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2024 Vol. 45, No. 2
Published: 2024-04-28
145
Recent Research Progress on Intelligent Flexible Mechanical Metamaterials and Their Properties
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 the 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, and we are particularly concerned with the first two types. Based on our previous work, we present the general approach of using analytical methods and numerical simulations to analyze the mechanical properties of negative Poisson's ratio, negative expansion, and multi-stable metamaterials under the assumption of small deformation and large deformation with multi-field coupling, respectively. In the assumption 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 test of IFMMs remain crucial. Advanced manufacturing techniques have brought new opportunities for the preparation of IFMMs, and currently, various methods are available to effectively prepare these materials. And the performance test of IFMMs includes both experiments applicable to traditional materials and special 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.
2024 Vol. 45 (2): 145-169 [
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170
Knowledge and Data‐driven Exploration of Bounds on Mechanical Properties: A Review
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, still 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 to find materials or structures with extreme mechanical performance, the key is to understand and quantify the structure-property relationship. In the past decades, many attempts and achievements have been made to model the structure-property relationship, including empirical/semiempirical formulas and first-principles calculations, while 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. Under the knowledge and data‐driven framework, recent studies have developed powerful theories of structure-property relationships. Based on these structure-property relationships, the material properties can be predicted from the structures, and conversely, the 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 the bounds on the mechanical properties. First, we present the advances in knowledge and data‐driven approaches for understanding and modeling of structure-property relationships. Then, we review the determined bounds on the mechanical properties and discovered materials or structures with extreme mechanical performance based on the knowledge and data-driven approaches. Finally, the challenges, opportunities, and some future directions are discussed.
2024 Vol. 45 (2): 170-187 [
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188
Residual Stress Inversion and Deformation Calculation Based on Theory of Elasticity
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. The residual stresses can lead to structural failure. During the cutting removal process of the workpiece, the residual stresses will gradually release and then cause deformation. The "birth-death element" technique of finite element analysis was used to simulate the material's cutting removal process. And then we transformed this process into the release of residual stresses. This study proposed a novel analytical method that combined radial basis function interpolation with geometric and physical equations. It was based on the plate shell theory, small deformation theory, elasticity theory, and the superposition principle. The method aimed to invert the residual stress field and calculate the resulting deformation.The paper was divided into two parts. In the first part, the influence of stress equilibrium equations was neglected. We used the radial basis function interpolation method 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 substituted into the geometric equations and then the plane displacement was calculated by strain integration from geometric equations. Based on 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. we inverted the buckling deformation caused by material removal in the thin plate. Then, the buckling deformation was substituted into the plate shell theory equations. We used them 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 of this paper is applicable to thin plate structures under elastic conditions. It is expected to estimate the residual stress distribution and predict the deformation in the thin plate cutting removal process.
2024 Vol. 45 (2): 188-200 [
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201
The Study on Mechanical Behavior and Energy Absorption Characteristics of Minimal Surface Structures Based on MJF
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 MultiJet 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 4.0MPa, 2.1MPa and 4.75MPa, respectively. The nominal stress value of the BCC lattice structure under the same volume is 2.0MPa. 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 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 BCC lattice structures. 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.
2024 Vol. 45 (2): 201-212 [
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213
Buckling Analysis of Functionally Graded Graphene-Reinforced Plates Based on Moving Kriging and Third-Order Deformation Theory
This paper proposed a new meshless model to solve the buckling behavior problem of functionally graded graphene-reinforced composite (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 avoid the problem of difficult implementation of the second type boundary conditions in meshless methods and eliminate the need for artificial introduction of 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 are determined by the mixture law. The meshless govern equation for buckling of the FG-GRC plate with seven unknowns are derived based on the principle of minimum potential energy. The convergence and effectiveness of the proposed method are verified by comparing with literature results. The numerical results show that the critical buckling load of the epoxy pure plate is smaller than that of the FG-GRC plate, and increases with the weight fraction of graphene platelets (gGPL). The reinforcement effects of the three GPL distribution patterns are in the order of FG-X > UD > FG-O. When the total number of layers (NL) of the FG-GRC plate is less than 10-15, the critical buckling load of the FG-O 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 compared to the epoxy pure plate in this stage. When NL > 10-15, the change rate of the critical buckling load of the FG-GRC plate becomes smoother. The critical buckling load of the FG-GRC plate increases sharply when the length-thickness ratio of the GPLs reaches around 1000. When the length-thickness ratio of GPLs exceeds 2000, the critical buckling load of the FG-GRC plate tends to be stable, and the length-width ratio and length-thickness ratio of the GPLs have no significant effect on the critical buckling load of the FG-GRC plate.
2024 Vol. 45 (2): 213-224 [
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225
Research on Thermal Shock Strength of Coating-Substrate Composite Structure Considering Non-Fourier Microscale Effect
The microscale effects of non-Fourier heat transfer are often disregarded in studies concerning thermal shocks. This paper establishes 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 coating and substrate was established for comparative study. It is found that model I demonstrates delayed change, localized distribution, and fluctuation of thermal stress within the coating, when the initial conditions and thermal perturbations are identical and the microscale effect of non-Fourier heat transfer is taken into account. In model I, the thermal stress at any position does not initiate change from zero. Conversely, model II shows no fluctuation, and the thermal stress at any position starts to change from zero. After the generation of model Ⅰ thermal stress, it is the first to reach the peak 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 larger. At the interface, model Ⅰ produces a "reflection effect", where the stress value and the stress drop are larger than that 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.
2024 Vol. 45 (2): 225-237 [
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238
Forced Vibration Analysis of Arbitrary Shells Based on 3D Continuous Shell Theory and Meshless Method
In this paper, a meshless model of an arbitrary shell is established based on 3D continuous shell theory and the moving-least squares (MLS) approximation, where the moving-least squares approximation is used not only for geometric surface interpolation, but also for displacement field approximation. The meshless control equation describing the forced vibration of the arbitrary shell is derived using Hamilton's principle, and the equation is solved by the time-domain implicit Newmark method, and the full transformation method is used to impose the essential boundary conditions. Finally, several representative shell cases are calculated by MATLAB meshless program, and the calculated results are compared with ABAQUS finite element solutions to verify the effectiveness and accuracy of the present method to solve the arbitrary shell forced vibration.
2024 Vol. 45 (2): 238-252 [
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253
Selecting Mapping Function with Highly Efficient Convergence (MFHEC) for ICM Method of Structural Topology Optimization
In this paper, the filter function in ICM method and the penalty function in variable density method are both referred as the mapping function. The problem of how to select the mapping function is studied; and the influence of different mapping functions on the convergence efficiency of structural topology optimization is discussed. Therefore, an approach is proposed to construct a mapping function to achieve high-efficient convergence. Five common forms of mapping functions are given. An optimization model and optimization method matching MFHEC (Mapping function with highly efficient convergence) are proposed. Firstly, the convergence speed of the filter function and quasi-filter function of the same form of mapping functions is compared. Then the convergence speed of the fast filter function of different forms of mapping functions is compared. Taking the structural topology optimization problem minimizing structural volume under displacement constraints as an example, the ICM method is adopted to solve the problem. Through numerical comparison, the efficient convergence of MFHEC function is verified.The results show that the fast filter function has faster convergence rate than other functions in the same form functions. Compared with five different forms of mapping functions, the filter function of power function form converges fastest. Finally, it should be emphasized that the conclusions of the mapping function studied in this paper are equally applicable for the filter function of ICM method and the penalty function of variable density method.
2024 Vol. 45 (2): 253-265 [
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266
Analysis of Plastic Zone at the I/II Composite Lip-Shaped Crack Tip
In this study, the preservation of angles transformation method is employed to establish a propagation model for I/II composite lip-shaped cracks under tensile loading conditions. Grounded in the Irwin 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 the mode I and mode II at the tip of lip-shaped cracks within the plastic zone. Additionally, stress distribution along the extension line of the lip-shaped crack tip is characterized. A tensile simulation model is developed, and comparisons are drawn between the theoretical solution for stress distribution at the lip-shaped crack tip and elastoplastic and linear elastic simulation results. It is found that, based on the Irwin small-scale yielding equivalent hypothesis, the modified dimensions of lip-shaped cracks lead to increased crack sizes and greater equivalent stress intensity factors. 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 Irwin small-scale yielding equivalent hypothesis, exhibits notable alignment 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.
2024 Vol. 45 (2): 266-278 [
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279
Stress Triaxiality of a Notched Round Bar under Axial Loading
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 notch can be used to calibrate the parameters in the plastic and damage models. However, there are two different formulas in the literatures to calculate the triaxiality of the minimum cross-sectional axis of notched round bar under tensile load, 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 elastic stage and in the specific a /R range, and the Bao-Wierzbicki formula is in good agreement with the experimental data and results of simulation, which can be used to calculate the arithmetic mean value of the triaxiality during the whole 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 and strain strengthening effect are further discussed. It is pointed out that different notch proportions will affect the neck stress field. The smaller the notch ratio is, the closer the stress triaxiality value in the elastic stage is to 1/3, When the notch ratio is too small, it will also affect the changes of stress triaxiality throughout the entire tensile process; The strain strengthening effect will change the trend of stress triaxiality during the stretching process, and the increase in strengthening modulus will lead to a decrease in the peak value of the plastic stage. The higher the strengthening modulus, the faster the decrease of stress triaxiality after entering the plastic stage.
2024 Vol. 45 (2): 279-288 [
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