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It is extremely difficult to accurately predict the rock damage evolution during the underground space development or the deep excavation activity. In this paper, based on the statistical damage mechanics, a plastic strain-induced damage model of porous rock was established to describe the damage evolution and the constitutive behavior of porous rock under different stress paths. In the proposed model, the modified porosity was introduced which considered the effect of the generalized plastic shear strain. Besides, the proposed damage evolution function was also controlled by the generalized plastic shear strain. To validate the proposed damage model, the sandstone is selected as the experimental specimen due to it is a typical porous rock, and a series of conventional tri-axial compressive experiments (CTC) and confining pressure unloading experiments under constant deviatoric stress (UCP-CDS) were carried out. Furthermore, the confining pressure unloading experimental data under increscent deviatoric stress (UCP-IDS) was referenced to further validate the applicability of the proposed model. The results showed that the deviatoric strain-damage curves were an “S” shape, moreover, the relationship between the damage variable with the unloading ratio was exponential function. The proposed damage model could better reflect the void volume change and the radial dilation during the unloading process. Moreover, the model could successfully capture the damage evolution law and the mechanical behavior of sandstone by matching a set of tri-axial compressive experiments under different stress paths. Finally, it is found that the strength, strain-hardening and strain-softening characteristics were controlled by the Weibull distributed parameters m0 and F0.HighlightsThe modified porosity was introduced which considered the effect of the generalized plastic shear strain.The relationship between the damage variable with the unloading ratio was exponential function.The proposed model could reflect the void volume and the radial dilation.The proposed model could reflect the stress-strain behavior under different stress paths.

Factors affecting the mechanical properties of the high-damping rubber plate mainly include temperature, shear strain rate, shear strain amplitude, and compressive stress. However, the existing studies focused on one factor and have not conducted detailed research on the coupling relationships between various factors. The influence on the mechanical properties of the high-damping rubber plate of one factor will change with the change in other factors. To study the coupling correlation, a series of horizontal cyclic loading tests were designed and carried out. Due to the simultaneous hyperelastic and viscoelastic properties of high-damping rubber, the hysteresis curve of the high-damping rubber plate is decomposed into a hyperelastic part and a damping part. Equations of the two parts are deduced by a theoretical method, and all the coefficients of the two parts are obtained by fitting the test results. Then, the variation coefficient is used to study the influence degree of each factor on these coefficients. Finally, the correlation variation coefficient is defined as the variation coefficient of variation coefficients and is used to quantify the coupling correlation between the factors. This study is of great significance in exploring the coupling correlation between the factors affecting the mechanical properties of the high-damping rubber plate.

Seismic coda wave attenuation (QC) reflects both intrinsic inelasticity and small‐scale heterogeneities in the Earth's crust, offering insights into its thermal state and structural complexity. Continental China, characterized by widespread plate boundary deformation, is among the most tectonically active regions globally. Using over a decade of data from the China National Seismic Network, we apply the Multiple Station and Multiple Event Method to estimate station‐side QC across 1–14 Hz, yielding high‐resolution maps that reveal block‐scale patterns aligned with tectonic boundaries. The Northeast, South, and North China blocks show consistently high QC values, while significantly lower values are observed in Xinjiang, Tibetan Plateau, and North–South Seismic Belt, consistent with theoretical expectations that low values are observed in active regions. Furthermore, we identify a negative correlation between QC and shear strain rate at higher frequencies, suggesting a fundamental link between attenuation and crustal stress heterogeneity.

The shear modulus behaviour of weathered red sandstone coarse-grained soil under drying–wetting cycles was investigated using a series of triaxial drained tests. Firstly, the properties of the relationship between shear stress q and shear strain ε s were analysed using the test curves of principal stress difference ( σ 1 - σ 3 ) and shear strain ε s based on a series of triaxial drained tests performed; Secondly, a method for solving tangent shear modulus G t was established according to the test curves of σ 1 - σ 3  –  ε s , and the effect of drying–wetting cycles on initial tangent shear modulus G i was analyzed; Finally, the normalisation equation of ( σ 1 - σ 3 )  –  ε s was proposed. The results are as follows: (1) Under the influence of drying–wetting cycles, the ( σ 1 - σ 3 ) - ε s test curve of weathered red sandstone coarse-grained soil are approximately hyperbolas, and the stress–strain relationship between ε s and ( σ 1 - σ 3 ) exhibits strain hardening. (2) The initial tangent shear modulus G i decreases with the increase of the number of drying–wetting cycles, and the decreased amplitude is large at high confining pressure. The change rate of the decrease of G i slows down gradually after 6 drying–wetting cycles. (3) Under drying–wetting cycles, the ultimate principal stress difference ( σ 1 - σ 3 ) ult meet the normalisation analysis conditions of the weathered red sandstone coarse-grained soil shear stress–shear strain relationship, and the linear normalisation degree of the shear stress–shear strain relationship is high.

Hypermobility of the trapeziometacarpal joint is commonly considered to be a potential risk factor for osteoarthritis. Nevertheless, the results remain controversial due to a lack of quantitative validation. The objective of this study was to evaluate the effect of joint laxity on the mechanical loadings of cartilage. A patient-specific finite element model of trapeziometacarpal joint passive stiffness was developed. The joint passive stiffness was modeled by creating linear springs all around the joint. The linear spring stiffness was determined by using an optimization process to fit force–displacement data measured during laxity tests performed on eight healthy volunteers. The estimated passive stiffness parameters were then included in a full thumb finite element simulation of a pinch grip task driven by muscle forces to evaluate the effect on trapeziometacarpal loading. The correlation between stiffness and the loading of cartilage in terms of joint contact pressure and maximum shear strain was analyzed. A significant negative correlation was found between the trapeziometacarpal joint passive stiffness and the contact pressure on trapezium cartilage during the simulated pinch grip task. These results therefore suggest that the hypermobility of the trapeziometacarpal joint could affect the contact pressure on trapezium cartilage and support the existence of an increased risk associated with hypermobility.

By considering the rotationality of shear flow, we distinguish between tube segments created by reptation before the inception of shear flow and those created during flow. Tube segments created before inception of shear flow experience both stretch and orientation, while tube segments created after inception of flow are not stretched, but are only aligned in the flow direction. Based on this idea, the Rotation Zero Stretch (RZS) model allows for a quantitative description of the start-up of shear flow and stress relaxation after step-shear strain experiments, in agreement with data of polystyrene long/short blends and corresponding polystyrene 3-arm star polymers investigated by Liu et al. (Polymer 2023, 281:126125), as well as the shear viscosity data of poly(propylene carbonate) melts reported by Yang et al. (Nihon Reoroji Gakkaishi 2022, 50:127–135). In the limit of steady-state shear flow, the RZS model converges to the Doi-Edwards IA model, which quantitatively describes the steady-state shear viscosity of linear polymer melts and long/short blends. The assumption of “non-stretching” of tube segments created during rotational flow is therefore in agreement with the available experimental evidence. Three-arm star polymers behave in a similar way as corresponding blends of long and short polymers confirming the solution effect of the short arm in asymmetric stars. The analysis of step-shear strain experiments reveals that stress relaxation is at first dominated by stretch relaxation, followed at times larger than the Rouse stretch relaxation time by relaxation of orientation as described by the damping function of the Doi-Edwards IA model. The RZS model does not require any nonlinear-viscoelastic parameter, but relies solely on the linear-viscoelastic relaxation modulus and the Rouse stretch relaxation time. Graphical Abstract

It is generally acknowledged that the stability evaluation of surrounding rock denotes nonlinear complex system engineering. In order to accurately and quantitatively assess the safety states of surrounding rock and provide a scientific basis for the prevention and control of surrounding rock stability, the analysis method of the synergetic theory of information entropy using the failure approach index has been proposed. By means of deriving the general relationship between the total two-dimensional plastic shear strain and the total three-dimensional plastic shear strain and obtaining the numerical limit analysis step of the plastic shear strain, the threshold value of the ultimate plastic shear strain can be determined, which has provided the key criterion for the calculation of the information entropy based on the failure approach index. In addition, combining with the synergetic theory of the principle of maximum information entropy, the evolution equation of the excavation step and information entropy based on the failure approach index of the surrounding rock system in underground mining space are established, and the equations of the general solution and particular solution as well as the expression of the destabilizing excavation step are given. To account for this, the method is applied to analyze the failure states of the floor surrounding rock after the mining of the 71 coal seam in Xutuan Coal Mine and involve the disturbance effect and stability control method of the underlying 72 coal seam roof from the macroscopic and microscopic aspects. Consequently, the validity of the analysis method of synergetic theory of information entropy based on the failure approach index has been verified, which presents an updated approach for the stability evaluation of surrounding rock systems that is of satisfactory capability and value in engineering applications.

A three-dimensional coupled model in a Eulerian framework has been developed in COMSOL Multiphysics software and used to study the complex phenomena of thermal and material flow during the friction stir welding (FSW) process. The moving heat source (tool) effect is modelled using a coordinate transformation. The frictional heat as a function of temperature-dependent yield strength of AA2219-T87 material and the deformation energy of plasticized material flow are considered. Further, the plasticized material flow around the rotating tool is modelled as non-Newtonian fluid using partial-sticking/sliding boundary condition with a computed slip factor ( δ ) at the workpiece-tool material interfaces. The coupled Eulerian model prediction accuracy has been validated against the experimental weldment zones and found a good agreement in terms of the shape and size. Subsequently, the effects of tool-pin profiles (cylindrical and conical) on thermal distribution, material flow, shear strain rates, thermal histories, and weldment zones were studied. It is found that the maximum temperatures, material flow velocities, and shear strain rates are low with the conical tool pin in contrast to the cylindrical one, and it is partly attributed to increased mixing of shoulder and pin-driven material flow around the rotating tool, which in turn decreased the size of weldment zones. Also, the maximum temperatures, material flow velocities, and shear strain rates on the advancing side are higher than those of the retreating side. Therefore, it is suggested to use the CFD model to design the FSW process and tool parameters in a cost-effective way in contrast to the tedious experimental route.

With the help of mechanical models and numerical calculations, the research obtained: (1) the range of compressive shear stress in well bore is in the shape of “dam body” with the dip angle of a reverse fault, also, the magnitude of the compressive shear stress is related to the load factor and the maximum compressive principal stress which have an increasing relationship; (2) the superposition stress of lateral abutment stress and SZZ of a working face is σA, which is related to the distance between reverse faults; (3) the closer the distance to the reverse fault and the greater the vertical well displacement and deformation as the advancement length of the working face increases, the sensitivity to the effects of the reverse fault and mining is: XDISP > ZDISP > YDISP, and the sensitivity to the boundary is such that: ZDISP > YDISP > XIDSP; (4) the closer the distance to the reverse fault and the larger the length of the working face, the greater the displacement and deformation of the vertical well. In addition, the sensitivity to the effects of reverse faults and mining is: XDISP > ZDISP > YDISP; (5) when the working face continues to be mined, the shear stress on the well bore and the circumference of the hole is sensitive to the influences of reverse faults as follows: SXZ > SYZ > SXY; (7) the density of strain energy at the well bore is most sensitive to the lateral distance to the working face strike mining line. Based on these results, it is proposed to arrange large-diameter pressure relief boreholes around the hole and arrange layers to eliminate the influence of the well bore boundary and eliminate the accumulation of shear strain energy around such a well bore.

Dilation behavior is of great importance for reasonable modeling of the stability of the host rock of the repository for high-level radioactive waste disposal. It is a suitable method for carrying out direct shear experiments to analyze the dilation behavior of rock with well understood physical meanings. Based on a series of direct shear experiments on granite samples from the Alxa candidate area under different normal stresses, the shear stress‒shear strain and shear stress‒normal strain relations have been studied in detail. Five typical stages have been divided associated with the fracturing process and deformation behaviors of the granite samples during the experimental process, and the method to determine the typical stress thresholds has been proposed. It has also been found that the increasing normal stress may reduce the maximum dilation angle, and when the normal stress is relatively lower, the negative dilation angle may occur during the post-peak stage. According to the data collected from the direct shear tests, an empirical model of the mobilized dilation angle dependent on normal stress and plastic shear strain is proposed. This mobilized dilation angle has clear physical meanings and can be used in plastic constitutive models of the host rock of the repository, and this analysis can also be put forward to other types of geomechanical problems, including the deformation behaviors related to landslide, earthquake, and so on.