Anisotropic materials find widespread applications across various engineering domains. The investigation on vibrational properties of anisotropic materials holds significance for structural vibration mitigation and safety design. This paper introduces a novel approach, the peridynamic operator method (PDOM), to construct a non-local anisotropic model and applies it to the analysis of free vibrations in anisotropic plates. The model incorporates the unique feature of PDOM, which transforms local differentials and their products into non-local integrals, thereby reformulating the strain energy density from its local form to a non-local form within classical anisotropic theory. Additionally, the paper employs a variational principle and introduces the free vibration equation to develop a PDOM solution for anisotropic free vibration problems. Three numerical examples are provided, including the free vibrations of a thin anisotropic rectangular plate, an anisotropic rectangular plate with cracks, and an anisotropic rectangular plate with holes. The results are compared with finite element results, showcasing the model's convergence, stability, and high computational accuracy in dealing with free vibrations of anisotropic plates with defects and discontinuities.

The ratchetting-fatigue interaction of engineering materials has been extensively investigated in the recent decades. However, as an essential engineering problem, the fatigue failure of notched components with ratchetting has not yet been well touched. It is known that the local stress/strain field at the notch root is a prerequisite for further fatigue life assessment. Neuber's rule is a widely used semi-analytical method for predicting the local stress/strain at the notch root, but its feasibility is not verified when remarkable ratchetting occurs at the root. Therefore, in this work, the cyclic deformation of a notched bar made of U75V steel under asymmetrically uniaxial stress-controlled cyclic loading is simulated using the finite element method. A cyclic elasto-plastic constitutive model is selected and verified according to the experimental results of U75V steel. A UMAT subroutine is developed and implanted into the finite element software Abaqus. Based on the simulation, the stress/strain distributions and corresponding stress/strain concentration coefficients at the notch root, as well as their evolutions during cyclic deformation, are studied. Then, the applicability of Neuber's rule to analyze the local stress-strain response at the notch root of notched components is discussed, taking ratchetting into consideration. The results show that during cyclic deformation, the local stress at the notch root is relaxed, and the stress concentration coefficient decreases accordingly. Meanwhile, the ratchetting strain becomes concentrated at the notch root, and the strain concentration coefficient increases with the number of cycles. The geometric mean of stress and strain concentration coefficients also gradually increases with the number of cycles, significantly differing from the theoretical stress concentration coefficients. This suggests that Neuber's rule cannot accurately describe the stress-strain response at the notch root of notched components when significant ratchetting behavior occurs. Therefore, modifications should be made to Neuber's rule to expand its application scope.

To investigate the vibration characteristics of graphene-platelet-reinforced porous composite (GPLRPC) cylindrical shells under arbitrary boundary conditions, a semi-analytical method using Gegenbauer polynomials as admissible functions is proposed in this paper. First, the effective material properties of the GPLRPC cylindrical shell are derived based on the Halpin-Tsai micromechanical model and open-cell body theory. The artificial spring technique is utilized to simulate the boundary conditions at both ends of the shell and continuous coupling conditions between shell segments. Then, based on the first-order shear deformation shell theory, the motion equations of the structure are derived and its dimensionless frequencies are obtained with the Rayleigh-Ritz method. Numerical calculations are performed to analyze the effects of boundary conditions, porosity coefficients, porosity types, graphene distribution patterns, graphene mass fractions, boundary spring stiffness, and geometric parameters on the vibration characteristics of the shell structure. The results show that Gegenbauer polynomials have excellent convergence and accuracy as admissible functions. It is also found that boundary conditions have different effects on the frequency of cylindrical shells, and the GPL-A distribution pattern and Type-II pore distribution exhibit the best stiffness enhancement effect. Additionally, it is observed that the influence of translational springs on frequency is greater than rotational springs, and the effect of cylindrical shell length-to-diameter ratio is greater, but the effect of diameter-to-thickness ratio is less. Overall, applying graphene to cylindrical shells has a wide range of applications, and the research results can provide data support and theoretical reference for the engineering design.

Coal-rock mass exhibits extremely complex and discontinuous deformation, as well as heterogeneous characteristics. Traditional numerical methods, such as the finite element method (FEM), are difficult to accurately describe the entire process of damage accumulation and progressive failure. Based on the non-local peridynamics (PD) method, the corresponding micro-modulus function and critical elongation are derived by reconstructing the kernel function of the constitutive force function. This approach introduces heterogeneity by incorporating random pre-breaking bonds into the homogeneous discrete model. As a result, peridynamics can be applied to the simulation and analysis of deformation and failure of natural heterogeneous materials and structures. Taking the Fucun coal mine as an example, a heterogeneous peridynamics simulation model is established. The deformation and failure laws of the roadway's surrounding rock and failure characteristics of coal pillars with different widths are analyzed. It is found that when the width of the coal pillar is 5 m, the roadway is at the edge of the extrusion deformation zone. The significant change in abutment pressure results in severe deformation and damage to the roadway's surrounding rock. When the width of the coal pillar increases to 6 m and 7 m, the roadway's surrounding rock gradually moves away from the extrusion deformation area. Consequently, the influence of the basic roof rotation movement in the goaf on the coal pillar weakens, resulting in reduced deformation and damage to the roadway. However, when the width of the coal pillar continues to increase, the roadway's surrounding rock enters an area where the stress increases. The high bearing pressure from the external stress field leads to an increase in deformation and damage to the roadway. Considering the deformation and damage characteristics of the roadway's surrounding rock and coal pillar, a reserved width of 7 m for the coal pillar is finally determined. The proposed peridynamics simulation model provides a new and effective simulation tool for optimizing the size of coal pillars in gob-side entry driving.

Elastic wave metamaterials are artificial periodic structures that can control elastic waves. They can be used in aeronautics and astronautics, vehicle engineering, and other fields. This paper proposes a tunable metamaterial with two magnetic resonators. In this structure, a stainless steel plate connects the magnetic resonator to the external frame. Adjusting the distance between the magnets can affect the in-plane stress of the stainless steel plate and thus the internal stiffness. By adjusting the cell structure, a double-cell system with different internal stiffnesses can be formed to achieve a wider coupling band gap. First, the variations of the stiffness of the thin plate and the negative stiffness of the magnetic force with the distance between two magnetic resonators are determined. The dispersion relationship and the transmissibility of the single-cell metamaterial with double magnetic resonators and the double-cell metamaterial formed by adjusting the distance between magnets are obtained using a theoretical model. Then, the effect of the distance between two magnetic resonators on the metamaterial bandgap and double-cell coupled bandgap in a specific case is further studied. Finally, an experimental model is designed and manufactured using 3D printing technology. The transmissibility curves at different distances between two magnetic resonators are measured, and the bandgap coupling results of double-cell metamaterial structures are verified. The theoretical prediction of the bandgap of the metamaterial agrees well with the experimental results. This adjustment method can provide a new idea for the active control of restraining elastic wave transmission.

Metals and alloys are widely used in industry due to their excellent mechanical properties. Researchers have been continuously searching new materials with better properties or mechanisms to enhance existing ones. In the metal and alloy forming process, hot deformation can effectively refine the grain and improve mechanical properties such as yield strength and tensile strength. Therefore, it is necessary to study the deformation behavior of metal and alloy materials at high temperatures. The hyperbolic-sinusoidal Arrhenius-type model has been widely used by researchers because of its good simulation effect at high temperatures. In this paper, the building process of the model is studied, and the modeling process is optimized with the help of a neural network model. A neural network model is constructed to efficiently determine the hyperbolic-sinusoidal Arrhenius-type equations, based on which the flow stress of high-entropy alloys (HEAs) for different high temperatures and strain rates can be well predicted. The reported hot deformation behaviors of Al_0.3CoCrFeNi HEAs are examined by current model. The results show that the coefficients obtained by the neural network method can better describe the experimental hot flow stress, especially at high strain rate or low temperature conditions. The root-mean-square error (RMSE) and the correlation coefficient R are used to assess the degree of difference between the results. The RMSE and R of the neural network method at total data are 27.7 and 0.985, respectively, which are better than 33.1 and 0.979 of the traditional method. To show the general applicability of the model, the hot deformation behaviors of (CoCrNi)₉₄Ti₃Al₃, FeCrCuNi₂Mn₂, and AlCrCuFeNi are analyzed by the model. The research work presented in this paper can improve the efficiency and accuracy of the hyperbolic-sinusoidal Arrhenius-type model and reduce the difficulty of establishing the model, and is of positive significance for the wide use of the model.

This study investigates the mechanical behavior of binary Cu-Zr metallic glass under cyclic loading using the molecular dynamics simulation method. Firstly, simulations of single indentation are performed on metallic glasses with four different alloy ratios (Cu₅₀Zr₅₀, Cu₅₄Zr₄₆, Cu₆₀Zr₄₀, and Cu₆₄Zr₃₆), and their corresponding force-depth curves are obtained. The evolution of their microstructures is analyzed using Voronoi indices. To further reveal the hardening mechanism of the metallic glasses under cyclic loading with different alloy ratios and loading rates, the hardness, average atomic volume, residual indentation depth, local shear strain, and large-strain atoms involved in indentation are analyzed. The results indicate that the yield capacity of metallic glass increases with the Cu content under different alloy ratios, primarily due to a higher Cu content resulting in more short-range-ordered structures, thus enhancing the yield capacity. Simulation results also show that after cyclic loading, the average hardness at large-depth indentation of metallic glass with the four different alloy ratios increases by 1.86% to 3.17% compared to that of single indentation. The generation and accumulation of shear bands during the cyclic process, as well as the decrease in the average atomic volume in the region beneath the indenter, lead to a denser structure, effectively resisting further deformation and serving as the main factors contributing to the hardening effect. After cyclic indentation of Cu₅₀Zr₅₀ metallic glass at different loading speeds (80 m/s, 100 m/s, and 150 m/s), it is found that the higher the loading rate, the more micro-plastic deformation, residual indentation depth, and large-strain atoms in the matrix. This leads to a higher average hardness and a more pronounced hardening effect in the metallic glass. This work not only contributes to a better understanding of the plastic deformation mechanism of binary Cu-Zr metallic glass under cyclic loading, but also provides reference data for potential applications and the design of new nanostructured materials.

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.

Bounds on the mechanical properties provide fundamental guidelines for finding materials or structures with extreme mechanical performance. However, the bounds on some important mechanical properties, such as Young's modulus and tensile strength, remain unknown, while the search for target extreme materials from infinite potential materials of element combinations across the periodic table is challenging. It has long been questioned: have we approached the bounds on these mechanical properties? Is there a material that is stiffer or harder than diamond? To determine the bounds on the mechanical properties and find materials or structures with extreme mechanical performance, the key is to understand and quantify the structure-property relationship. Over the past decades, many attempts and achievements have been made to model the structure-property relationship, such as empirical/semiempirical formulas, first-principles calculations, machine learning, but these approaches often suffer from limitations in terms of accuracy, efficiency, universality, or interpretability. With the accumulation of knowledge and data, knowledge and data-driven understanding and modeling of structure-property relationships have shown immense potential. Recent studies within the knowledge and data-driven framework have led to the development of powerful theories for structure-property relationships. Based on these structure-property relationships, material properties can be predicted from structures, and conversely, structures can be designed for target material properties. Consequently, the bounds on some important mechanical properties have been determined, and numerous materials or structures with mechanical properties close to the theoretical bounds have been designed and fabricated. Our work provides an overview of the recent progress in these explorations of bounds on mechanical properties. First, we present the advances in knowledge and data-driven approaches for understanding and modeling structure-property relationships. Then, we review the determined bounds on mechanical properties and discovered materials or structures with extreme mechanical performance based on the knowledge and data-driven approaches. Finally, we discuss the challenges, opportunities, and some future directions in this field.

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.