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The freezing method is an effective approach for constructing coal mine shafts through water-rich soft rock strata. The frozen wall produced by this technique stops the movement of water and offers temporary support, ensuring the safety and stability of the shaft working face. However, most frozen rock masses generally comprise ice-filled flaws and frozen intact rock. A frozen fissured rock mass undergoing the long-term effects of excavation unloading under in situ stress gradually accumulates damage or creep deformation over time; this damage is mainly responsible for the significant deformation, cracking and even instability of the frozen rock wall. To study the creep characteristics of ice-filled fissured rock masses under unloading conditions, a series of conventional triaxial compression tests and triaxial unloading creep tests were performed on ice-filled flawed red sandstone specimens from the Shilawusu mine in Northwest China using a self-developed DRTS-500 subzero rock triaxial testing system. In conjunction with the experimental data, the instantaneous strength and deformation characteristics of the rock specimens were analyzed, and their creep deformation characteristics and damage evolution characteristics were discussed. In this paper, based on the nonlinear creep characteristics of frozen rock, fractional calculus theory and damage theory, a new nonlinear creep damage model of frozen fissured red sandstone was defined in series with the improved Burgers model and elastoplastic damage model. The proposed creep model can reasonably describe the creep deformation of frozen fissured red sandstone. Classical elastoplastic mechanics and creep theory were used to derive the three-dimensional creep damage constitutive equation, and the results of creep experiments and simulation results of the creep damage constitutive model were very consistent in this study. The new creep model not only reflects the whole creep deformation process of frozen fissured red sandstone but also exhibits better performance than the classical Burger model and improved Nishihara model in describing the primary creep stage and accelerating creep stage. Therefore, the proposed nonlinear creep damage model is suitable for studying the mechanical creep properties of frozen fissured rock under unloading conditions. The results can provide an important reference for the long-term stability assessment of frozen rock walls of coal mine shafts.

The flow behaviour of AA2060 Al alloy under warm/hot deformation conditions is complicated because of its dependency on strain rates (ε˙), strain (ε), and deformation modes. Thus, it is crucial to reveal and predict the flow behaviours of this alloy at a wide range of temperatures (T) and ε˙ using different constitutive models. Firstly, the isothermal tensile tests were carried out via a Gleeble-3800 thermomechanical simulator at a T range of 100, 200, 300, 400, and 500 °C and ε˙ range of 0.01, 0.1, 1, and 10 s−1 to reveal the warm/hot flow behaviours of AA2060 alloy sheet. Consequently, three phenomenological-based constitutive models (L-MJC, S1-MJC, S2-MJC) and a modified Zerilli–Armstrong (MZA) model representing physically based constitutive models were developed to precisely predict the flow behaviour of AA2060 alloy sheet under a wide range of T and ε˙. The predictability of the developed constitutive models was assessed and compared using various statistical parameters, including the correlation coefficient (R), average absolute relative error (AARE), and root mean square error (RMSE). By comparing the results determined from these models and those obtained from experimentations, and confirmed by R, AARE, and RMSE values, it is concluded that the predicted stresses determined from the S2-MJC model align closely with the experimental stresses, demonstrating a remarkable fit compared to the S1-MJC, L-MJC, and MZA models. This is because of the linking impact between softening, the strain rate, and strain hardening in the S2-MJC model. It is widely known that the dislocation process is affected by softening and strain rates. This is attributed to the interactions that occurred between ε and ε˙ from one side and between ε, ε˙, and T from the other side using an extensive set of constants correlating the constitutive components of dynamic recovery and softening mechanisms.

This paper considers an anisotropic hyperelastic soft tissue model, originally proposed for native valve tissue and referred to herein as the Lee–Sacks model, in an isogeometric thin shell analysis framework that can be readily combined with immersogeometric fluid–structure interaction (FSI) analysis for high-fidelity simulations of bioprosthetic heart valves (BHVs) interacting with blood flow. We find that the Lee–Sacks model is well-suited to reproduce the anisotropic stress–strain behavior of the cross-linked bovine pericardial tissues that are commonly used in BHVs. An automated procedure for parameter selection leads to an instance of the Lee–Sacks model that matches biaxial stress–strain data from the literature more closely, over a wider range of strains, than other soft tissue models. The relative simplicity of the Lee–Sacks model is attractive for computationally-demanding applications such as FSI analysis and we use the model to demonstrate how the presence and direction of material anisotropy affect the FSI dynamics of BHV leaflets.

Rocks naturally containing many flaws are frequently subjected to dynamic impact loading. Understanding the dynamic mechanical response and developing the dynamic constitutive model of flawed rocks are essentially important for the construction safety and stability assessment of rock engineering. In this study, dynamic impact tests are conducted on multi-flawed rocks with different geometries using the split Hopkinson pressure bar (SHPB). By virtue of pulse shaping technique, dynamic stress equilibrium of flawed rock specimens is well achieved. Experimental results indicate that the dynamic strength is significantly affected by both flaw geometry and strain rate. Energy dissipation density also shows strong rate-dependence and is positively correlated to dynamic strength of flawed rocks. With the aid of high-speed digital image correlation (DIC) analysis and sieve tests, progressive cracking behaviors and fragmentation characteristics of multi-flawed rocks under impact loading are comprehensively analyzed. Generally, mixed compression-shear cracking dominates the failure of flawed rocks under dynamic impact loading, and the shear cracking and fragmentation degree of specimens are promoted under higher strain rate. In addition, a dynamic damage constitutive model is proposed to characterize the dynamic strength and deformation properties of flawed rocks under high strain rates. Our proposed constitutive model comprehensively considered the effects of strain rate and coupled damage induced by micro-defects and macro-flaws on the dynamic mechanical response of flawed rocks. A good consistency of the dynamic stress–strain curves of the flawed rocks is observed between the constitutive model prediction and experimental results.HighlightsAnalyzed the dynamic mechanical response and cracking behaviors of multi-flawed rocks under impact loading.A dynamic damage constitutive model of flawed rocks is proposed and validated by experimental results.Microscope dynamic fracture mechanism of multi-flawed rocks is interpreted by SEM observation.

Water-bearing fractured rock masses are prone to geological hazards due to freeze–thaw (FT) damage, which brings adverse effects on the stability of rock engineering. In order to study the FT damage characteristics of rocks, the intact and pre-cracked cyan sandstone samples were taken as the research objects, with pre-crack inclination angles β of 0°, 45°, and 90°, respectively. The effects of FT cycle on stress–strain curve, peak strength, apparent stiffness and FT coefficient of cyan sandstone samples were studied by uniaxial compression test. Based on macroscopic damage variables, a damage constitutive model of cyan sandstone is proposed combined with strain equivalence hypothesis and Weibull distribution hypothesis. Considering that the strain equivalence hypothesis is difficult to reflect the compaction effect of microcracks, the damage constitutive equation is modified by taking the ratio of the secant modulus of the actual stress–strain curve to that of the classical Lemaitre damage constitutive curve as the correction coefficient. The application results show that the modified constitutive model can well describe the stress–strain relationship of cyan sandstone before the peak strength, which verifies the reliability of the model parameters derived from the test data, and the practicability of the damage characterization method and correction coefficient. The results can provide theoretical reference for the study of FT damage of rocks in cold regions.

The nonlinear mechanical behavior and temperature sensitivity of HTPB propellant for solid rocket motors were investigated. The rate-dependent mechanical properties of the propellant were examined through a combination of experiments and numerical simulations. Experimental results demonstrate that the tensile mechanical properties of HTPB propellant are rate-dependent at 223 K and 323 K; stresses at a given strain gradually increase with increasing strain rate. By use a generalized nonlinear ZWT intrinsic model, the tensile mechanical behavior of HTPB propellant under a wide range of strain rates was to described. A numerical simulation of a uniaxial tensile test was performed using a UMAT subroutine. The results demonstrate that the model accurately represents the mechanical properties of the HTPB propellant.

Since the classical element model cannot describe the nonlinear characteristics of rock during the entire compressive creep process, nonlinear elements and creep damage are generally introduced in the model to resolve this issue. However, several previous studies have reckoned that creep damage in rock only occurs in the accelerated creep stage and is only described by the Weibull distribution. Nevertheless, the creep damage mechanism of rocks is still not clearly understood. In this study, a reasonable representation of the damage variables of solid materials is presented. Specifically, based on the Gurson damage model, the damage state functions reflecting the constant creep stage and accelerated creep stage of rock are established. Further, the one-dimensional and three-dimensional creep damage constitutive equations of rock are derived by modifying the Nishihara model. Finally, the creep-acoustic emission tests of phyllite under different confining pressures are conducted to examine the creep damage characteristics of phyllite. And the proposed constitutive model is verified by analyzing the results of creep tests performed on saturated phyllite. Overall, this study reveals the relationship between the creep characteristics of rocks and the corresponding damage evolution pattern, which bridges the gap between the traditional theory and the quantitative analysis of rock creep and its damage pattern.

Fine-particle suspensions (such as cornstarch mixed with water) exhibit dramatic changes in viscosity when sheared, producing fascinating behaviors that captivate children and rheologists alike. Examination of these mixtures in simple flow geometries suggests intergranular repulsion and its influence on the frictional nature of granular contacts is central to this effect—for mixtures at rest or shearing slowly, repulsion prevents frictional contacts from forming between particles, whereas when sheared more forcefully, granular stresses overcome the repulsion allowing particles to interact frictionally and form microscopic structures that resist flow. Previous constitutive studies of these mixtures have focused on particular cases, typically limited to 2D, steady, simple shearing flows. In this work, we introduce a predictive and general, 3D continuum model for this material, using mixture theory to couple the fluid and particle phases. Playing a central role in the model, we introduce a microstructural state variable, whose evolution is deduced from small-scale physical arguments and checked with existing data. Our space- and time-dependent model is implemented numerically in a variety of unsteady, nonuniform flow configurations where it is shown to accurately capture a variety of key behaviors: 1) the continuous shear-thickening (CST) and discontinuous shear-thickening (DST) behavior observed in steady flows, 2) the time-dependent propagation of “shear jamming fronts,” 3) the time-dependent propagation of “impactactivated jamming fronts,” and 4) the non-Newtonian, “running on oobleck” effect, wherein fast locomotors stay afloat while slow ones sink.

Water-weakening effect is one of the most important causes triggering large deformation and failure of soft-rock engineering; however, few studies have paid attention to damage evolution and constitutive relationship of rock in water-weakening process. In this paper, laboratory tests are first carried out to estimate the evolution of mechanical properties along with changes of immersion time for shale samples. Then with the aid of X-ray diffraction and scanning electron microscope, mechanism of parameter degradation for shale under immersion conditions is investigated from the microscopic perspective. Based on the generalized strain equivalent principle and the theory of statistical microscopic damage mechanics, a damage constitutive model of rock subjected to water-weakening effect and uniaxial loading is established by considering the influence of void-compression stage, and the proposed model is verified to be in good agreement with the experiment results. This paper provides an effective approach to analyze the constitutive relationship of rock subjected to water-weakening effect and uniaxial loading.

Weakly cemented soft rock (WCSR) strata are widespread in Western China, and their creep characteristics with geo-stress change significantly affect coal mine safety production. To study the long-term mechanical properties of WCSR, creep tests were performed under an initial confining pressure of 0–6 MPa. The results indicated that with a greater initial confining pressure, the WCSR enters the stable creep stage faster. Using the experimental data, a nonlinear damage constitutive model was constructed to describe the creep failure process while considering the residual strength characteristics of the WCSR sample. Each parameter in the constitutive equation was analyzed for its influence on the creep characteristics of the WCSR. It was found that the axial stress, axial deformation, and stable creep rate of WCSR samples entering the stable creep stage under different initial confining pressures are 18.67 MPa, 1.49% and 0.011%/h, respectively. Based on this study, criteria for determining the creep deformation stability of the WCSR roadways and support suggestions are proposed. These findings will aid in further understanding of the creep failure mechanism and control ideas regarding WCSR roadways.HighlightsThe effect of the initial confining pressure on the creep characteristics of weakly cemented soft rock was investigated.The effect of the initial confining pressure on the macroscopic and mesoscopic creep failure modes of weakly cemented soft rock was investigated.A nonlinear fractional-order damage constitutive model was proposed to describe the creep failure process of weakly cemented soft rock based on its residual strength characteristics.Based on the deformation and stress characteristics of weakly cemented soft rock under different initial confining pressures, a criterion for determining weakly cemented soft rock roadway deformation stability is proposed.