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  • Wuju Wan, Junhua Xiao, Zhixi Guo
    Chinese Journal of Solid Mechanics. 2025, 46(1): 93-104.

    Materials with negative Poisson's ratios, as typical mechanical metamaterials, exhibit indentation resistance when impacted, significantly enhancing their impact resistance while remaining lightweight and capable of high energy absorption. Previous research primarily focused on the mechanical properties of honeycomb structures under forward impacts, with limited studies on the dynamic response of multi-cell structures with negative Poisson's ratios—particularly those made of double material cells—under inclined loads. However, structural failures from inclined load impacts are unavoidable in engineering practice. This study integrates gradient design in multicellular structures with inclined load impacts to analyze energy absorption and crushing deformation modes of structures. We propose a gradient bimaterial negative Poisson's ratio honeycomb structure featuring a curved edge concave bimaterial cell. By changing the materials of the transverse and longitudinal curved bars, we design four types of material gradient honeycomb structures: positive gradient, negative gradient, symmetrical positive gradient, and symmetrical negative gradient. Using numerical methods, we examine the dynamic behavior of each gradient structure under in-plane oblique impact loading. It is found that the honeycomb structure with a negative gradient bimaterial arrangement performs best in energy absorption during oblique impacts. We detail the deformation mode, nominal stress-strain curve, and energy absorption of the negative gradient structure at different impact velocities and impact oblique angles. Results indicate that both impact velocity and impact oblique angle significantly affect energy absorption. Regardless of speed, the smaller the impact oblique angle, the better the energy absorption of the honeycomb structure, meaning crashworthiness decreases as the impact oblique angle increases.

  • Wenbo Dong, Ziguang Chen
    Chinese Journal of Solid Mechanics. 2025, 46(1): 1-14.

    Sandstone is a typical discontinuous and heterogeneous material characterized by a significant presence of pores. Porosity is a crucial factor that influences the complex characteristics of sandstone, notably affecting its compressive strength and deformation parameters. It is of considerable theoretical significance and engineering value to investigate the impact of porosity on the fracture behavior of sandstone under compressive loading. In this paper, we apply both the Intermediately-Homogenized PeriDynamic (IH-PD) model and the Fully-Homogenized PeriDynamic (FH-PD) model to examine the fracture behavior of sandstone containing a single oval flaw subjected to uniaxial compression. The IH-PD model incorporates porosity as pre-existing PD damages, wherein mechanical bonds connected to PD nodes are randomly pre-broken to achieve the desired porosity. The IH-PD model considers the heterogeneous characteristics of sandstone without detailing the explicit geometry of the actual pores. Simulation results from the IH-PD model indicate that both pore size and particle size influence the fracture mode of sandstone under uniaxial compression. A comparative analysis of fracture modes and stress-strain curves from IH-PD simulations, FH-PD simulations, and experimental measurements confirms the accuracy and superiority of the IH-PD model in simulating compressive fracture behavior. The results indicate that only the IH-PD model, which accounts for the inherent heterogeneities of sandstone, can adequately reflect the variations in crack paths caused by changes in pore distribution. Moreover, the IH-PD model successfully reproduces tortuous crack paths, captures transverse cracks in sandstone under compression, and exhibits asymmetric fracture modes, which markedly differ from the FH-PD simulation outcomes. This work employs the IH-PD model to investigate the fracture behavior of sandstone containing a single oval flaw with varying porosity levels under uniaxial compression, elucidating the influence of porosity on the failure modes of sandstone. The findings underscore the significant impact of porosity on the paths, roughness, and tortuosity of cracks. As porosity increases, the cracks exhibit greater tortuosity and roughness, and the symmetry of fracture modes becomes more easily disrupted.

  • Yan Lu, Hongjing Li, Xiaopeng Yang, Yinquan Zhai
    Chinese Journal of Solid Mechanics. 2025, 46(1): 79-92.

    Traditional methods for analyzing the P-Δ effect in tall structures often fail to adequately account for time-varying axial forces, which can lead to an underestimation of its impact on structural safety. This paper introduces a high-order accurate analysis method based on the weak-form quadrature element method (QEM). We develop Hermite-type quadrature element models for both distributed and concentrated mass structures. The proposed method is capable of addressing dynamic P-Δ effects caused by arbitrary axial loads without iterative computations, yielding precise solutions. Its efficacy and accuracy are validated through comparative analysis involving three distinct case studies. Numerical results confirm that the proposed approach delivers highly accurate P-Δ effect analyses, achieving exceptional precision in dynamic response with a single quadrature element, even in complex structural systems. Overall, this method offers a novel and efficient solution for detailed analysis of P-Δ effects in tall structures.

  • Xinyu Wang, Dongtong Yang, Sen Tang, Beihai Huang, Bo Xu, Chong Wang, Qingyuan Wang
    Chinese Journal of Solid Mechanics. 2024, 45(6): 724-734.

    Thin-walled metal components frequently undergo multiaxial bending fatigue during operation, necessitating an experimental method to replicate loading conditions for investigating material properties. In this study, a novel biaxial bending test method using ultrasonic fatigue technology was proposed. The design involved a cruciform TC4 titanium alloy specimen tuned to a natural frequency of 20 kHz based on the principle of harmonic vibration, featuring vertically superimposed fourth-order and third-order bending modes to ensure the maximum stress region remained in the test section. Arc transitions were utilized in other regions to mitigate stress concentration. Finite element simulations and strain gauge tests were conducted to calibrate stress amplitudes in the specimens. Analysis of S-N curves, crack propagation paths, and fracture morphologies revealed the failure mechanisms of biaxial bending fatigue in the very high cycle regime under varied loading conditions. It was found that TC4 titanium alloy exhibited no fatigue limit in the very high cycle regime, showing a continuous downward trend. Owing to gradient stress distribution, biaxial bending fatigue demonstrated significantly longer fatigue life compared to uniaxial ultrasonic fatigue. Meanwhile, crack propagation behavior resembled conventional biaxial fatigue, producing H-shaped or Y-shaped cracks. Fracture surfaces exhibited a brittle characteristic in a large area of the crack initiation zone, with morphology primarily characterized by facets and tearing ridges formed through facet coalescence. In contrast to uniaxial bending fatigue, the facets in biaxial bending showed a batten pattern akin to multiaxial fatigue failure.

  • Jun Hua, Xiaoru Xing, Yunlong Xie, Dong Zhao
    Chinese Journal of Solid Mechanics. 2024, 45(6): 776-794.

    Magnesium (Mg), a lightweight metal material, is constrained in its applications due to poor plasticity and low strength at high temperatures. Graphene (Gr) possesses a large specific surface area and high strength, making it an ideal reinforcement for improving the mechanical properties of materials. A molecular dynamics (MD) simulation was employed to investigate the mechanical behaviors of single-crystal Mg and Gr/Mg composites under compressive loading. Through the analysis of stress-strain curves, atomic structure diagrams, and dislocation distributions, the microscopic deformation mechanisms of single-crystal Mg and Gr/Mg composites under compressive loading were explored. Additionally, the influence of factors such as the number of Gr layers, loading strain rate, and temperature on the mechanical properties of materials was studied. Results reveal that single-crystal Mg exhibits anisotropic characteristics under compressive loading. Addition of Gr enables the activation of difficult-to-initiate slip systems in the Mg matrix due to grain refinement. This leads to stress release and difficulty in initiating twinning deformation. Near the Gr interface, defects such as dislocations and twins nucleate and proliferate, effectively transferring the load to Gr, thereby elevating the average flow stress during the plastic deformation stage of the composites. Furthermore, the Mg matrix restricts the folding and bending of Gr, leading to an enhancement in material toughness. As a result, when the Gr/Mg composite is compressed along the [0 0 0 1] crystal direction to a strain of 0.35, the Gr remains intact without fracture. Dislocations in Gr/Mg composite materials cannot penetrate the Gr layer, thus suppressing Mg matrix damage. Increased dislocation lines can resist compressive plastic deformation. In composites featuring multiple layers of Gr, the yield stress, yield strain, and average flow stress during the plastic deformation stage increase with the number of Gr layers. Additionally, the yield strain is higher when Gr layers are separated compared to being stacked. Within the temperature range of 10 K-600 K, the elastic modulus and yield stress of Gr/Mg composites decrease with increasing temperature. However, the strain rate has a minor effect on the elastic modulus and average flow stress during the plastic deformation of Gr/Mg composites. Nonetheless, increasing the strain rate can enhance the yield stress and yield strain of the composites.

  • Linlong Xu, Xiaogang Ji, Huabin Li, Hao Jiang
    Chinese Journal of Solid Mechanics. 2024, 45(6): 795-807.

    This study examines the tensile properties of skin suturing interfaces created through a silica gel reverse molding process, focusing on the reliability of clinical adhesive properties post-suturing. Four types of skin suturing interfaces, inspired by natural bionic structures, are designed, with primary attention on their tensile stiffness. An equivalent mechanical model is constructed using mechanical theories of suturing interfaces, and a theoretical model is developed to predict the tensile stiffness of each structure. Numerical simulations and physical experiments are conducted to analyze the brittle failure behavior and tensile failure modes of the suturing structures. The influences of shape factor, tooth tip angle, and tip region on the tensile properties of the interface are thoroughly investigated. A parameter mapping model using tensile strength as the evaluation index is constructed for each sensitive factor. It is found that the skin suturing interface exhibits brittle failure behavior, with the zigzag structure showing significantly higher tensile stiffness compared to other suturing structures. As the tooth tip angle increases, the stiffness of the suturing structure decreases, while the tip area enhances the tensile properties of the interface. These results are anticipated to help improve skin wound healing rate after clinical suturing.

  • Xuehui Yu, Ting Li, Anshuai Wang, Mingshi Wang
    Chinese Journal of Solid Mechanics. 2024, 45(6): 831-845.

    This study investigated the dynamic response of continuous-density-graded aluminum foam sandwich tubes subjected to internal explosion loads. A finite element model for continuous-density-graded aluminum foam and sandwich tubes was established in polar coordinates using 3D-Voronoi technology. The influences of core density distributions, such as positive-gradient, negative-gradient, and V-shaped gradient including middle-high-gradient (high in the middle and low at both ends) and middle-low-gradient (low in the middle and high at both ends), core density gradient, assembly methods of tube walls and the core, and the length-to-diameter ratio of explosives on the anti-shock performance of the sandwich tube structure were analyzed. Results demonstrate that, for the same core density gradient, the maximum deformation of the outer tube in the sandwich tube with a negative-gradient core is the least, while the sandwich tube with a middle-low-gradient core exhibits the highest specific energy absorption, and the sandwich tube with a middle-high-gradient core shows the weakest anti-shock performance. As core density gradient increases, the maximum deformation of the outer tube in the sandwich tube with a negative-gradient core significantly decreases. The specific energy absorption for the sandwich tube with a middle-low-gradient core rises initially before declining, while the anti-explosion performance of the sandwich tube with a middle-high-gradient core deteriorates. Optimal bonding between tube walls and the core effectively improves the specific energy absorption of sandwich tubes with a uniform, negative-gradient, or middle-low-gradient core, but it also increases the maximum deformation of the outer tube. For varying length-to-diameter ratios of explosives, the maximum deformation of the outer tube in the sandwich tube with a negative-gradient core is smaller. The present work aims to provide valuable insights for designing such structures for protective engineering applications.

  • Yueyou Tang, Qiang Wang, Jian He, Liang Xia
    Chinese Journal of Solid Mechanics. 2024, 45(6): 709-723.

    In the topology optimization of compliant mechanisms, positional and shape factors significantly affect structural mechanical properties. The formation of concentrated hinge regions not only weakens structural strength but also hinders manufacturability. To this end, we propose a topology optimization method for hinge-free compliant mechanisms, incorporating geometric nonlinearity and utilizing the bi-directional evolutionary structural optimization (BESO) method. Initially, the design domain is discretized, where the 0-1 distribution of the BESO method prevents element distortion during nonlinear finite element analysis, thus enhancing numerical stability and convergence. The deformations of the compliant mechanism at the input and output are constrained under unit excitation, effectively suppressing the emergence of concentrated hinges. This leads to improved structural strength and manufacturability. Finally, hinge-free mechanisms are fabricated via additive manufacturing. Experimental results from samples show excellent agreement with finite element simulations, validating the effectiveness of the proposed hinge-suppression strategy in compliant mechanism design.

  • Guanghong Miao, Shun Li, Xiangyu Chu, Cheng Yuan
    Chinese Journal of Solid Mechanics. 2024, 45(6): 748-758.

    This study investigates the electromechanical characteristics of a conical dielectric elastomer actuator in a non-ideal state, specifically focusing on the dielectric constant related to tensile deformation. By using the Ogden elastic strain energy function with multiple material constants and incorporating a linear permittivity that depends on the tensile rate, the constitutive relation for a non-ideal state is further deduced. The model is solved employing the shooting method, allowing for analysis of the mechanical performance and electromechanical stability of conical dielectric elastomers. We observe significant out-of-plane nonlinear axisymmetric deformation when the membrane is subjected to external force and external voltage, both with and without pre-stretch. By changing the voltage while maintaining constant external force, we identify model parameters and assess how varying electrostriction coefficients impact radial strength, circumferential stretch, and the true electric field. As the electrostriction coefficient decreases, tensile deformation in the membrane becomes increasingly uniform under no pre-stretch conditions, and the true electric field distribution tends to become more even. Under prestretch conditions, tensile deformation in the membrane remains stable, and the true electric field distribution is more consistent. When the electrostriction coefficient is sufficiently small, both the tensile deformation and the true electric field distribution tend to be stable, enhancing the overall stability of the dielectric elastomer. It is found that the prestretch condition exhibits greater stability than the no pre-stretch scenario. This research enhances our understanding of the electromechanical properties in non-ideal states, providing a theoretical foundation for the stable operation of conical dielectric elastomers in practical applications. The findings can guide the design of conical dielectric elastomer actuators, assisting engineers in optimizing design parameters to improve the performance and reliability of actuators.

  • Zhiyang Chen, Wenguang Liu, Long Cheng, Hongxia Chen
    Chinese Journal of Solid Mechanics. 2024, 45(6): 820-830.

    This study focuses on the aerothermoelastic characteristics of composite laminated panels with fully simply-supported boundaries in supersonic airflow, implementing macro fiber composites (MFCs) for active flutter-boundary control. In modeling the equation of motion, the influence of in-plane thermal load on transverse bending deflection is considered, and the aerodynamic pressure in supersonic airflow is calculated on the basis of supersonic piston theory. Motion differential equations of the structural system are derived from classical laminated plate theory and Hamilton's principle with the assumed mode method, then transformed into state space equations. By solving the state matrix eigenvalues, natural frequencies of the structural system are obtained. Aerothermoelastic characteristics of the laminated panel are analyzed via the frequency domain method, assessing the effects of ply angle and geometric parameters of the laminated panel on critical flutter aerodynamic pressure and critical buckling temperature. The proportional feedback control method is used to design the controller, and flutter boundaries of the laminated panel are computed under different control gain coefficients. Results demonstrate that the laminated panel with a ply angle of [90°/-90°/90°] exhibits the lowest aerothermoelastic stability across various aspect ratios. For larger ply angles, an increase in aspect ratio enhances the aerothermoelastic stability of the laminated panel. Adjusting MFC ply angles effectively increases critical flutter aerodynamic pressure. Moreover, the proportional feedback control method can significantly enhance flutter boundaries, but the control gain coefficient requires to be adjusted to ensure stability and performance of the control system. A control gain coefficient that is too small results in weak control, while one that is too large can destabilize the structural system.