponding points caused by unclear grayscale boundaries of traditional chessboard calibration patterns and the high computational complexity of image matching algorithms in high-speed and high-resolution scenarios, this paper proposes a method for measuring the three-dimensional deformation of rotating blades based on concentric circle calibration and GPU-SIFT feature point search. Firstly, a concentric circle calibration method based on arc segment combination for extracting circle center is proposed. By fitting the circular calibration pattern with extracted marker points, errors introduced by unclear grayscale boundaries of chessboard patterns are avoided, thereby improving the accuracy of calibration parameters. Secondly, an image matching algorithm based on GPU-SIFT feature point search is presented. By optimizing the storage location of scale space process data, the performance of the SIFT algorithm is maximized, leading to improved image matching speed. Lastly, the calculation of displacement and strain fields is achieved using the P3P theory and local least squares fitting method, respectively. The experimental results show that the proposed system and method for 3D deformation measurement achieve a strain measurement accuracy of 80 με. Moreover, they successfully measure the surface deformation of turbofan blades under the conditions of 3000 rpm and 6000 rpm. Through this method, it can improve the deformation measurement capability of large engine manufacturers for high-speed rotating blades and provide reliable technical support.

An illumination-robust edge detection method for nuclear fuel assembly deformation measurement

Fuel assemblies (FAs) are critical components of nuclear reactor cores. The excessive deformation of FAs can pose a serious risk of safety accidents in nuclear power plants. Hence, regular monitoring of the deformation of the FAs is necessary. To accomplish this task, the most critical challenge lies in accurately extracting the edges of FAs in the nuclear underwater environment with spatial variations in illumination. In this paper, a novel illumination-robust edge detection method is proposed. Firstly, tilt correction is applied to arrange the fuel rods vertically in the image. Then, the center of each fuel rod is located through grayscale projection and filtered by rod center spacing variance minimization. Subsequently, adaptive thresholding is employed to obtain a binary image. Finally, the edges are identified by searching in the vicinity of rod centers in the binary image. The effectiveness and robustness of the proposed method have been validated in experiments, and the approach has been successfully applied to the FA deformation measurement in nuclear power plants.

Stereo-DICNet: An efficient and unified speckle matching network for stereo digital image correlation measurement

Digital image correlation (DIC) is an image-based, non-contact optical measurement technique for measuring the deformation of objects. Recently, deep learning has been preliminarily used in monocular-DIC measurement and has brought significant advantages in efficiency and robustness. However, the deep learning-based stereo-DIC methods is still underexplored, although stereo-DIC can measure three-dimensional deformation and shape compared to monocular-DIC. Different from monocular-DIC, stereo-DIC not only requires temporal matching (inter-frame) but also stereo matching (inter-camera), and the difference in image deformation scale between the two matching tasks make it difficult to perform them using a unified network. To solve this problem, we propose a unified speckle matching network that can be used for deformation measurement at different scales, referred to as Stereo-DICNet. Stereo-DICNet consists of three modules: feature extraction, cost volume generation, and displacement map prediction. Firstly, the feature extraction module composed of the residual layer and the spatial pyramid pooling layer is designed to extract the features of different receptive fields. Then, an attention connect volume was proposed to represent the similarity information between pixels at different spatial scales. Finally, the displacement map is predicted by a stacked hourglass-shaped sub-net. Simulation and physical experiments verify that Stereo-DICNet can perform both temporal matching and stereo matching. Moreover, material tensile experiments show that the MAE of Stereo-DICNet in the U, V, and W directions are no more than 0.005 mm, 0.015 mm, 0.01 mm respectively.

Automatic crack tip localization in enormous DIC images to in-situ characterize high-temperature fatigue crack growth behavior

Digital Image Correlation (DIC), with its advantages of full-field, non-contact and applicability to extreme environments, is a powerful deformation measurement technique to in-situ monitor the high-temperature fatigue crack propagation behavior. For the DIC-based fracture mechanics analyses of cracking, crack tip position in DIC images, which is usually determined visually and manually, plays a significant role. However, the long-term fatigue-DIC experiment at both room-and high-temperatures poses a real challenge due to the huge amount of DIC images, lower image quality at high-temperature, and even the invisibility of cracks. In this paper, a fully automated algorithm for localizing the crack tip is proposed based on the crack tip displacement field and the immune algorithm. Compared to traditional algorithms, it does not necessitate iterative initial values of crack tip location, and permits precise and fast determination of critical fracture mechanics parameters, such as the Stress Intensity Factors (SIFs). The algorithm reliability is validated by both numerical simulation and fatigue testing of nickel-based superalloy GH4169 at room temperature and 650℃. It is shown that crack tip position and SIF values can be precisely and automatically determined within 7 s per image using an ordinary low-cost computer, which significantly improves the analyzing efficiency.

Feasibility and reproducibility of cardiovascular magnetic resonance-feature tracking for quantitative right atrial function in dilated cardiomyopathy patients.

The importance of right heart assessment in dilated cardiomyopathy (DCM) is increasingly recognized. The development of cardiovascular magnetic resonance-feature tracking (CMR-FT) has provided a novel approach to quantify myocardial deformation and evaluate cardiac function. In this study, we aimed to evaluate the feasibility and reproducibility of CMR-FT for the quantitative derivation of right atrial (RA) strain and strain rate (SR) in patients with DCM. A total of 68 DCM patients (84% male; aged 50.6±13.2 years) and 58 healthy controls (81% male; aged 48.4±11.2 years) were retrospectively enrolled from September 2018 to August 2022 at the First Affiliated Hospital of Zhejiang Chinese Medical University and Shenzhen Clinical Medical College of Guangzhou University of Chinese Medicine. RA reservoir, conduit, and booster strain (εs, εe, and εa) and peak positive, peak early negative, and peak late negative SR (SRs, SRe, and SRa) were measured using CMR-FT and compared between 2 groups using Student's t-test. Intra- and inter-observer reproducibility was evaluated using intraclass correlation coefficients (ICC) and Bland-Altman plots. Compared to healthy controls, DCM patients showed significantly lower RA strain (εs: 19.7%±9.0% vs. 44.4%±9.7%; εe: 7.9%±5.3% vs. 25.8%±8.6%; εa: 11.8%±6.2% vs. 18.6%±5.1%, all P<0.001) and SR (SRs: 1.17±0.48 vs. 1.92±0.62 s-1; SRe: -0.85±0.56 vs. -1.94±0.63 s-1; SRa: -1.39±0.71 vs. -2.01±0.65 s-1, all P<0.001). There was no significant difference in RA maximum volume index between the 2 groups. Simple linear regression analysis demonstrated a significant correlation between N-terminal B-type natriuretic peptide (NT-proBNP), RA emptying fraction passive (RAEF passive), and RA εe [(NT-proBNP and εe): r=-0.48, P<0.001, 95% confidence interval (CI): -0.64 to -0.26; and (RAEF passive and εe): r=0.41, P=0.001, 95% CI: 0.22 to 0.56, respectively] in DCM patients. Intra- and inter-observer reproducibility was excellent (all ICCs >0.85) for RA deformation measurements. CMR-FT is a promising, noninvasive approach for the quantitative assessment of RA phasic function in patients with DCM. DCM patients exhibit impaired RA reservoir, conduit, and booster pump function prior to visible RA enlargement.

In-vivo characterization of scleral rigidity in myopic eyes using fundus-pulsation optical coherence elastography

The sclera plays an important role in the structural integrity of the eye. However, as myopia progresses, the elongation of the eyeball exerts stretching forces on the posterior sclera, which typically happens in conjunction with scleral remodeling that causes rigidity loss. These biomechanical alterations can cause localized eyeball deformation and vision impairment. Therefore, monitoring scleral rigidity is clinically important for the management and risk assessment of myopia. In this study, we propose fundus pulsation optical coherence elastography (FP-OCE) to characterize posterior scleral rigidity in living humans. This methodology is based on a choroidal pulsation model, where the scleral rigidity is inversely associated with the choroidal max strain obtained through phase-sensitive optical coherence tomography (PhS-OCT) measurement of choroidal deformation and thickness. Using FP-OCE, we conducted a pilot clinical study to explore the relationship between choroidal strain and myopia severity. The results revealed a significant increase in choroidal max strain in pathologic myopia, indicating a critical threshold beyond which scleral rigidity decreases significantly. Our findings offer a potential new method for monitoring myopia progression and evaluating therapies that alter scleral mechanical properties.

Research and application of a flexible measuring array for deep displacement of landslides

Abstract. The multidimensional and multi-sliding surface measurement of deep-seated displacement on landslides poses a significant technical challenge in landslide monitoring and early warning. The fixed-borehole inclinometer serves as an important measurement method based on drilling for this purpose. In this study, a novel flexible measurement array for deep-seated landslide displacement and its installation and measurement processes were developed, enabling higher accuracy in full-hole multidimensional deformation measurement. The measurement array consists of individual measurement probes as basic units, connected in series through coaxial cables and high-pressure rubber hoses, forming a flexible measurement array. Each probe is equipped with acceleration and magnetic field sensors, allowing for the measurement of borehole inclination and azimuth angles and providing a more comprehensive understanding of the deformation of deep-seated landslides. This flexible measurement array resolves the limitations of traditional fixed inclinometers, such as limited probe quantity or inaccurate installation positions that fail to reflect the deformation trend of the landslide body. Moreover, it eliminates the need for auxiliary installation accessories like pulleys and inclinometer pipes, simplifying the mechanical structure and installation process, which represents an advancement in methodology and an improvement in measurement techniques. This array provides a more comprehensive and improved monitoring tool for disaster prevention and mitigation, thereby enhancing the level of geological hazard monitoring and early warning technology.

Coaxial panoramic 3D-DIC system for full inner surface deformation measurement

A coaxial panoramic three-dimensional digital image correlation (3D-DIC) system was developed for full 360o inner surface deformation measurement. The panoramic observation was realized by using a convex mirror. Two cameras were arranged coaxially to ensure the largest overlapping observation area. After the coordinate transformation and correlation calculation, the 3D displacement and strain distributions were reconstructed. The principles of the system were presented in detail, and the internal morphology and deformation of pipes subjected to compression loading were described to verify the effectiveness, practicality, and accuracy of the proposed system.

Robust and efficient implementation of finite strain generalized continuum models for material failure: Analytical, numerical, and automatic differentiation with hyper-dual numbers

Generalized continuum models for representing nonlinear material behavior including material failure in the finite strain regime are commonly formulated based on scalar elastic and dissipation potential functions. The evolution of stresses and internal variables, i.e., the material state, is governed by partial derivatives of the potential functions with respect to deformation and stress measures. Furthermore, for application of such models in implicit nonlinear finite element analysis tangent operators, consistent with the numerical integration algorithm, are required. In this work, we study analytical, numerical and automatic differentiation schemes for the implementation of coupled, generalized continuum models considering finite inelastic deformations and fracture. This includes the application of finite difference approximations, complex-step derivative approximations and automatic differentiation based on hyper-dual numbers. For the use of automatic differentiation, a semi-analytical split approach is introduced for increasing the computational efficiency. Based on a comprehensive 2D and 3D finite element study, we demonstrate the superior properties of automatic differentiation compared to numerical differentiation methods with regards to accuracy and robustness. Furthermore, the additional computational cost for automatic differentiation using the proposed split approach becomes negligible for large problems.