Search Results (136)

The impact mechanism of long-term creep in gas-containing coal on coal and gas outbursts has not been fully elucidated and remains insufficiently understood for the purpose of disaster engineering control. This investigation conducted triaxial creep experiments on raw coal specimens under controlled confining pressures, axial stresses, and gas pressures. Through systematic analysis of coal’s physical responses across different loading conditions, we developed and validated a novel creep damage constitutive model for gas-saturated coal through laboratory data calibration. The key findings reveal three characteristic creep regimes: (1) a decelerating phase dominates under low stress conditions, (2) progressive transitions to combined decelerating–steady-state creep with increasing stress, and (3) triphasic decelerating–steady–accelerating behavior at critical stress levels. Comparative analysis shows that gas-free specimens exhibit lower cumulative strain than the 0.5 MPa gas-saturated counterparts, with gas presence accelerating creep progression and reducing the time to failure. Measured creep rates demonstrate stress-dependent behavior: primary creep progresses at 0.002–0.011%/min, decaying exponentially to secondary creep rates below 0.001%/min. Steady-state creep rates follow a power law relationship when subject to deviatoric stress (R² = 0.96). Through the integration of Burgers viscoelastic model with the effective stress principle for porous media, we propose an enhanced constitutive model, incorporating gas adsorption-induced dilatational stresses. This advancement provides a theoretical foundation for predicting time-dependent deformation in deep coal reservoirs and informs monitoring strategies concerning gas-bearing strata stability. This study contributes to the theoretical understanding and engineering monitoring of creep behavior in deep coal rocks. Full article

This study proposes a coupled constitutive model that captures the anisotropic failure characteristics and damage evolution of nickel-based single-crystal (SX) superalloys under various temperature conditions. The model accounts for both creep rate and material damage evolution, enabling accurate prediction of the typical three-stage creep curves, macroscopic fracture morphologies, and microstructural features under uniaxial tensile creep for specimens with different crystallographic orientations. Creep behavior of SX superalloys was simulated under multiple orientations and various temperature-stress conditions using the proposed model. The resulting creep curves aligned well with experimental observations, thereby validating the model’s feasibility and accuracy. Furthermore, a finite element model of cylindrical specimens was established, and simulations of the macroscopic fracture morphology were performed using a user-defined material subroutine. By integrating the rafting theory governed by interfacial energy density, the model successfully predicts the rafting morphology of the microstructure at the fracture surface for different crystallographic orientations. The proposed model maintains low programming complexity and computational cost while effectively predicting the creep life and deformation behavior of anisotropic materials. The model accurately captures the three-stage creep deformation behavior of SX specimens and provides reliable predictions of stress fields and microstructural changes at critical cross-sections. The model demonstrates high accuracy in life prediction, with all predicted results falling within a ±1.5× error band and an average error of 14.6%. Full article

The time-dependent creep behavior of coal is essential for assessing long-term structural stability and operational safety in deep coal mining. Therefore, this work develops a full-stage creep constitutive model. By integrating fractional calculus theory with statistical damage mechanics, a nonlinear fractional-order (FO) damage creep model is constructed through serial connection of elastic, viscous, viscoelastic, and viscoelastic–plastic components. Based on this model, both one-dimensional and three-dimensional (3D) fractional creep damage constitutive equations are acquired. Model parameters are identified using experimental data from deep coal samples in the mining area. The result curves of the improved model coincide with experimental data points, accurately describing the deceleration creep stage (DCS), steady-state creep stage (SCS), and accelerated creep stage (ACS). Furthermore, a sensitivity analysis elucidates the impact of model parameters on coal creep behavior, thereby confirming the model’s robustness and applicability. Consequently, the proposed model offers a solid theoretical basis for evaluating the sustained stability of deep coal mining and has great application potential in deep underground engineering. Full article

To reveal the long-term deformation behavior of high-volume fly ash-based backfill under continuous mining and backfilling, a fly ash–cement backfill material with 73.0% fly ash content was developed, and creep characteristic tests considering initial damage were conducted. The results demonstrate that: (1) A calculation method for the initial damage of backfill based on stress–strain hysteresis loop cycles is proposed, with cumulative characteristics of initial damage across mining phases analyzed; (2) Creep behaviors of backfill affected by initial damage are investigated, revealing the weakening effect of initial damage on long-term bearing capacity; (3) An enhanced, nonlinear plastic damage element is developed, enabling the construction of an HKBN constitutive model capable of characterizing the complete creep behavior of backfill materials. The research establishes a theoretical framework for engineering applications of backfill materials with early-age strength below 5 MPa, while significantly enhancing the utilization efficiency of coal-based solid wastes. Full article

The rheological behavior of firefighting foam is the basis for analyzing foam flow and foam spreading. This experimental study investigates the complex rheological behavior of rapidly aging firefighting foams, specifically focusing on alcohol-resistant aqueous film-forming foam. The primary objective is to characterize the time-dependent viscoelasticity, yielding, and viscous flow of firefighting foam under controlled shear conditions, addressing the significant challenge posed by its rapid structural evolution (drainage and coarsening) during measurement. Using a cylindrical Couette rheometer, conductivity measurements for the liquid fraction, and microscopy for the bubble size analysis, the study quantifies how foam aging impacts key rheological parameters. The results show that the creep and relaxation response of the firefighting foam in the linear viscoelastic region conforms to the Burgers model. The firefighting foam shows ductile yielding and significant shear thinning, and its flow curve under slow shear can be well represented by the Herschel–Bulkley model. Foam drainage and coarsening have competitive effects on the rheology of the firefighting foam, which results in monotonic and nonmonotonic variations in the rheological response in the linear and nonlinear viscoelastic regions, respectively. The work reveals that established empirical relationships between rheology, liquid fraction, and bubble size for general aqueous foams are inadequate for firefighting foams, highlighting the need for foam-specific constitutive models. Full article

Understanding the complex mechanical behavior of osteochondral tissues in silico is essential for improving experimental models and advancing research in joint health and degeneration. This review provides a comprehensive analysis of the constitutive models currently used to represent the different layers of the osteochondral region, from articular cartilage to subchondral bone, including intermediate regions such as the tidemark and the calcified cartilage layer. Each layer exhibits unique structural and mechanical properties, necessitating a layer-specific modeling approach. Through critical comparison of existing mathematical models, the viscoelastic model is suggested as a pragmatic starting point for modeling articular cartilage zones, the tidemark, and the calcified cartilage layer, as it captures essential time-dependent behaviors such as creep and stress relaxation while ensuring computational efficiency for initial coupling studies. On the other hand, a linear elastic model was identified as an optimal starting point for both the subchondral bone plate and the subchondral trabecular bone, reflecting their dense and stiff nature, and providing a coherent framework for early-stage multilayer integration. This layered modeling approach enables the development of physiologically coherent and computationally efficient representations of osteochondral region modeling. Furthermore, by establishing a layer-specific modeling approach, this review paves the way for modular in silico simulations through the coupling of computational models. Such an integrative framework supports scaffold design, in vitro experimentation, preclinical validation, and the mechanobiological exploration of osteochondral degeneration and repair. These efforts are essential for deepening our understanding of tissue responses under both physiological and pathological conditions. Ultimately, this work provides a robust theoretical foundation for future in silico and in vitro studies aimed at advancing osteochondral tissue regeneration strategies. Full article

Marine soft clay is characterized by a high water content and low strength, exhibiting pronounced creep deformation under long-term loading that threatens the serviceability and durability of coastal infrastructure. Accordingly, this study develops a creep constitutive model that combines elastic, plastic, and viscous effects and quantitatively evaluates time-dependent deformation under varying water contents and stress levels to provide reliable prediction tools for tunnel, excavation, and pile-foundation design. Cyclic creep tests were carried out on reconstituted marine soft clay with water contents of 40–60% and stress ratios of 0.4–1.2 using a pneumatic, fully digital, closed-loop triaxial apparatus. A “nonlinear spring–Bingham slider–dual viscous dashpot in parallel with a standard Kelvin dashpot” element assembly was proposed, and the complete stress–strain relationship was derived. Experimental data were fitted with Python to generate a creep-strain polynomial and verify the model accuracy. The predicted–measured creep difference remained within 10%, and the surface-fit coefficient of determination reached R² = 0.97, enabling rapid estimation of deformation for the given stress and time conditions. The findings offer an effective method for the precise long-term settlement prediction of marine soft clay and significantly enhance the reliability of the deformation assessments in coastal civil-engineering projects. Full article

The paper introduces a user material for Abaqus, detailing the modeling of elasto-viscoplasticity under diverse thermomechanical conditions. Converting constitutive equations into a robust code requires extensive efforts to solve numerous crucial numerical challenges. In addition to deriving the equations, detailing the code is also crucial for an efficient implementation of a rheological model. The algorithm for multiaxial Prandtl operator approach presented here provides both. The subroutines of the numerical code are explained in detail and solutions to ensure numerical stability are demonstrated. The multiaxial Prandtl operator approach allows a simple and effective calculation of fatigue damage, creep damage, e.g., or dissipated energy using available uniaxial methods. To demonstrate practical application, the paper illustrates the usefulness of the code by analyzing perforated plates under tension–compression and shear loading. This contribution enriches the computational modeling of elasto-viscoplasticity for the finite element method. Full article

Different temperatures and continuous loads have significant effects on the long-term performance of asphalt concrete facings. The effects of temperature and stress on creep strain and creep rate were analyzed by designing a bending creep test of impermeable asphalt concrete under different temperatures and stresses. Based on the test data, a time–temperature–stress-dependent creep constitutive model was constructed to predict the long-term creep behavior of asphalt concrete at low temperature. The results showed that the creep behavior of asphalt concrete showed significant temperature and stress dependence. The creep behavior accelerated as the temperature or stress increased, especially under high-stress conditions, indicating obvious nonlinear characteristics. Under the condition of 0.2376 MPa, when the temperature increased from 0 °C to 20 °C, the strain at the creep time of 9330 s nearly increased by 24 times. Under 0 °C, the loading stress increased from 0.2376 MPa to 1.3176 MPa, and the strain nearly increased by six times at a creep time of 880 s. The creep strain is expected to increase to 8% after 8 years at −15 °C and 0.2376 MPa. The results can provide a scientific basis for engineering practice and significant implications for designing and maintaining asphalt concrete facings. Full article

Rock creep commonly appears in rock mass engineering, and it should be paid appropriate attention. In this paper, studies on creep constitutive models of rocks were reviewed, and it was found that the types of creep constitutive models can generally be classified into two categories: theoretical formulas and combinations of creep bodies. Moreover, the combination of creep bodies has been used mainly for describing the creep characteristics of rocks; however, creep constitutive models have been constructed based on the subjectivity of studies in most cases, which is not objective or scientific enough. To avoid the subjectivity of establishing the creep constitutive model by using creep bodies, improved gene expression programming was utilized to construct the creep model. To verify the validity of the proposed method, two examples were given, and the corresponding creep constitutive models were obtained. The calculation results indicated that the proposed improved gene expression programming can be applied to establish a creep constitutive model in practice. Full article

This article presents experimental and numerical studies on the creep deformation of 7055-T6 Al and 2197-T8 Al-Li T-joints. Firstly, the optimal process parameters for creep tensile tests (CATs) are determined to be 155 °C, 130 MPa, and 8 h. Based on this, different modes of ultrasonic vibration are introduced. It is found that under the same amplitude, the creep limit of intermittent vibration is 64.7‰ to 97.2‰ higher than that of continuous vibration, and the tensile strength of the former specimens is significantly better than that of the latter. Further analysis reveals that during long-duration or high-amplitude vibrations, the joint material exhibits hardening effects, while short-duration, low-amplitude intermittent vibrations result in softening effects. When the amplitude is 12.53 μm, the material exhibits optimal comprehensive mechanical properties, with yield strengths, tensile strengths, and elongations of 402.1 MPa, 429.3 MPa, and 7.9%, respectively. Additionally, based on the mechanisms of superposition and acoustic softening effects, an improved creep aging constitutive model is established, which incorporates the creep process, stress superposition, and ultrasonic softening changes and is applied in ABAQUS. It is found that at an amplitude of 12.53 μm, the residual stress in the joint is more thoroughly eliminated and distributed more evenly, measuring 97.35 MPa. Moreover, the creep strain calculated using the above model in a finite element analysis shows a high degree of agreement with the experimental results, indicating that the proposed model can more accurately predict the creep deformation behavior of FSWed T-joints during the CAT process. Full article

The time-dependent deformation control of weakly cemented soft rock in deep underground engineering is a critical scientific issue that directly affects the long-term stability of roadways. Traditional Nishihsara models encounter limitations in accurately capturing the weakening effects of material parameters during rock creep failure and in describing the accelerated creep stage, making them insufficient for analyzing the creep failure mechanisms of weakly cemented surrounding rock. To address these limitations, this study integrates SEM and X-ray scanning results to reveal the microscopic degradation process during creep: under external forces, clay minerals, primarily bonded face-to-face or through cementation, gradually fracture, leading to continuous microcrack propagation and progressive parameter degradation. Based on damage theory, an enhanced Nishihara creep model is proposed, incorporating a time-dependent damage factor to characterize the attenuation of the elastic modulus and a nonlinear winding element connected in series to represent the accelerated creep stage. The corresponding three-dimensional constitutive equations are derived. Using the Levenberg–Marquardt (L-M) algorithm for parameter inversion, the model achieves over 98% fitting accuracy across the full creep stages of weakly cemented soft rock, validating its applicability to other rock types such as salt rock and anthracite. The damage creep model is numerically implemented through secondary development in FLAC3D 6.0, with simulation results showing less than 5% deviation from experimental data and the failure mode is similar. These findings provide a solid theoretical foundation for further understanding the creep behavior of weakly cemented soft rocks. Full article

Pressure hulls are the primary pressure-bearing structures in submersibles and deep-sea space stations, which are essential for marine scientific research. Due to repeated dive cycles and extended operational periods, these hulls undergo creep deformation over time, posing risks to their structural integrity. This paper provides a comprehensive review of research on the creep behavior of pressure hulls, focusing on three key aspects: creep testing, creep constitutive models, and numerical simulation techniques. Initially, various creep testing methodologies are presented, with the experimental data serving as a foundational basis for subsequent analyses. Experimental data from creep tests form the foundation for constructing and validating constitutive models, which are critical for predicting long-term deformation. The review also explores advanced numerical simulation techniques, such as user subroutines and multiscale modeling, to analyze creep in complex pressure hull structures. Finally, based on the insights from the reviewed studies, the paper proposed potential directions for future research to address current challenges and enhance the design and maintenance of pressure hulls. Full article

In the loess-filling project, the original structural loess under the filling will produce creep deformation under the isometric consolidation stress state, affecting the upper building’s safe construction and later operation. Therefore, studying the creep deformation characteristics of structural loess under different consolidation coefficients is significant. In this paper, the following results are obtained by combining test and theoretical analysis. In view of the structural loess under the filling, the triaxial creep test of undisturbed loess under different isometric consolidation coefficients, confining pressures and shear stress levels was completed, and the creep deformation law of structural loess was obtained. The creep characteristics of undisturbed loess are found to be diversified under different coefficients, confining pressures, and shear stresses, including initial instantaneous deformation, subsequent creep attenuation deformation, and final stable creep deformation. The damage creep constitutive model of undisturbed loess is established, taking the binary medium model as the framework, the cementation element adopts the Nishihara model, the friction element introduces the overstress model and considers the isometric consolidation effect, and the damage creep constitutive model of undisturbed loess is established. The theoretical model is obtained by determining the relevant parameters of the constitutive model. The theoretical curve is compared with the experimental curve and shows that the damage creep model established in this paper can better reflect the creep of structural loess under isometric consolidation conditions well. The research results can provide systematic theoretical support and an experimental basis for the deformation problems involved in the filling project in the loess area. Full article

A variable-order time-fractional Kelvin peridynamics model is proposed, where the variable order is utilized to reflect the changes of viscosity in viscoelastic materials to effectively capture the damage and deformation of rock steady creep. The corresponding constitutive model is established by coupling a spring and an Abel dashpot. Through the Caputo definition of fractional-order derivatives, finite increment formulations for the constitutive model are derived to facilitate numerical implementation by an explicit time integration scheme. We accordingly introduce a model parameter evaluation method for practical applications. To verify the validity and correctness of the model, constant-order time-fractional peridynamics is used to compare with the proposed model via a sandstone compress creep numerical test, and the results show that the latter can simulate nonlinear creep behavior more efficiently. Additionally, the numerical simulation of practical engineering is conducted. Compared with constant-order time-fractional peridynamics, the proposed model can improve the simulation accuracy by 16.7% with fewer model parameters. Full article