Additive Decomposition Research Articles

Instability Analysis and Decomposition of Output of Oilseeds Crops in Rajasthan and India

Aim: The study deals with analysis of instability of area production and productivity of major oilseeds in Rajasthan and India. It also includes calculation of sources of growth of production over the period of study. Area effect, yield effect and interaction effect for crop production were calculated. Place and Duration: The time series data of thirty years, 1990-91 to 2019-20, was analyzed. The data were further divided into Three decades, period I(1990-91 to 1999-2000), period II (2000-01 to 2009-10) and period III (2010-11 to 2019-20). Area production and productivity of major oilseed crops (Rapeseed-mustard, groundnut and soybean) for all three decade in Rajasthan and India were analyzed. Methodology: This paper deals with the analysis of instability in area production and productivity of major oilseed crops in Rajasthan and India. The Cuddy Della Vella Index has been used for instability analysis. It also includes the decomposition analysis to determine factors that were responsible for the change in production of the crops. The additive decomposition method has been used to determine area, yield and interaction effect. Results: Calculations revealed that the magnitude of instability in Rajasthan during period II (2000-01 to 2009-10) remained high for all the selected crops. There was instability of 32.49 percent and 34.40 percent for area and production, respectively, while 13.34 percent of variation was found in productivity. In Rajasthan, the lowest instability was observed during period III (2010-11 to 2019-20) with variation of 7.44 percent, 9.47 percent and 6.62 percent for area production and productivity of groundnut. In India, the highest instability was during period II. The area of Rapeseed-mustard has shown the highest (17.72%) instability compared to the instability of the area of other crops. Variation of production and productivity of groundnut was recorded at 24.79 and 21.88 percent, respectively, which is highest among the selected crops. The decomposition analysis revealed that the area effect was a major source for the growth of production of oilseed in Rajasthan as compared to the yield effect and interaction effect. During period I (1990-91 to 1999-2000), the area effect for rapeseed mustard, groundnut and soybean was 68.08, 87.97 and 91.35 percent. In India, both area and yield effect have a major contribution to the growth of production. During period I, the yield effect (57.50 %) was responsible for growth of rapeseed-mustard production, while groundnut and soybean had a high contribution of area effect with magnitudes of 70.86 percent and 84 percent. Area effects for groundnut and soybean were 118.44 percent and 58.06 percent during period II, respectively. Area effect (42.90%) and yield effect (45.76%) were equally responsible for the growth of rapeseed-mustard. During period III, the yield effect for rapeseed-mustard and soybean was 101.34 percent and 257.7 percent, respectively, while the area effect (52.29 %) was responsible for growth in groundnut production. Conclusion: It has been found that groundnut was the most stable crop in term of area production and productivity. The major source for the growth of production was area effect and Yield effect while interaction effect has least impact on production of crops.

Bayesian Optimization with Additive Kernels for a Stepwise Calibration of Simulation Models for Cost-Effectiveness Analysis

AbstractA critical aspect of simulation models used in cost-effectiveness analysis lies in accurately representing the natural history of diseases, requiring parameters such as probabilities and disease burden rates. While most of these parameters can be sourced from scientific literature, they often require calibration to align with the model’s expected outcomes. Traditional optimization methods can be time-consuming and computationally expensive, as they often rely on simplistic heuristics that may not ensure feasible solutions. In this study, we explore using Bayesian optimization to enhance the calibration process by leveraging domain-specific knowledge and exploiting structural properties within the solution space. Specifically, we investigate the impact of additive kernel decomposition and a stepwise approach, which capitalizes on the sequential block structure inherent in simulation models. This approach breaks down large optimization problems into smaller ones without compromising solution quality. In some instances, parameters obtained using this methodology may exhibit less error than those derived from naive calibration techniques. We compare this approach with two state-of-the-art high-dimensional Bayesian Optimization techniques: SAASBO and BAxUS. Our findings demonstrate that Bayesian optimization significantly enhances the calibration process, resulting in faster convergence and improved solutions, particularly for larger simulation models. This improvement is most pronounced when combined with a stepwise calibration methodology.

Three-dimensional meso-scale modeling of asphalt concrete

An efficient method to address the three-dimensional modeling of the visco-elasto-plastic material behavior, specifically of bituminous conglomerates used in asphalt concrete production, is proposed. The method resorts to one of the most recent formulations for asphalt creep modeling, represented by the modified Huet-Sayegh fractional rheological model. The Grünwald-Letnikov representation of the fractional operator is adopted to treat the operator numerically in an efficient manner. Further, a coupling scheme between the creep model and elasto-plasticity is proposed by adopting the additive decomposition of the total strain tensor. This enables the numerical assessment of the mechanical behavior for bituminous materials under short- to long-term loading. In this context, both constant strain rate tests, and creep recovery tests are numerically simulated.Numerical analyses are conducted at the meso-scale with the aim to evaluate the development of inelastic strains in the binder during creep, due to the local interaction between the different material components.

UKRAINE AND REPUBLIC OF MOLDOVA IN COOPERATION WITH THE EU AFTER 2014 YEAR: MODELS AND IMPACTS

Abstract. The paper is devoted to solving the problem of co-integration between Ukraine and the Republic of Moldova in the context of foreign trade. The study of co-integration makes it possible to determine common trends in the development of foreign trade and, based on the analysis of the dynamics of the development of one country, to forecast the development of foreign trade in another country. The study of the main indicators of foreign trade was carried out: volumes of exports, imports, trade balance. The share of export-import operations with the EU in the total volume of foreign trade of Ukraine and Moldova was chosen as the studied indicator. The article proposes to consider cointegrations both between long-term trends, which characterize the trend of foreign trade development, and between short-term trends, which reflect the cyclical component. A co-integration research mechanism has been developed, which includes three blocks: a block of analysis of literary sources, a block of mathematical tools, and a block of applied use. The use of decomposition models, trend models, spectral analysis, orthogonality indicators and pairwise correlations is proposed as a mathematical toolkit. Using the Foster-Stewart method, an analysis of the presence of a trend in the variance and average was carried out. The above calculations showed the presence of a trend and cyclical component, which allowed the use of additive decomposition models. For the study of long-term trends, a linear trend model was chosen for both Moldova and Ukraine. A spectral analysis of the cyclic component was carried out, which made it possible to identify five main harmonics with a unique frequency and amplitude. The combination of these harmonics caused 95.8% and 90.4% of the cyclical component for Moldova and Ukraine, respectively. An analysis of cointegration between short-term and long-term trend functions was conducted, which revealed medium cointegration in the long-term trend and high cointegration in the short-term trend. The cointegration analysis of the indicator values proved a high degree of cointegration for both long-term and short-term trends.

Tackling Noisy Labels With Network Parameter Additive Decomposition.

Given data with noisy labels, over-parameterized deep networks suffer overfitting mislabeled data, resulting in poor generalization. The memorization effect of deep networks shows that although the networks have the ability to memorize all noisy data, they would first memorize clean training data, and then gradually memorize mislabeled training data. A simple and effective method that exploits the memorization effect to combat noisy labels is early stopping. However, early stopping cannot distinguish the memorization of clean data and mislabeled data, resulting in the network still inevitably overfitting mislabeled data in the early training stage. In this paper, to decouple the memorization of clean data and mislabeled data, and further reduce the side effect of mislabeled data, we perform additive decomposition on network parameters. Namely, all parameters are additively decomposed into two groups, i.e., parameters w are decomposed as w=σ+γ. Afterward, the parameters σ are considered to memorize clean data, while the parameters γ are considered to memorize mislabeled data. Benefiting from the memorization effect, the updates of the parameters σ are encouraged to fully memorize clean data in early training, and then discouraged with the increase of training epochs to reduce interference of mislabeled data. The updates of the parameters γ are the opposite. In testing, only the parameters σ are employed to enhance generalization. Extensive experiments on both simulated and real-world benchmarks confirm the superior performance of our method.

Thermodynamically-consistent constitutive modeling of moisture- and thermo-responsive shape memory polymers

Abstract Taking into account that shape memory polymer (SMP)-based devices are often subject to multiple environmental conditions during application, it is difficult to accurately predict their shape memory effect (SME). Thus, constitutive modeling for SMPs in multi-field environments is of great importance. However, most of the models available are limited to describing the temperature-driven SME and do not refer to multi-field conditions. In this paper, a constitutive model for SMPs in hygrothermal environments is developed under a consistent thermodynamic framework. The derivation is based on an additive decomposition of the Helmholtz free energy density and satisfying the first law and second law of thermodynamics. In this paper, the absorbed moisture is categorized into free and bound phases and it is considered that they have different effects on the material properties. Accordingly, it is the first time to study the variation of configurational entropy with different phases in the polymer–moisture system during the moisture diffusion process. For the first time, the validity of the constitutive model proposed in this paper can be confirmed by systematically comparing the modeling results and experimental data of various types of hygrothermal-induced shape memory cycles.

Modelling and Characterisation of Orthotropic Damage in Aluminium Alloy 2024.

The aim of the work presented in this paper was development of a thermodynamically consistent constitutive model for orthotopic metals and determination of its parameters based on standard characterisation methods used in the aerospace industry. The model was derived with additive decomposition of the strain tensor and consisted of an elastic part, derived from Helmholtz free energy, Hill's thermodynamic potential, which controls evolution of plastic deformation, and damage orthotopic potential, which controls evolution of damage in material. Damage effects were incorporated using the continuum damage mechanics approach, with the effective stress and energy equivalence principle. Material characterisation and derivation of model parameters was conducted with standard specimens with a uniform cross-section, although a number of tests with non-uniform cross-sections were also conducted here. The tests were designed to assess the extent of damage in material over a range of plastic deformation values, where displacement was measured locally using digital image correlation. The new model was implemented as a user material subroutine in Abaqus and verified and validated against the experimental results for aerospace-grade aluminium alloy 2024-T3. Verification was conducted in a series of single element tests, designed to separately validate elasticity, plasticity and damage-related parts of the model. Validation at this stage of the development was based on comparison of the numerical results with experimental data obtained in the quasistatic characterisation tests, which illustrated the ability of the modelling approach to predict experimentally observed behaviour. A validated user material subroutine allows for efficient simulation-led design improvements of aluminium components, such as stiffened panels and the other thin-wall structures used in the aerospace industry.

Perbandingan prediksi jumlah penjualan kapas menggunakan metode dekomposisi aditif dan multiplikatif

PT Taruna Kusuma Purinusa is a company that focuses on the beauty cotton industry with the Selection Cotton brand label. Their product sales are spread in various cities including Malang City. This study aims to determine fluctuations and predict the amount of sales of cotton PT Taruna Kusuma Purinusa Malang and simultaneously compare the two methods of Decomposition, namely Multiplicative Decomposition and Additive Decomposition. The data is secondary on cotton sales from January 2019 to May 2023. The research procedure begins by analyzing the components of the decomposition, namely the trend (𝑇), seasonal (𝑆), cyclical (𝐶) and random (𝐼) components, then multiplying the value of these components. The prediction results show that cotton sales from June to December 2023 are as follows: 1,759,864 in June, 1,691,855 in July, 1,744,614 in August, 1,720,060 in September, 1,746,516 in October, 1,850,913 in November, and 1,893,669 in December. In addition, the proper forecasting method used in the Cotton Sales data at PT Taruna Kusuma Purnisua Malang is the additive decomposition method.

The discontinuous strain method: accurately representing fatigue and failure

AbstractFatigue simulation requires accurate modeling of unloading and reloading. However, classical ductile damage models treat deformations after complete failure as irrecoverable—which leads to unphysical behavior during unloading. This unphysical behavior stems from the continued accumulation of plastic strains after failure, resulting in an incorrect stress state at crack closure. As a remedy, we introduce a discontinuous strain in the additive elasto-plastic strain decomposition, which absorbs the excess strain after failure. This allows representing pre- and post-cracking regimes in a fully continuous setting, wherein the transition from the elasto-plastic response to cracking can be triggered at any arbitrary stage in a completely smooth manner. Moreover, the presented methodology does not exhibit the spurious energy release observed in hybrid approaches. In addition, our approach guarantees mesh-independent results by relying on a characteristic length scale—based on the discretization’s resolution. We name this new methodology the discontinuous strain method. The proposed approach requires only minor modifications of conventional plastic-damage routines. To convey the method in a didactic manner, the algorithmic modifications are first discussed for one- and subsequently for two-/three-dimensional implementations. Using a simple ductile constitutive model, the discontinuous strain method is validated against established two-dimensional benchmarks. The method is, however, independent of the employed constitutive model. Elastic, plastic, and damage models may thus be chosen arbitrarily. Furthermore, computational efforts associated with the method are minimal, rendering it advantageous for accurately representing low-cycle fatigue but potentially also for other scenarios requiring a discontinuity representation within a plastic-damage framework. An open-source implementation is provided to make the proposed method accessible.

A Comparative Study of Detrending Methods on Crop Yield Time Series for Drought Studies

Detrending is a statistical technique that removes systematic variations or trends from time series data, allowing analysts to focus on the underlying patterns or fluctuations. While multiple detrending approaches have been applied but rarely discussed their consistency of outcomes and effectiveness in accurately capturing better yield trends. The validation of drought occurrences has proven to be a challenging task due to the non-stationary characteristics of time series data related to crop yield. This research utilizes time series of cotton yield data from the Marathwada region covering the period from 1998 to 2021. Three traditional trend models, including simple linear regression, second-order polynomial regression and central moving average were applied. Additionally, two machine learning models (random forest and support vector regression) were tested with a novel approach. Moreover, two decomposition models (additive and multiplicative) were used to remove non-linear trends in crop yield time series data. The performance of the chosen models was evaluated based on metrics such as root mean square error, mean absolute error, Nash-Sutcliffe efficiency, and index of agreement. The results suggest that the most effective detrending approach involves combining a random forest machine learning model with an additive decomposition model.

Comparative analysis of additive decomposition using one-dimensional and two–dimensional gas chromatography: Part II - Irgafos 168 and zinc stearate

Plastic production has experienced a significant increase in the last sixty years due to its cost-efficiency and adaptable characteristics, leading to the extensive use of additives to improve its performance and longevity. Due to the high demand for plastic, plastic waste production has increased, contaminating the environment and living beings by leaching additives, among other substances. Pyrolysis stands out among recycling techniques because it can handle mixed polymer waste feedstock. However, understanding the pyrolyzates distribution of additives is fundamental to assessing pyrolysis process of plastic waste. This study investigated the pyrolysis product distributions of two commonly used antioxidants, namely, Irgafos 168 and zinc stearate (ZnSt), using one-dimensional gas chromatography equipped with a quadruple mass spectrometer (GC–MS) and two-dimensional gas chromatography coupled to flame ionization detector and time–of–flight mass spectrometer (GC×GC–FID/TOF–MS). While GC separation technique provided limited information on product distribution, GC×GC offered enhanced resolution and identification of the decomposition products. In the pyrolysis of Irgafos 168 at 550 °C, GC identified 18 products, while GC×GC identified 198 products, representing an increase of approximately 11-fold. Similarly, for ZnSt, GC identified 67 products, while GC×GC identified 434 products, representing a 6-fold increase. GC×GC identified decomposition products from 15 different chemical classes for Irgafos 168 and 16 chemical classes for ZnSt, compared to 4 and 11 chemical classes identified by GC, respectively. Phenols and their derivatives were the major chemical class in the decomposition products of Irgafos 168 with a yield of 9.51 wt.%. In contrast, olefinic products were the dominant ones for ZnSt, with a yield of 9.73 wt.%. The major decomposition product of Irgafos 168 and ZnSt was 2‑tert‑butyl‑methylphenol (C11H16O) and C6 olefin (C6H12) with yields of 3.88 wt.%, and 1.13 wt.%, respectively. Utilizing the GC×GC separation method improved the ability to identify decomposition products, which can ultimately lead to a better understanding of antioxidant degradation that occurs during the pyrolysis process. GC×GC also provided thorough characterization of minor and co-eluted products along with major antioxidant degradation products. Additionally, the decomposition product distribution of Irgafos 168 and ZnSt was also compared with the primary antioxidants, Irganox 1010, Irganox 1076, and BHT, studied in part 1. The analysis indicated that the olefinic chemical class was the predominant one in Irganox 1010, Irganox 1076, and ZnSt, while ketones were the major chemical class in the decomposition of BHT and phenolics had the highest yield in Irgafos 168.

Adaptive dynamic‐surface repetitive control for uncertain nonlinear systems with mismatched disturbances and input delay

AbstractBased on additive state decomposition technique, this article presents an adaptive dynamic‐surface repetitive control method for a class of uncertain nonlinear systems with mismatched disturbances and input delay. First, the original uncertain nonlinear system is decomposed into a linear time invariant (LTI) primary system responsible for the periodic signal tracing and rejection task, and a nonlinear secondary system with input time delay responsible for the robust stabilization task. A modified repetitive controller with a small correction to the delay constant is then independently designed for the LTI primary system, while an adaptive dynamic surface controller is designed for the nonlinear secondary system. Stability analysis is performed for each subsystem and the design procedure of the whole system is presented in detail. Finally, comparative simulations with other repetitive control and dynamic surface control methods show that the presented method not only relaxes the constraints on the reference inputs and exogenous disturbances, but also ensures that the system has better disturbance rejection and periodic‐signal tracking performance in both transient and steady states. As a result, this method broadens the application of both repetitive control and dynamic surface control.

An Assessment of Changes in the Thermal Environment during the COVID-19 Lockdown: Case Studies from the Greenland and Norwegian Seas

The COVID-19 lockdown had a significant impact on human activities, reducing anthropogenic heat and CO2 emissions. To effectively assess the impact of the lockdown on the thermal environment, we used the sliding paired t-test, which we improved from the traditional sliding t-test by introducing the paired t-test for sliding statistical tests, to test the abrupt change in the thermal environment. Furthermore, an additive decomposition model and wavelet analysis method were used to analyze the characteristics of trend and irregular change, coherence, and phase difference of the time series data with respect to the thermal environment. We chose the Greenland Sea and the Norwegian Sea, regions highly sensitive to changes in climate and ocean circulation, as case studies and used remote sensing data of the sea surface temperature (SST) and the atmospheric CO2 concentration data obtained from the Goddard Earth Sciences Data and Information Services Center from January 2015 to December 2021 for the analysis. The results show that although the annual spatial mean SST in 2020 is lower than the mean of all 7 years in most areas of the two seas, there is no evidence of a significant mutation in the decrease in the SST during the lockdown in 2020 compared with the temperatures before, according to the sliding paired t-test. The analysis of the irregular components of the monthly mean SST decomposed by an additive decomposition model also does not show the anomalously low SST during the lockdown in 2020. In addition, the lockdown had almost no impact on the increasing trend of CO2 concentration. The wavelet analysis also shows that there is no obvious anomaly in coherence or phase difference between the periodic variation of the SST and the CO2 concentrations in 2020 compared with other years. These results suggest that the direct effect of the COVID-19 lockdown on the thermal environment of the study area could be negligible.

Computational decomposition and composition technique for approximate solution of nonstationary problems

Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional equations can be reduced by additive decomposition of the problem operator(s) and composition of the approximate solution using particular explicit–implicit time approximations. Such a technique is currently applied in conditions where the decomposition step is uncomplicated. A general approach is proposed to construct decomposition–composition algorithms for evolution equations in finite-dimensional Hilbert spaces. It is based on two main variants of the decomposition of the unit operator in the corresponding spaces at the decomposition stage and the application of additive operator-difference schemes at the composition stage. The general results are illustrated on the boundary value problem for a second-order parabolic equation by constructing standard splitting schemes on spatial variables and region-additive schemes (domain decomposition schemes).

Explaining the Mechanism of Multiscale Groundwater Drought Events: A New Perspective From Interpretable Deep Learning Model

AbstractThis study presents a new approach to understand the causes of groundwater drought events with interpretable deep learning (DL) models. As prerequisites, accurate long short‐term memory (LSTM) models for simulating groundwater are built for 16 regions representing three types of spatial scales in the southeastern United States, and standardized groundwater index is applied to identify 233 groundwater drought events. Two interpretation methods, expected gradients (EG) and additive decomposition (AD), are adopted to decipher the DL‐captured patterns and inner workings of LSTM networks. The EG results show that: (a) temperature‐related features were the primary drivers of large‐scale groundwater droughts, with their importance increasing from 56.1% to 63.1% as the drought events approached from 6 months to 15 days. Conversely, precipitation‐related features were found to be the dominant factors in the formation of groundwater drought in small‐scale catchments, with the overall importance ranging from 59.8% to 53.3%; (b) Seasonal variations in the importance of temperature‐related factors are inversely related between large and small spatial scales, being more significant in summer for larger regions and in winter for catchments; and (c) temperature‐related factors exhibited an overall “trigger effect” on causing groundwater drought events in the studying areas. The AD method unveiled how the LSTM network behaved differently in retaining and discarding information when emulating different groundwater droughts. In summary, this study provides a new perspective for the causes of groundwater drought events and highlights the potential and prospect of interpretable DL in enhancing our understanding of hydrological processes.

Additive vs. Multiplicative Luminosity-color Decomposition

Additive vs. Multiplicative Luminosity-color Decomposition

An Efficient FEniCS implementation for coupling lithium-ion battery charge/discharge processes with fatigue phase-field fracture

Accurately predicting the fatigue failure of lithium-ion battery electrode particles during charge–discharge cycles is essential for enhancing their structural reliability and lifespan. The fatigue failure of lithium-ion battery electrode particles during charge–discharge cycles poses a significant challenge in maintaining structural reliability and lifespan. To address this critical issue, this study presents a mathematical formulation for fatigue failure in lithium-ion batteries, utilizing the phase-field approach to fracture modeling. This approach, widely employed for fracture failure analysis, offers a comprehensive framework for capturing the complex interplay between mechanical deformation, chemical lithium concentration, and crack formation. Specifically, an additive decomposition of the strain tensor is employed to account for the swelling and shrinkage effects induced by lithium diffusion. Moreover, open-source code (https://github.com/noiiG) is provided, constituting a convenient platform for future developments, e.g., multi-field coupled problems. The developed chemo-mechanical model undergoes fatigue failure package is written in FEniCS as a popular free open-source computing platform for solving partial differential equations in which simplifies the implementation of parallel FEM simulations. Several numerical simulations with two different case studies corresponding to monotonic charge process and fatigue charge/discharge process are performed to demonstrate the correctness of our algorithmic developments.

On schemes evinced by generalized additive decompositions and their regularity

We define and explicitly construct schemes evinced by generalized additive decompositions (GADs) of a given d-homogeneous polynomial F. We employ GADs to investigate the regularity of 0-dimensional schemes apolar to F, focusing on those satisfying some minimality conditions. We show that irredundant schemes to F need not be d-regular, unless they are evinced by special GADs of F. Instead, we prove that tangential decompositions of minimal length are always d-regular, as well as irredundant apolar schemes of length at most 2d+1.

Decomposition and Holt-Winters Enhanced by the Whale Optimization Algorithm for Forecasting the Amount of Water Inflow into the Large Dam Reservoirs in Southern Thailand

This study introduces hybrid forecasting models integrating the Whale Optimization Algorithm (WOA) with Holt-Winters (HW) and decomposition methods, applied in both additive and multiplicative models, for time series forecasting. Focusing on monthly water inflow into four dam reservoirs in Southern Thailand, the study compares these hybrid models against classical statistical models, Grid Search for Holt-Winters (Grid-HW) and Classical Decomposition (Classic-D). The analysis comprises two phases: the training dataset phase and the testing dataset phase. In the training phase, WOA demonstrates superior parameter optimization, enhancing both HW and decomposition methods, resulting in lower Mean Absolute Error (MAE) values compared to classical models. In the testing phase, performance metrics such as Root Mean Square Error (RMSE), MAE, and Symmetric Mean Absolute Percentage Error (sMAPE) are employed. The findings reveal that the Whale Optimization Algorithm with Holt-Winters (WOA-HW) and Decomposition (WOA-D) models surpass classical approaches in long-term forecasting accuracy for three dam reservoirs. Over 24 data points, the WOA with Multiplicative Holt-Winters (WOA-HWx) is optimal for Pran Buri dam, the WOA with Additive Decomposition (WOA-D+) for Bang Lang dam, and the WOA with Multiplicative Decomposition (WOA-Dx) for Kaeng Krachan dam. The Box-Jenkins approach, further refined through a Box-Cox transformation employing a natural logarithm, emerged as the superior forecasting model for Rajjaprabha dam. This model satisfied all critical statistical criteria, including normality of residuals (Anderson-Darling: 0.359, p-value: 0.433), homoscedasticity (Levene's test: 1.24, p-value: 0.274), independence (Ljung-Box test: 14.10, p-value: 0.169), and zero mean (t-test: -0.39, p-value: 0.702), establishing its robustness and reliability for forecast analysis.

Geometrically exact 3D beam theory with embedded strong discontinuities for modeling of localized failure in bending

In this work, we propose the elastoplastic model of a three-dimensional (3D) geometrically exact beam, which can capture localized bending deformation leading to a plastic hinge. This is a follow-up work to Tojaga et al. (2023), where we only studied the fracture of fiber-like beam structures that break in mode I or mode II, here extended to handle beam-like behavior with bending failure and the main difficulty of the non-vectorial character of large 3D rotations. The Reissner model is chosen for representing the large elastic and large plastic deformations of such a beam model, which leads to the multiplicative decomposition of the rotation tensor. We shown how to replace this with the corresponding additive decomposition of the rotation vector derivatives, to be performed in the material description in the tangent space of SO(3) manifold in the initial configuration. The plasticity model for which we give a more detailed implementation employs a Rankin-like multi-surface plasticity criteria, where each moment vector component (i.e. torsion or bending) is considered separately. The non-local variational formulation is proposed to deal with the softening phenomena characteristic of localized bending failure, where the fracture energy is introduced as the main parameter for softening. The discrete approximation is built in terms of the embedded-discontinuity finite element method (ED-FEM), which introduces a jump in rotation vector that can be handled at the level of a particular beam element. This kind of approach builds upon the best approximation property of the FEM discrete approximation in the energy norm and provides the best-approximation property for the dissipated energy computations, and thus optimal computational accuracy if the quantity of interest is inelastic dissipation. The computations are carried out by the operator split method, which separates the computations of global state variables (displacements and moments) from local (plastic curvature) variables. Several illustrative examples are provided to confirm an excellent performance of the proposed methodology.