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.

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.