The minimal surface structure is a continuous and smooth porous structure. It has the advantages of low density, high intensity, and excellent energy absorption capability. This paper has studied the mechanical properties and energy absorption characteristics of the minimal surface prepared by additive manufacturing process using nylon PA12. First, using the parametric modelling method, three kinds of minimal surface porous structures (G-surface, P-surface, and D-surface) with the same volume fraction of 20% are designed. The corresponding minimal surface structures are manufactured with Multi Jet Fusion (MJF) additive manufacturing technology. The mechanical response and energy absorption characteristics of different minimal surface structures are then analyzed by combining quasi-static compression tests and numerical simulations. For the mechanical response, it is found that the three kinds of minimal surface structures show better load-bearing capacities compared with the traditional BCC lattice structure. In detail, the nominal stresses of the three minimal surface structures (G-surface, P-surface, and D-surface) are 4.0 MPa, 2.1 MPa, and 4.75 MPa, respectively. The nominal stress value of the BCC lattice structure under the same volume is 2.0 MPa. It is clear that all values of the three minimal surface structures are significantly higher than that of the BCC lattice structure. For the study of energy absorption, the energy absorption per unit volume is used as one of key parameter to evaluate the energy absorption characteristic of the porous structure. The results indicate that the values of the energy absorption per unit volume for the three minimal surface structures (G-surface, P-surface, and D-surface) are all higher than that of the BCC lattice structure. The energy absorption per unit volume for the three minimal surface structures can approximately reach 7, 4, and 8 times that of the BCC lattice structure. In conclusion, the minimal surface structure can show excellent characteristics of mechanical property and energy absorption and has extensive application prospects in the fields of aerospace, automotive industry, and machinery.

The emergence of graphene nanoplatelets (GPLs) has enabled the development of lightweight and high-strength plates, making it a prominent area of research in science and engineering. Therefore, it is essential to study the buckling performance of functionally graded graphene-reinforced composite (FG-GRC) plates. This paper presents a new meshless model to solve the buckling behavior problem of FG-GRC plates. The model is based on an improved Reddy-type third-order shear deformation theory (TSDT) with seven degrees of freedom and a moving Kriging (MK) interpolation method, which can overcome the challenge of implementing the second-type boundary conditions in meshless methods and eliminate the need for shear correction factors. The model is applicable to thin/medium/thick plate problems and has high computational accuracy. The Halpin-Tsai model is used to predict the effective Young's modulus of the FG-GRC plate, and the effective Poisson's ratio is determined using the mixture law. The meshless governing equation for the buckling of the FG-GRC plate with seven unknowns is derived based on the principle of minimum potential energy. The convergence and effectiveness of the proposed method are verified by comparing it with literature results. The numerical results demonstrate that when the total number of layers (N_L) of the FG-GRC plate is less than 10-15, the critical buckling load of the FG-O-type and FG-X-type plates changes more drastically than that of the epoxy pure plate, indicating that the stiffness of the graphene-reinforced plate decreases (or increases) rapidly in this stage, as opposed to the epoxy pure plate. However, when N_L exceeds 10-15, the change rate of the critical buckling load for the FG-GRC plate becomes smoother. Furthermore, the critical buckling load of the FG-GRC plate increases sharply when the length-thickness ratio of the GPLs reaches around 1000. Once the length-thickness ratio of GPLs surpasses 2000, the critical buckling load of the FG-GRC plate tends to stabilize, and the length-width ratio and length-thickness ratio of the GPLs have no significant effect on it. Overall, the research findings of this study not only contribute to the understanding of FG-GRC plates but also offer practical and insightful recommendations for their design and theoretical research.

The microscale effects of non-Fourier heat transfer are often ignored in studies concerning thermal shocks. This paper presents a one-dimensional physical model representing the composite structure of a flat plate coating and substrate. Model I considers the hyperbolic heat transfer of the coating and the parabolic heat transfer of the substrate. Additionally, appropriate boundary conditions are determined based on the heat transfer behavior at the interface. On this basis, a thermoelastic mechanics model of the coating and substrate is formulated. The model is discretized using the implicit difference method to acquire the numerical solution for the temperature field. Subsequently, the stress field is determined, and specific examples are provided. At the same time, mathematical model II of parabolic heat transfer for both the coating and substrate is established for comparative study. It is found that model I demonstrates delayed change, localized distribution, and fluctuation of thermal stress within the coating when taking into account the microscale effect of non-Fourier heat transfer, assuming identical initial conditions and thermal perturbations. In model I, the thermal stress at any position does not start from zero. Conversely, model II shows no fluctuation, and the thermal stress at any position starts to change from zero. After the generation of thermal stress of model I, it reaches the peak first, and the peak value is larger than that of model II. In the substrate, the thermal stress of model I is larger than that of model II, and the gradient of change is higher. At the interface, model I exhibits a “reflection effect”, where the stress value and the stress drop are larger than those of model II. The comparison shows that the thermal shock to model I is more complicated and intense. This study provides a useful reference for ensuring the reliability of coatings under extreme heat transfer environments.

Shell structures are widely used in engineering, especially in aerospace and civil engineering. As a result, the study on dynamic behaviors of shell structures is crucial for engineering applications. Over the years, shell theory has undergone continuous improvement and development, leading to analytical solutions for specific shell structures. However, solving analytical solutions for complex shell structures with intricate shapes becomes highly challenging and even unattainable. Therefore, numerical methods like the finite element method (FEM) and the meshless method are employed for further solutions. The meshless method is a powerful complement to FEM, relying solely on nodal information for the formation of shape functions and enabling easy construction of higher-order smooth approximations. Consequently, it naturally holds an advantage in the numerical analysis of plate shell structures. Based on the 3D continuous shell theory and the moving least-squares (MLS) approximation, a meshless model for arbitrary shells is established in this paper. The MLS approximation is used not only for geometric surface interpolation, but also for displacement field approximation. The meshless equation governing the forced vibration of arbitrary shells is derived under Hamilton's principle and solved using the time-domain implicit Newmark method. The full transformation method is used to impose the essential boundary conditions. The code for the proposed method is developed in the MATLAB platform and used to compute several representative shell examples, obtaining the first ten natural frequencies of each shell type and the time history deflection at the center point under different pulse loads, considering both with and without damping. The calculated results are compared with ABAQUS solutions to verify the effectiveness and accuracy of the presented method. When using the meshless method to solve the forced vibration of arbitrary shell structures, it does not rely on grid partitioning. This enables effective analysis of various shell structures with different shapes, showcasing its strong adaptability and vast potential for applications.

In this paper, the filter function in the ICM method and the penalty function in the variable density method are both referred as the mapping functions. Different forms of mapping functions have a significant impact on the convergence efficiency of structural topology optimization. Therefore, it is necessary to study how to construct a suitable mapping function for the optimization model. Aimed at this problem, how to construct and select a mapping function in the establishment of the structural topology optimization model is studied, and the influence of different mapping functions on the convergence efficiency of structural topology optimization is discussed. An approach is proposed to construct a mapping function to achieve high-efficiency convergence in structural topology optimization. Five common forms of mapping functions are also given. An optimization model and a solution algorithm matching the mapping function with highly efficient convergence (MFHEC) are proposed. Firstly, the convergence rates of the filter function and the quasi-filter function of the same form of mapping functions are compared. Then the convergence rates of the fast filter function of different forms of mapping functions are compared. Taking the structural topology optimization problem of minimizing structural volume under displacement constraints as an example, the ICM method is adopted to establish the models and solve the problems. The higher convergence efficiency of MFHEC is verified by the results of numerical comparison. The results show that the fast filter function has a faster convergence rate than other functions in the same form of mapping functions. Compared with five different forms of mapping functions, the filter function of power function form has the fastest convergence efficiency. Finally, it should be emphasized that the conclusions of the mapping function studied in this paper are equally applicable to the filter function of the ICM method and the penalty function of the variable density method. The proposed method for constructing MFHEC is very useful for improving the efficiency of the ICM method and the variable density method.

In this study, the angle-preserving transformation method is employed to establish a propagation model for I/II composite lip-shaped cracks under tensile loading conditions. Based on Irwin's small-scale yielding equivalent hypothesis, a plastic propagation zone model is formulated for Ⅰ-Ⅱ composite lip-shaped cracks under tensile loading. This model provides expressions for the stress intensity factors (SIFs) of mode I and mode II at the tip of lip-shaped cracks within the plastic zone. Additionally, the stress distribution along the extension line of the lip-shaped crack tip is characterized. A tensile simulation model is developed, and the theoretical solution for stress distribution at the lip-shaped crack tip is compared with the elastoplastic and linear elastic simulation results. It is found that, based on Irwin's small-scale yielding equivalent hypothesis, the modified dimensions of lip-shaped cracks lead to increased crack sizes and greater equivalent SIFs. Geometric alterations in lip-shaped crack parameters also influence the plastic zone, with larger semi-lengths resulting in larger plastic zones under equivalent width-to-length ratios. Conversely, greater width-to-length ratios lead to smaller plastic zones under equivalent semi-lengths. Moreover, an increase in the inclination angle of the lip-shaped crack corresponds to a proportional increase in the plastic zone size. The plastic correction theory at the lip-shaped crack tip, founded on the basis of Irwin's small-scale yielding equivalent hypothesis, aligns well with plastic finite element simulations. As the inclination angle of the lip-shaped crack rises, stress levels at the crack tip diminish. On the one hand, this phenomenon arises from the transition from mode I crack extension to Ⅰ-Ⅱ composite crack extension, coupled with stress yielding at the concave region of the lip-shaped crack for larger inclination angles. On the other hand, this stress yielding serves to mitigate stress concentration at the crack tip, ultimately resulting in reduced stress levels at the crack tip.

Stress triaxiality is a parameter that expresses the stress state and can be used as a variable to characterize the plasticity and fracture damage model of materials. It plays an important role in structural strength and failure analysis. The round bar tensile test with a notch can be used to calibrate the parameters in the plastic and damage models. However, there are two different formulas in the literature to calculate the triaxiality of the minimum cross-sectional axis of a notched round bar under tensile loading, which were proposed by internationally renowned scholars Bridgman and Wierzbicki, respectively. Their differences often cause confusion in application. Through refined finite element numerical analysis, this article attempts to clarify the validity and applicability of the two formulas. The results show that the Bridgman formula is more accurate only in the elastic stage and in a specific a/R range. The Bao-Wierzbicki formula, on the other hand, is in good agreement with the experimental data and simulation results, which can be used to calculate the arithmetic mean value of triaxiality during the entire tensile process. Based on further analysis, a new revised stress triaxiality formula in the plastic stage under elastic-perfectly-plastic condition is proposed, and the notch geometry effect and strain-hardening effect are further discussed. It is pointed out that notch ratio can affect the neck stress field. The smaller is the notch ratio, the closer is the stress triaxiality value in the elastic stage to 1/3. When the notch ratio is too small, it can also affect the change of stress triaxiality throughout the entire tensile process. The strain-hardening effect can change the trend of stress triaxiality during the stretching process, and an increase in the strengthening modulus will lead to a decrease in the peak value of the plastic stage. The higher is the strengthening modulus, the faster is the decrease of stress triaxiality after entering the plastic stage.

Structural components in the fields of aviation, aerospace, weapons, and energy are often subjected to repeated impacts of small loads (or low energy). This type of load is different from the single-pulse impact of high energy and the conventional low-strain-rate fatigue, which is called impact fatigue. Because the energy-based impact fatigue test methods can only detect the relation between impact energy and fatigue life, the industrial application of impact fatigue test results in structural design and performance evaluation has been limited. Therefore, this paper focuses on exploring a new impact fatigue loading method. First, based on a brief review of the development of existing impact fatigue test methods, this paper affirms the superiority of the stress wave method based on the Hopkinson bar principle, and raises the problem of non-constant amplitude loading in impact fatigue tests. The waveform generated by the Hopkinson bar is controllable and measurable, which is beneficial to realizing constant-amplitude cyclic loading. Then, three impact fatigue loading techniques (namely the one-wave, two-wave, and three-wave techniques) based on the Hopkinson bar are proposed. The feasibility of these methods is verified through experiments, focusing on studying whether there is a non-constant amplitude loading problem caused by secondary loading. The three-wave technique is found to be the most effective impact fatigue loading method because it can achieve constant amplitude loading and obtain comprehensive test data. Finally, a constant-amplitude dynamic shear fatigue test method is developed using the three-wave technique. Impact fatigue performance tests are carried out on the TC4 titanium alloy. The test loading frequency is 0.1 Hz, and the test strain rate ranges from 6800/s to 8400/s. It is proved that this method can realize dynamic shear fatigue testing of metal materials at the strain rate level of 10³/s. This study provides a new idea for the constant-amplitude impact fatigue test. By changing the forms of the specimen and the loading bars, the impact fatigue loading in other loading modes (such as tension, compression, etc.) can also be realized.

During penetration, the temperature of the projectile will sharply rise due to the large amount of heat generated by the sliding friction between the projectile and the target. High temperature can soften the projectile, potentially change its shape, penetration mechanism, and further affect the penetration ability. In order to study the temperature rise of the projectile during high-speed penetration, a two-part temperature rise calculation model of the penetration is established. In the first part, the heat flux data set of the projectile at different positions in the process of penetration is obtained according to rigid body dynamics theory and the friction heat generation mechanism. The second part takes the heat flux data set as the boundary condition and calculates the temperature distribution of the projectile based on heat conduction theory and the finite difference algorithm. The stability of the model is discussed from the two aspects of time step and projectile mesh, and appropriate values are selected. The calculation model of temperature rise is used to study the heat flux and temperature distribution of the projectile, and the factors influencing the temperature rise of the projectile are discussed and analyzed. The results show that the temperature rise is obvious during high-speed penetration, but it only lasts for a very short time, and the high temperature is mainly distributed near the surface of the projectile head. The position of the highest surface temperature outside the projectile during penetration is related to the shape of the projectile. During the penetration time, the ratio of the heat conduction distance to the radius of the projectile decreases with the increase of the size of the projectile. The research results are useful for the design and material selection of high-speed penetration projectiles.

In hypervelocity impact problems, it is difficult to accurately obtain the crater morphology under certain conditions. Studying the damage zone can compensate for this limitation and serve as an important basis for understanding the impact mechanism and validating numerical simulations. However, there has been limited research on numerical simulation of the damage zone due to the lack of experimentally validated criteria. This paper presents a summary of the existing quantitative measurement results for the damage zone. The findings reveal that, for the same target, the depths of the damage zone obtained through multiple microscopic testing methods are relatively consistent, which facilitates the analysis of the damage zone. Based on the iSALE code, the applicability of total plastic strain (TPS), damage factor (D), and peak pressure as criteria for assessing the damage zone is analyzed. The results indicate that, TPS=0.1 is appropriate as a damage criterion, D=1 could be used as a damage criterion with caution, while peak pressure is not a suitable damage criterion. Through parametric analysis, it is found that the damage zone gradually decreases with increasing porosity and target strength.