Loading History Research Articles

The anti-dogbone: Evaluating and designing optimal tensile specimens for deep learning of constitutive relations

Traditional tensile testing with “dogbone”-shaped specimen (ASTM E8, first standardized in 1924) strives for strain uniformity. Multiple tests with such samples help fit simple constitutive relation parameters on real materials. With the development of deep learning, the concept of employing entirely data-driven constitutive relations to capture more intricate material behavior has arisen. Nevertheless, these methods demand experimental data that are distributed throughout the complete stress–strain configuration space to effectively train the machine learning models. This is particularly crucial for mechanisms like hardening, which are time-dependent and sensitive to loading history. In this work, we investigate the potential to efficiently gather a wider range of experimental data points in the stress–strain configuration space using non-uniform samples and displacement-field mapping, leveraging advancements in computer vision techniques. We developed a metric to quantify stress state diversity in 2D tensile experiments and used it to optimize the shape of the sheet sample. The goal was to increase stress–strain diversity obtained within a single test, particularly in the linear elastic regime. Additional geometric constraints can be introduced on the design features, considering factors such as size and curvature to adapt to the microstructural characteristics of the sample material.

Numerical model for suction anchor under vertical impact loading

In marine engineering, suction anchors are widely employed as the supporting foundation for many types of fixed or floating structures. One of the important control conditions for the service of marine foundations is the impact loading in extreme environments. This study proposes a numerical model to predict the dynamic behavior of suction anchors under impact loading. A mass module is added to the numerical model to quantify the effect of anchor inertia. The t-z springs are positioned along the depth to reflect the soil layer stress and accurately calculate the skirt wall friction. Considering the seepage effect, the differential pressure development, internal soil stress loss and external soil stress enhancement are also reflected. Subsequently, the influence of anchor aspect ratio and loading history are investigated. As the foundation uplift movement is further pronounced, the friction resistance gradually works, resulting in the weakening of inertial force. The existence of pretension loading makes friction resistance take effect earlier, and accelerates its attenuation during the impact loading stage.

UPRIGHT BIPEDAL EXERCISE TRAINING IMPROVES INTERVERTEBRAL DISC HEALTH: A SYSTEMATIC REVIEW AND META-ANALYSIS

INTRODUCTION & AIMS The structure and function of human tissue, such as bone, muscle and tendon, can be improved with targeted exercise training. However, the effects of exercise training on intervertebral disc tissue has received comparably less attention. With a scope to identify types of exercise training that improve intervertebral disc health, this study examined the impact of historical exercise, sport and/or physical activity on quantitative intervertebral disc outcomes. METHODS The protocol was prospectively registered with PROSPERO (CRD42022366391). Five databases (inception to 30th September 2022), 17 trial registries and reference lists and forwards/backwards citations were searched. Inclusion criteria followed the Participants (human), Exposure (exercise, sport or physical activity for greater than one week), Comparators (non-exercise, sport or physical activity control group), Outcomes (magnetic resonance imaging measures of lumbar intervertebral disc health on a continuous scale [e.g. T2, signal intensity, intervertebral disc height]) and Study design (any) framework. Pairwise random-effects restricted maximum likelihood meta-analysis estimated standardised mean difference (Hedges g). RESULTS From the search yield of 2,150 records, 12 reports representing 10 studies (participants: 874) were deemed eligible. When compared to any comparator, upright bipedal exposures (g [95%CI]: 0.31 [0.06, 0.55]; P=0.014; studies: 6; participants: 346; I2: 87%), were associated with greater intervertebral disc health. However, no physical loading exposure (g [95%CI]: 0.29 [-0.23, 0.82]; P=0.275; studies: 10; participants: 874), non-upright/non-contact exposures (g [95%CI]: 0.70 [1.25, 2.64]; P=0.336; studies: 5; participants: 260), extreme trunk range of motion exposures (g [95%CI]: -0.28 [-1.60, 1.04]; P=0.456; studies: 3; participants: 230) and aerobic-based exposures (g [95%CI]: 0.48 [0.08, 1.04]; P=0.094) were associated. Sensitivity analyses supported the robustness of primary and secondary effect estimates. CONCLUSION Greater intervertebral disc health associated with a prior history of upright bipedal physical loading indicates prospective interventions examining upright bipedal exercise effects on intervertebral disc health are warranted.

Influence of pre-seismic history on the cyclic response of seasonal frozen silty sand

The implementation of the Belt and Road strategy has increased construction activities in regions with seasonally frozen soil, such as the Qinghai–Tibet plateau. Numerous infrastructure systems in the region are built on seasonally frozen soil, rendering them susceptible to high-frequency seismic loads. Previous studies have demonstrated the significant influence of pre-seismic loads on the mechanical responses of soils. However, research on the influence of pre-seismic loads on seasonally frozen soil is limited. Therefore, two groups of cyclic triaxial tests are conducted in this study to investigate the impact of pre-seismic load and freeze-thaw history on the cyclic response of silty sand. Sample reconstitution and freeze-thaw procedures are described in detail. The test results indicate that the cyclic strength of silty sand decreases with the freeze-thaw history, although the influence diminishes with an increase in the number of freeze-thaw cycles. Additionally, a small pre-seismic load enhances the silty-sand strength, regardless of the freeze-thaw history it underwent. The findings of this study offer valuable insights for engineering construction in areas prone to seasonal freezing and earthquakes.

Ductile damage and fracture characterizations in bi-cyclic biaxial experiments

This paper discusses novel extremely low-cycle bi-cyclic biaxial reverse experiments with large strains. Various tests with tension–compression–tension (TCT) shear cyclic loads, superimposed by either non-reverse or reverse cyclic loading patterns, are newly designed to investigate the plastic, damage, and fracture behavior. These experiments fill the gaps in carrying out complex reverse loading by utilizing 4mm thick biaxially loaded cruciform specimens. The deformed specimens in different loading stages are examined metallographically with micrographs to elucidate the influence of loading histories on the occurrence and evolution of micro-defects. In addition, scanning electron microscopy (SEM) is also used to analyze the fractured surfaces and verify the anisotropic damage mechanism. An advanced anisotropic cyclic plastic-damage continuum model is utilized to characterize the material behavior, including the Bauschinger effect, the stress-differential effect and the non-hardening effect after shear reverse loading as well as stress-state-induced damage mechanisms. Due to the utilization of the digital image correlation (DIC) technique, the numerical results can be compared with the experimental ones in both load–displacement curves and strain fields, respectively. The elastic strain triaxiality and strain Lode parameter are introduced, providing a novel perspective for analyzing the cyclic loading experiments.

Advanced deep operator networks to predict multiphysics solution fields in materials processing and additive manufacturing

Unlike classical artificial neural networks, which require retraining for each new set of parametric inputs, the Deep Operator Network (DeepONet), a lately introduced deep learning framework, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to complete solution fields. In this paper, two newly devised DeepONet formulations with sequential learning and Residual U-Net (ResUNet) architectures are trained for the first time to simultaneously predict complete thermal and mechanical solution fields under variable loading histories, process parameters, and even variable geometries. Two real-world applications are demonstrated: 1- coupled thermo-mechanical analysis of steel continuous casting with multiple visco-plastic constitutive laws and 2- sequentially coupled directed energy deposition for additive manufacturing. Despite highly challenging spatially variable target distributions, DeepONets can infer reasonably accurate full-field temperature and stress solutions several orders of magnitude faster than traditional and highly optimized finite-element analysis (FEA), even when FEA simulations are run on the latest high-performance computing platforms. The proposed DeepONet model’s ability to provide field predictions almost instantly for unseen input parameters opens the door for future preliminary evaluation and design optimization of these vital industrial processes.

Experimental study on response and precursor of pressure stimulated currents of combined coal-rock under cycling stress

The coal-rock combination body is prone to rock burst and surface subsidence under loading, and adopting effective monitoring methods are valuable. In this paper, cyclic loading and unloading (CLU) tests were conducted to investigate the response and precursor of pressure stimulated currents (PSCs) in coal-rock combination samples. The results indicate that the PSCs of the coal-rock combination samples have good response characteristics to stress. Furthermore, the PSCs between the two components are significantly larger and more stable than those of the coal body, which can clearly reflect the failure under a progressive failure mechanism and are related to the difference in the resistivities and microstructures of the components. During the CLU tests, the PSCs of each cycle are well fitted by the Gaussian distribution and have a memory effect. During the loading or unloading process of each cycle, the variation in PSCs with stress conforms to the power function relationship with exponent k. As the cycle number increases, the rates of increase in PSC under stress are gradually weakened, and the indexes of PSCs including exponent k increase or decrease sharply first and then remain stable or even decrease, which is due to the loading history. The stable state of these indexes with obvious inflection points in later cycles of CLU tests can be considered a precursor of coal-rock failure. The PSC flow direction between the two components is exactly opposite to that in the coal body. The results provide new ideas for the monitoring and prediction of coal-rock combination body failure, which is helpful for the prevention of geological disasters in mines.

Research on the force-magnetic relationship of bridge steel under tensile stress based on magnetic memory effect

It’s of great significance to conduct the nondestructive evaluation of steel bridges to extend their service life. The metal magnetic memory testing (MMMT) method can effectively evaluate the stress states of ferromagnetic components. To improve the accuracy and reliability of the stress evaluation on bridge steel structures based on MMMT technology, an improved force-magnetic coupling model considering loading history is proposed, which can reflect the impact of material mechanical properties on magnetization behavior. The MMMT is carried out on the Q345qD bridge steel plates under load-unload tensile stress considering the relative location between the specimen and the geomagnetic field, according to the rotation angle θr. It comprehensively analyzes the variation laws of representative tangential and normal components of the magnetic signal, i.e. Hm(y) and Hm(z), corresponding to different inspection parameters during the loading process. The mean value Ay of the Hm(y) curves and the linear fitting slope Kz of Hm(z) curves are applied to characterize the variation laws of magnetic signal with respect to the applied load Fa. According to the fitting curves of Ay and Kz with Fa, it quantitatively demonstrates the applied loads. It further puts forward the normalized magnetic characteristic parameters Ayn and Kzn to characterize the force-magnetic relationship of the specimen, which are less affected by the position of the specimen in geomagnetic field. Finally, the proposed force-magnetic coupling model is applied to calculate the variation of normalized magnetization ΔMn. The theoretical results are compared with the synthetic magnetic characteristic parameter AKn obtained by experiment. It shows an average error of 8.53% between ΔMn and AKn, which proves the feasibility and effectiveness of the force-magnetic coupling model proposed in this paper.

Identifying multiple synergistic factors on the susceptibility to stress relaxation cracking in variously heat-treated weldments

The 347H austenitic stainless steel has been widely used for pressure vessels and pipeline (PVP) applications due to its excellent creep and corrosion resistance, which fit ideally to the harsh conditions in petrochemical industries, fossil fuel or nuclear power plants, and modern energy storages. However, a failure mode has been commonly observed with cracks emerging at the heat affected zone (HAZ) of weldments during post-weld heat treatment (PWHT) or under intermediate to high temperature service conditions. This phenomenon is termed as Stress Relaxation Cracking (SRC) since the purpose of PWHT is to relieve the welding-induced residual stress fields, or as Stress Age Cracking (SAC) if failure happens during service. A leading literature explanation of this failure suggests that the residual stress relaxation and the precipitation dissolution and/or re-precipitation occur in the same temperature range, which can lead to locally high strains and thus to crack at the grain boundaries. Since in situ spatial measurements of residual stress fields, microstructural evolution, and failure processes are nearly infeasible, this work recourses to a micromechanical finite element framework that models the high temperature failure as the nucleation and growth of grain boundary cavities, whereas various parameters such as thermomechanical loading history and its evolution, the competition of grain-interior dislocation creep and grain-boundary diffusion in failure lifetime, and microstructural heterogeneities (such as the precipitate free zone near grain boundaries) can be quantitatively incorporated. It can be concluded from these microstructure-explicit simulations that an accurate knowledge of residual stress evolution and a carefully calibrated set of material constitutive parameters are the essential prerequisites for lifetime predictions. The understanding of individual governing factors also leads to a mechanistic interpretation of the observed SRC susceptibility C-curves. These results suggest that the criticality of residual stress evolution, but not the precipitation-induced local strains, be the leading factor for SRC.

Direct recording and reading of mechanical force by afterglow evaluation of multi-piezo mechanoluminescent material Li0.12Na0.88NbO3 on well-designed morphotropic phase boundary

Mechanoluminescence (ML) refers to the photon emission from materials subjected to mechanical stimuli. A general concept concerning ML materials is that they cannot directly record a stress history (mechanical record; MR). Here, we report an approach that retrieves a quantitative recording of stress history through the afterglow characteristics analysis of a specific multi-piezo ML material Li0.12Na0.88NbO3:Pr (LNNO), which has been designated to exist near the structural phase boundary of rhombohedral R3c and orthorhombic P21ma. Contrary to the general expectation that the afterglow characteristics are irrelevant to mechanical loading history, LNNO was strongly correlated with the stress distribution after UV excitation. This enabled us to read the recorded stress precisely from the afterglow image of the material. Furthermore, the spatial distribution of the MR was also realized, showing the capability of the readout of stress history in both time and space. This unusual MR function is attributed to eliminating shallow trap sites, which affected the afterglow characteristics upon applying mechanical load.

Time-dependent soil–structure interaction analysis using a macro-element foundation model

The delayed settlement of foundations due to soil consolidation, creep or particle breakage can alter the internal load distribution and differential settlements in a superstructure through soil–structure interaction (SSI). The study introduces a novel methodology to simulate time-dependent SSI that overcomes the complexity of incorporating the time-dependent behaviour of foundations into routine SSI analysis. The proposed approach represents the superstructure as a condensed stiffness matrix, and replaces the foundations and underlying soils with macro-element foundation models that encapsulate the foundation–soil interaction into load–displacement relationships derived from constitutive models. To examine the performance of the proposed method, a macro-element model for time-dependent analysis of shallow foundations on sand was integrated with structural analysis to simulate two tests performed in a geotechnical centrifuge on a 3D-printed aluminium framed structure supported by footings on sand. The simulated responses of the superstructure and foundations were found to agree well with those observed in the centrifuge tests. Parametric analyses were conducted to investigate the effect of loading history, load level on the superstructure, and creep tendency of soil on post-construction load redistribution and differential settlements. The findings suggest that creep of foundations on sand facilitates load redistribution in the structure from heavily loaded sections to lightly loaded sections. Moreover, post-construction load redistribution depends on the differential creep between footings and should be considered for structures that are quickly constructed or at high levels of strength mobilisation (low factor of safety). Overall, the study highlights the potential of the proposed methodology in analysing the time-dependent SSI and its applicability in practical SSI analysis.

Nonlinear fatigue life prediction model based on isodamage curve considering two‐block loading

AbstractA non‐linear life prediction model considering the loading history is proposed based on isodamage curve. The stress‐controlled low‐high block loading of low cycle fatigue (LCF) at high temperature, with various previous cycles, was performed on a nickel‐based superalloy. The damage evolvement of the prior loading was revealed using scanning electron microscopy under the low‐high block loading, especially the failure mechanism of coaxing effect. In addition, load history correlation factor was introduced to describe the influence of prior cycle. Based on the Ni‐based superalloy, the life prediction model of two‐step loading, including the low‐high block (LH) and high‐low block loading (HL), was proposed, agreeing well with the experimental results for different metals. Compared with other life prediction models, the proposed model demonstrated the higher prediction accuracy and wider applicability.

Strain-based running-reliability characterisation in time-domain for risk monitoring under various load conditions

This aim of this paper is to characterise the strain-based fatigue life data in time-domain using the newly modelled running-reliability technique that considers the load sequence effect. Current established conventional strain life models do not consider dependence for fatigue life of low or high amplitudes, on which with occur first in the load history. Finite element analysis is carried out to ensure the strain signals are captured at the most critical region during road test at various conditions. Fatigue life of 2.74 × 104 to 6.07 × 105 cycle/block with mean cycle to failure of 4.32 × 106 to 7.00 × 106 cycle/block is predicted based on the cycle sequence effect using cycle-counting method. The newly modelled running-reliability technique is formulated to extract the features of high amplitude excitation obtained from the strain signals for characterising the fatigue reliability features under load sequence effect. Hence, the reliability-hazard relationship for fatigue reliability characterisation of strain-based approach in time-domain using running-reliability technique.

Modified cam clay bounding surface hyper-viscoplastic model

Clays exhibit complex mechanical behaviour with significant viscous, nonlinear, and hysteric characteristics, beyond the prediction capacity of the well-known modified cam clay (MCC) model. This paper extends the MCC model to address these important limitations. The proposed family of models is constructed entirely within the hyperplasticity framework deduced from thermodynamic extremal principles. More specifically, the previously developed MCC hyper-viscoplastic model based on the isotache concept is extended to incorporate multiple internal variables and to capture recent loading history, hysteresis, and smooth response of the material. This is achieved by defining an inelastic free energy and an element that implements a bounding surface within hyperplasticity, resulting in pressure dependency in both reversible and irreversible processes with a unique critical state envelope, and only eight material parameters with a readily measurable viscous parameter. A kinematic hardening in the logistic differential form in stress space is derived that enables the proposed model to function effectively across a wide range of stresses. Based on this kinematic hardening rule, the current stress state acts as an asymptotic attractor for the back/shift stresses whose evolution rates are proportional to their current state.

Experimental lap-shear tests on friction dampers with single and double slotted holes

Several experimental lap shear tests have been performed to assess the initial values of the slip resistance and their evolution during a cyclic loading history. Both friction dampers with parallel slotted holes and double slotted holes have been investigated. Friction devices with shims made of a previously tested material, called M4, have been tested and the tribological behaviour, the degradation of the friction coefficient, the influence of the bolts’ preload and the effect of Belleville washers have also been investigated. Moreover, a phenomenological model for the force-displacement response has been calibrated for the modelling of the cyclic response of the friction device. This is particularly important for the development of non-linear dynamic analyses of seismic resistant frames equipped with friction joints aiming at an accurate prediction of the structural response during a seismic event. Finally, a quality control of the friction properties of different batches of friction shims has been performed by means of the Fisher-Berens and Snedecor tests.

Short-Term Electric Load Forecasting Based on Signal Decomposition and Improved TCN Algorithm

In the realm of power systems, short-term electric load forecasting is pivotal for ensuring supply–demand balance, optimizing generation planning, reducing operational costs, and maintaining grid stability. Short-term load curves are characteristically coarse, revealing high-frequency data upon decomposition that exhibit pronounced non-linearity and significant noise, complicating efforts to enhance forecasting precision. To address these challenges, this study introduces an innovative model. This model employs complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) to bifurcate the original load data into low- and high-frequency components. For the smoother low-frequency data, a temporal convolutional network (TCN) is utilized, whereas the high-frequency components, which encapsulate detailed load history information yet suffer from a lower fitting accuracy, are processed using an enhanced soft thresholding TCN (SF-TCN) optimized with the slime mould algorithm (SMA). Experimental tests of this methodology on load forecasts for the forthcoming 24 h across all seasons have demonstrated its superior forecasting accuracy compared to that of non-decomposed models, such as support vector regression (SVR), recurrent neural network (RNN), gated recurrent unit (GRU), long short-term memory (LSTM), convolutional neural network-LSTM (CNN-LSTM), TCN, Informer, and decomposed models, including CEEMDAN-TCN and CEEMDAN-TCN-SMA.

Variability and loss of uniqueness of numerical solutions in FEM×DEM modeling with second gradient enhancement

AbstractIn the last decade, a new multi‐scale FEM×DEM approach has been developed using Finite Element Method (FEM) coupled with Discrete Element Method (DEM) as a constitutive law to account for the specificities of the mechanical behavior of granular materials. In FEM×DEM model, a DEM calculation is performed on a particle assembly (volume element—VE) at each Gauss point. Recent publications have demonstrated that FEM×DEM approach naturally captures the discrete and anisotropic nature of granular materials. Despite its advantages, FEM×DEM with classical FEM, suffers from mesh dependency, especially when material enters softening phase and exhibits strain localization. To overcome this limitation, FEM×DEM model has been enriched by incorporating a local second gradient model. Nevertheless, the existence of multiple possible solutions is observed. In this paper, we study the variability and loss of uniqueness of numerical solutions to a boundary value problem. Different VEs with equivalent mechanical properties are generated and used to model the pressuremeter tests by means of FEM×DEM. The modeling results show a great variability of the numerical results, both in shape of borehole and in different modes of shear bands. For the same VE, the loss of uniqueness of numerical solutions is evidenced by a slight modification of loading history at the level of the internal pressure applied to the borehole. Finally, we show that when a certain heterogeneity is introduced by using different VEs within the same BVP, even if the uniqueness of the solution is not guaranteed, the set of possible solutions seems more restrained.

Phase shift-based resonance assessment for in-service high-speed railway bridges

Resonance in high-speed railway bridges can deteriorate the structural integrity and running safety of a train; thus, the resonant speed needs to be identified. Previous studies have proposed resonant conditions analytically, but their applications to in-service bridges are limited. Free vibration after the passage of a train was utilized to assess resonance, but it could not capture the natural frequency of the coupled system because the train-bridge interaction was neglected. This study proposed a practical framework for quantifying the resonance in a high-speed railway bridge using a phase shift. The static displacement of the railway bridge was numerically reconstructed using the train loading history. Phase angles were extracted by comparing the static and dynamic displacements, which were directly utilized to develop a novel resonance indicator in this study. Numerical simulations and field demonstrations validated the applicability of the proposed method for understanding the resonance behavior of full-scale railway bridges.

I-FENN with Temporal Convolutional Networks: Expediting the load-history analysis of non-local gradient damage propagation

In this paper, we demonstrate for the first time how the Integrated Finite Element Neural Network (I-FENN) framework, previously proposed by the authors [1,2], can efficiently simulate the entire loading history of non-local gradient damage propagation. To achieve this goal, we first adopt a Temporal Convolutional Network (TCN) as the neural network of choice to capture the history-dependent evolution of the non-local strain in a coarsely meshed domain. The quality of the network predictions governs the computational performance of I-FENN, and therefore we perform an extended investigation aimed at enhancing them. We explore a data-driven vs. physics-informed TCN setup to arrive at an optimum network training, evaluating the network based on a coherent set of relevant performance metrics. We address the crucial issue of training a physics-informed network with input data that span vastly different length scales by proposing a systematic way of input normalization and output un-normalization. We then integrate the trained TCN within the nonlinear iterative FEM solver and apply I-FENN to simulate the damage propagation analysis. I-FENN is always applied in mesh idealizations different from the one used for the TCN training, showcasing the framework’s ability to be used at progressively refined mesh resolutions. We illustrate several cases that I-FENN completes the simulation using either a modified or a full Newton–Raphson scheme, and we showcase its computational savings compared to both the classical monolithic and staggered FEM solvers. We underline that we satisfy very strict convergence criteria for every increment across the entire simulation, providing clear evidence of the robustness and accuracy of I-FENN. All the code and data used in this work will be made publicly available upon publication of the article.

A Numerical Method for Unstable Propagation of Damage in Fiber-Reinforced Plastics with an Implicit Static FE Solver

Finite element analyses of the propagation of damage such as fiber compressive failure and delamination have greatly contributed to the understanding of failure mechanisms of fiber-reinforced plastics owing to extensive studies on methodologies using Continuum Damage Mechanics and Fracture Mechanics. Problems without the need for consideration of inertia, such as Double-Cantilever Beam tests, are usually solved by implicit FE solvers, and explicit FE solvers are appropriate for phenomena that progress with very high velocity such as impact problems. However, quasi-static problems with unstable damage propagation observed in experiments such as Open-Hole Compression tests are still not easy to solve for both types of solvers. We propose a method to enable the static FE solver to solve problems with unstable propagation of damage. In the present method, an additional process of convergence checks on the averaged energy release rate of damaged elements is incorporated in a conventional Newton–Raphson scheme. The feasibility of the present method was validated by two numerical examples consisting of analyses of Open-Hole Compression tests and Double-Cantilever Beam tests. The results of the analyses of OHC tests showed that the present method was applicable to problems with unstable damage propagation. In addition, the results from the analyses of DCB tests with the present method indicated that mesh density and loading history are not significantly influential to the solution.