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.

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.

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.

Ultrasonic resonance technology is the most effective method for studying the ultra-high-cycle fatigue properties of metallic materials. Ultrasonic fatigue specimens typically need a distinctive geometric design to fulfill the resonance requirements. Conventional specimens, such as round rods and dog bones, do not have planar characteristics, making quantitative microscopic characterization difficult. This paper presents an ultra-high-cycle tensile fatigue specimen with a featured plane based on a traditional dog-bone tension-compression specimen design. Different from the traditional specimen design, the dog-bone specimen herein has a flat observation area, readily enabling quantitative microscopic characterization. Using GH4169 nickel-based alloy as an example, the proposed plane-featured dog-bone fatigue specimen design is validated. As expected, the ultrasonic fatigue test results show that the proposed dog-bone plane specimen can resonate at 20 kHz. The measured fatigue life data are basically consistent with available S-N results in the literature. The proposed method provides new ideas for the design of ultrasonic cycle fatigue specimens and helps in the study of micro-deformation mechanisms of ultra-high-cycle fatigue.

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 angle of repose in particle systems is a fundamental scientific problem in particle science. A deep understanding of its influencing factors and patterns of variation is of great significance for optimization in fields such as civil and chemical engineering. However, existing research based on experiments is limited by available types of particles and measurement methods, making it difficult to comprehensively reveal the impact regulations of various physical parameters on the angle of repose. This paper conducts a high-precision numerical study on the angle of repose in particle systems using the discrete element method (DEM), uncovering the most important particle property parameters that affect the angle of repose. DEM is a numerical method that directly simulates the motion of complex particle systems. Specifically, this study adopts a rolling friction coefficient to characterize the influence of non-sphericity on the simulation and validates the established model with existing experimental data. In addition, binary images of the heap projection in the vertical plane are utilized to calculate the angle of repose reasonably. Simulation results show that both sliding and rolling friction coefficients are positively correlated with the angle of repose. Increasing the sliding friction coefficient can double the angle of repose, while increasing the angle of repose caused by the rolling friction coefficient will reach an upper threshold. Once reaching this value, the angle of repose cannot be further increased. The particle's Young's modulus and restitution coefficient have a relatively small impact on the angle of repose. At the same time, this study employs the DEM to investigate the heat transfer characteristics of granular heaps. It is observed that during heating, the region with the highest heat flux within granular heaps migrates from the bottom to the top. These results reveal the most important factors affecting the angle of repose and can guide engineering optimization.

Mechanical metamaterials (or meta-structures) exhibit extraordinary physical and mechanical properties due to their unique microstructural designs. By combining the design ideas of mechanical metamaterials with intelligent and flexible materials (IFMs), it is possible to create intelligent flexible mechanical metamaterials (IFMMs) with self-sensing and self-actuating capabilities. This paper takes conventional mechanical metamaterials as a starting point and analyzes the fundamental design ideas, deformation mechanisms, and mechanical properties of IFMMs. According to recent research progress on IFMMs, this novel metamaterial is categorized as mechanical metamaterial based on shape memory polymers (SMPs), hydrogel, magnetoactive soft materials, and dielectric elastomers, with a particular focus on the first two types. On the basis of our previous work, we present a general approach that utilizes analytical methods and numerical simulations to analyze the mechanical properties of negative Poisson's ratio, negative expansion, and multi-stable metamaterials under the assumptions of small deformation and large deformation with multi-field coupling, respectively. In the case of small deformation, the use of beam theory and energy methods proves to be essential for obtaining fundamental mechanical parameters of the materials. Moreover, accurate constitutive models and numerical implementation under large deformation and multi-field coupling offer the possibility to analyze more complex deformations and structures. In addition, the preparation and performance testing of IFMMs remain crucial. Advanced manufacturing techniques have introduced new opportunities for the preparation of IFMMs, and currently, various methods are available to effectively prepare these materials. The performance testing of IFMMs includes both experiments applicable to traditional materials and specialized experiments only for IFMs. Finally, this paper concludes by highlighting some key issues and potential trends of IFMMs. These challenges primarily revolve around material properties, fabrication methods, mechanical models, and structural designs. This review may bring beneficial inspiration for the future development of IFMMs.

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.

During the manufacturing process of a rough workpiece, the non-uniformity of material mechanical properties can result in the generation of residual stresses within the workpiece, which can lead to structural failure. During the cutting removal process of the workpiece, the residual stresses gradually release, causing deformation. In this study, the "birth-death element" technique of finite element analysis was used to simulate the cutting removal process of the material. This process was then transformed into the release of residual stresses. A novel analytical method combining radial basis function interpolation with geometric and physical equations was proposed based on plate shell theory, small-deformation theory, theory of elasticity, and the superposition principle. The method aimed to invert the residual stress field and calculate the resulting deformation. This study was divided into two parts. In the first part, the influence of stress equilibrium equations was neglected, and the radial basis function interpolation method was used to invert the release of residual stresses in thin plates according to the initial residual stress field and the residual stress field after material removal. Next, the stresses were substituted into the physical equations to calculate the strain. The strain was then substituted into the geometric equations, and the plane displacement was calculated by strain integration from geometric equations. Based on the plate shell theory equations, the buckling deformation was inverted according to the plane displacement. In the second part, the reverse process of the first part was performed. Firstly, the buckling deformation caused by material removal in the thin plate was inverted. Then, the buckling deformation was substituted into the plate shell theory equations to invert the release of residual stress and the reconstructed residual stress field. The results demonstrated the reversibility of these two processes. Furthermore, the analytical solutions showed high agreement with the finite element solutions. This suggested that the analytical method proposed in this paper is applicable to thin-plate structures under elastic conditions and can be used to estimate residual stress distribution and predict deformation in the thin-plate cutting removal process.