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2022 Vol. 43, No. 5 Published: 2022-10-28

	519	Research progress on multimodal atomic force microscopy

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2022.031
		Among the various properties of materials at the nanoscale, nanomechanical properties are the basic properties that need to be ensured for nanoscale materials and devices. Therefore, the development of reliable and quantitative mechanical property measurement methods at the nanoscale is of great significance. Atomic Force Microscope (AFM), as an important platform for nanoscale mechanical measurements, is widely used in micro/nanoscale topography and mechanical properties imaging. By simultaneously exciting two or more vibrational modes of the cantilever, multimodal AFM can achieve high resolution, high sensitivity, quantitative, non-destructive, and rapid nanomechanical imaging, which has a promising prospect. Focusing on multimodal AFM, the basic principles of multimodal AFM are first introduced. Subsequently, the main advances in the study of cantilever dynamics and imaging techniques in multimodal AFM are reviewed. Then, typical applications of multimodal AFM are summarized and discussed. Finally, the possible future research topics of multimodal AFM are prospected.
		2022 Vol. 43 (5): 519-540 [Abstract] ( 121 ) HTML (1 KB) PDF (0 KB) ( 96 )

	541	BIMATERIAL INTERFACE CRACK ANALYSIS BY USING AN IMPROVED GENERALIZED FINITE DIFFERENCE METHOD

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2022.006
		Cracks on the interface of the bimaterial could be present either as a result of the manufacturing defects, and/or mismatch between the different material properties of the bimaterial. The asymptotic near-tip field for bimaterial interfacial cracks presents an oscillatory behavior which is very different from that for cracks in homogeneous materials. Due to the oscillatory behavior related to the complex eigenvalues, modeling such interface cracks by the conventional solution procedures designed for homogeneous materials is inadequate, and may not lead to accurate solutions by using the well-established and widely applied finite element method (FEM) or boundary element method (BEM), even when a very fine mesh near the crack-tip is employed. In the present paper, we document the attempt to apply the generalized finite difference method (GFDM) for fracture analysis of bimaterials containing interfacial cracks. The main idea of the method is based on the theories of local Taylor series expansion and moving-least square approximation. Since the method is meshless and no element connectivity is needed, it can be viewed as a competitive alternative for bimaterial interface crack analysis. In our calculations, a multi-domain technique is employed to handle the non-homogeneity of the dissimilar materials, and the displacement extrapolation method (DEM) is introduced to compute the complex stress intensity factors (SIFs) for cracked dissimilar materials. An improved GFDM formulation is proposed to further improve the accuracy and stability of the GFDM for fracture mechanics analysis. Two benchmark numerical examples are well studied to demonstrate the accuracy and stability of the present method for interface crack analysis of composite bimaterials. In the following-up works, other interesting and important problems, such as thermal effects and dynamic effects, and crack propagation and arrest should be considered. The present work provides an efficient alternative and the corresponding results form a solid basis for these interesting research topics.
		2022 Vol. 43 (5): 541-550 [Abstract] ( 134 ) HTML (1 KB) PDF (0 KB) ( 89 )

	551	Optimal design of shell-lattice infill integrated supporting structure based on Moving Morphable Components method and its application in China Space Station

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2022.010
		China Space Station is the most complex manned spacecraft developed by China, in which the efficient and lightweight design of the payload supporting structure is a technical challenge encountered during the engineering development process. In order to reduce the weight of the support structure as much as possible while ensuring the service performance, an additive manufactured shell-lattice infill integrated structure is selected as its structural form, and its lightweight design is realized through topology optimization techniques. This paper summarized the design method of self-supporting lattice structure inspired by crystal symmetry for additive manufacturing; develops an optimization design approach of shell-lattice infill integrated supporting structure based on the moving morphable components (MMC) method; Taking advantage of the MMC method with explicit structural geometric parameters and the ability to obtain clear optimal force transfer paths, an additive manufacturing-oriented shell-lattice infill integrated topology optimization mathematical formulation is proposed, with the fundamental structural frequency as the constraint and the lightest weight as the optimization objective. After the optimization process, the additive manufacturing model was reconstructed by Nurbs surface based on the optimal structural force transfer path and the information of structural feature sizes on this path, which was finally fabricated by selective laser melting (SLM) process. In order to verify the effectiveness of the design, the support structure and the equipment mass simulated parts were verified by single machine vibration test. The experimental results show that the weight of the support structure is reduced by 50%, and the fundamental frequency is increased by 35% through the MMC-based topology optimization design. At present, the support structure has been successfully launched with the China space station, and the relevant equipment is operating stably in orbit. It is the first successful application and in-orbit verification of shell-lattice infill integrated structure based on the MMC topology optimization method in China's manned space field.
		2022 Vol. 43 (5): 551-563 [Abstract] ( 358 ) HTML (1 KB) PDF (0 KB) ( 110 )

	564	Design of Uni-mode Metamaterial Based on Distorted Periodic Kagome Truss Lattices

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2022.011
		Metamaterials with zero-energy mode are a kind of elastic material that some eigenvalues of the elastic matrix are zero. By counting the number of zero eigenvalues, they are classified as from uni-mode to penta-mode material. To date, only penta-mode materials have been studied in depth and found important applications in manipulation of underwater acoustic wave and elastic wave, while other types of material with zero-energy modes remain almost untouched. In this study, we present a comprehensive development for design of two-dimensional uni-mode material based on periodic distorted Kagome truss lattices. By using the Cauchy-Born hypothesis and matrix formulation of truss systems, we developed a homogenization method for general lattices which are under-constrained. Under the macroscopic strain field, the method can take care of non-affine relaxation due to the microscopic mechanism, thus can correctly predict the rank deficient effective elastic tensor. Further, the relation between the microscopic self-stress and mechanism states as well as the macroscopic hard and soft modes is clarified. In particular, for distorted Kagome lattices, we are able to analytically express the soft mode by irreducible geometric parameters, while the rest parameters including the bar stiffnesses are responsible only for hard modes. To match a given elastic tensor, we proposed a two-level design scheme to seek microstructural parameters with high efficiency and accuracy. It is revealed that the distorted Kagome lattice is able to realize a wide spectrum of uni-mode materials via tuning its configuration. Finally, the developed method was verified in conjunction with unusual wave behaviors found in uni-mode materials, and excellent agreement was achieved between the theoretical and numerical predictions. We found that the slowness curve of an uni-mode material may possess opened shape, which is not found in ordinary orthotropic materials, and can be utilized in wideband negative refraction of elastic wave beam. The work may initiate design of more general metamaterials with zero-energy mode, and may inspire further explorations on applications other than those of penta-mode material.
		2022 Vol. 43 (5): 564-576 [Abstract] ( 153 ) HTML (1 KB) PDF (0 KB) ( 92 )

	577	Research on geometric parameters of damage behavior of suture joint structure

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2022.012
		Inspired by the geometric interface in nature, extracting the mathematical model, establishing the suture joint structure through 3D printing. and the secondary development of ABAQUS pre-processing combined with Python and MATLAB GUI, and the finite element model of the suture joint structure was generated. Numerical simulation explores the effects of different baseline shapes and tip angles on the damage behavior and load-bearing capacity of suture joint structures. And on the premise of verifying the validity of the simulation model, numerical simulation is used to explore the influence of the interlocking effect of the arc baseline amplitude on the load-bearing capacity of the suture joint structure.
		2022 Vol. 43 (5): 577-584 [Abstract] ( 108 ) HTML (1 KB) PDF (0 KB) ( 117 )

	585	Study on fatigue life prediction method of cast magnesium alloy ZM6 considering the effect of internal pores

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2022.015
		Cast magnesium alloy ZM6 is a typical material used in the manufacturing of helicopter reducer casing. However, the internal defects produced during the casting process have a significant effect on the fatigue properties of the material. In this paper, the fatigue damage model and life prediction method of ZM6 material with internal pore defects are studied. First, X-ray tomography scan of specimens made of three batches of blank material is conducted, and the distribution characteristics of internal pores is obtained. It can be observed that the pore distributions are much different for three batches of specimens. In addition, the randomly distributed small pores and few large dimension pores are both observed for each tested specimen, which will provide the basic data for the following influencing analysis of pores. Afterwards, high cycle fatigue tests of 48 specimens are conducted under two stress ratios and several stress levels, and the fatigue life results of each batch of specimens are obtained. After that, the correlation between life result and the distribution of internal pores is further studied. It can be concluded that the porosity and the large near-surface pores are the two key factors affecting the fatigue lives of specimens. Accordingly, based on the theory of damage mechanics, a fatigue damage model is then proposed to reflect the influences of porosity and large near-surface pores by introducing the initial elastic modulus of representative volume element (RVE) and the equivalent local stress and strain fields around the key pore. The corresponding parameters calibration method is presented as well. This model is then combined with the ABAQUS software platform to implement the numerical calculation of fatigue damage evolution of specimen with internal pores. Finally, the proposed theoretical model and calculation method are used to predict the fatigue lives of specimens, and the prediction results agree well with the experimental data, which validates the applicability of the proposed method.
		2022 Vol. 43 (5): 585-602 [Abstract] ( 185 ) HTML (1 KB) PDF (0 KB) ( 106 )

	603	Analysis of free vibration and forced vibration of Timoshenko curved beam based on meshless method

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2022.016
		Curved beam has the advantages of beautiful appearance and good mechanical performance, so it has been widely used in engineering. A moving-least squares (MLS) meshless method is proposed in this paper to solve the free vibration and forced vibration problems of Timoshenko curved beams, and the first-order shear deformation theory (FSDT) is adopted. Firstly, a series of discrete points is used to establish the meshless model of the curved beam. Then, the potential energy and kinetic energy equations of the curved beam are derived. The equations governing the free vibration and forced vibration of the curved beam are given according to the Hamiltonian principle, and the full transformation method is employed to deal with the essential boundary conditions because the boundary conditions cannot be directly applied by the meshless method. Lastly, the natural frequencies and vibration modes are obtained by solving the corresponding equations. At the end of this paper, the effectiveness of the meshless method is verified by numerical examples, and the results show that the proposed method has good convergence characteristics. In addition, the effects of various boundary conditions, span height ratios, variable sections and curvatures on the free vibration and forced vibration of curved beams are discussed. The calculated results are compared with the literature solution or ABAQUS solution, which shows that the meshless method has high accuracy and is suitable for actual engineering projects.
		2022 Vol. 43 (5): 603-613 [Abstract] ( 158 ) HTML (1 KB) PDF (0 KB) ( 114 )

	614	Fracture Mode Transition in Three-point Bending of Concrete Beams: A Peridynamic Investigation

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2022.017
		Concrete is a widely used artificial composite material. Its damage and fracture properties determine the reliability and safety of many engineering structures. The macroscopic damage and cracking of concrete structures are closely related to their heterogeneous microstructures. When a bottom-notched concrete beam undergoes a three-point bending failure, as the notch position shifts from the center to the edge, the crack initiation location transits from the top of the notch to the bottom center of the beam. In this paper, the intermediately homogenized peridynamic (IH-PD) model and fully homogenized peridynamic (FH-PD) model are used to study the three-point bending fracture of concrete beams. The IH-PD model randomly generates different bond combinations based on the volume fraction of aggregates in concrete and introduces microscale heterogeneities into the model without describing the shape and distribution of aggregates in detail. The IH-PD model applies the simplest material constitutive relationship of a prototype microelastic brittle to mimic the micro-scale brittle nature of concrete. By comparing the relationship between the fracture mode and the notch position obtained by the IH-PD model, the FH-PD model, and from the experimental observation, it is found that only the IH-PD model considering the heterogeneities of concrete, can reproduce the experimental results, indicating that the behavior of the three-point bending fracture mode of notched concrete beams changing with the notch position is mainly related to the microstructures. Note that in the IH-PD model, the horizon size depends on aggregates' size, which benefits from studying the influence of aggregates' size on the fracture mode. The simulation results show that aggregates' size is a factor leading to the size effect of concrete structures' mechanical behavior. In addition, the randomly distributed pores are introduced into the IH-PD model by setting pre-damage, and the influence of concrete porosity on the fracture modes of concrete beams is discussed. The results show that the porosity influents the critical notch position of the fracture mode transition state and has a certain influence on the crack path direction and the roughness of the crack surface.
		2022 Vol. 43 (5): 614-624 [Abstract] ( 124 ) HTML (1 KB) PDF (0 KB) ( 90 )

	625	Three-Dimensional Elastic Constants and Influence of Oxidation Degree on Mechanical Properties of Multilayer Graphene Oxide

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2022.019
		Macroscopic graphene oxide film is composed of multilayer graphene oxide.The mechanical properties of multilayer graphene oxide can be described from three aspects : in-plane tensile, normal tensile and interlayer shear properties. The in-plane tensile properties are related to the strength of carbon-carbon bonds, and the transformation of sp2 to sp3 hybrid forms is the main reason for affecting the binding energy of carbon atoms. Normal tensile and interlaminar shear properties are related to interlayer interaction, and the strength of hydrogen bond and van der Waals interaction are two factors affecting interlayer interaction. Here we treat multilayer graphene oxide as a special three-dimensional orthotropic materials--transversely isotropic material, formulate a three-dimensional model of multilayer graphene oxide with hydroxyl and epoxy groups randomly distributed on the surface of graphene, and the in-plane tensile, normal tensile and interlaminar shear behaviors of multilayer graphene oxide are studied by molecular dynamics method. All five independent elastic constants E2, E3, μ12, μ32 and G23 of multilayer graphene oxide are obtained. Then, the three-dimensional elastic matrix (flexibility matrix and stiffness matrix) is determined, and the influence of oxidation degree on the elastic constants and strength is further analyzed. It is found that normal tensile and interlaminar shear properties are much lower than in-plane tensile properties. With the increase of oxidation degree R, the in-plane Young's modulus E2 and tensile strength σ2max of multilayer graphene oxide decrease gradually, and the normal Young's modulus E3 and tensile strength σ3max, interlayer shear modulus G23 and shear strength τ23max increase gradually, but the influence on Poisson's ratio is small. The in-plane tensile fracture position is determined by the bond energy between the oxidation groups (hydroxyl and carboxyl) and carbon atoms. The number of hydrogen bonds is an important factor affecting the interlayer properties.
		2022 Vol. 43 (5): 625-635 [Abstract] ( 194 ) HTML (1 KB) PDF (0 KB) ( 103 )

	636	Evaluation Method of V-notch Stress Field and N-SIF Based on Singular Intensity Factor

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2022.020
		According to the theory of linear elastic fracture mechanics, the stress field at V-notch is singular, the stress value tends to infinity, and the peak stress cannot be directly used to evaluate the fatigue strength. By introducing the singular intensity factor "as", the semi-analytical formulas of edge crack notch stress distribution and notch stress intensity factor (N-SIF) were derived. Considering the factors such as opening angle and geometric size, a simple formula of notch stress evaluation was obtained based on singular intensity factor fitting, which can be used to quickly evaluate notch stress field and N-SIF value. Comparing the evaluation results of the simple formula with those of the finite element method and traditional literature, the results show that the simple formula in this paper can accurately predict the stress field and N-SIF value on the bisector of a single V-notch angle under tensile load, thus realizing the rapid evaluation of the stress field of notch samples.
		2022 Vol. 43 (5): 636-645 [Abstract] ( 152 ) HTML (1 KB) PDF (0 KB) ( 90 )

	646	Study on shear creep damage characteristics of shale block under impact disturbance

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2022.021
		Blasting is necessary to work in most open-pit mining and the impact disturbance produced by continuous blasting operations will weaken the long-term stability of open-pit slopes. In order to study the influence of impact disturbance effect on the creep characteristics of rock, we processed the argillaceous shale from the weak interlayer into rock samples with a size of 150mm75mm75mm, and carried out shear creep tests under different impact energy disturbances with the self-developed rock impact-shear creep test system . We draw the following conclusions based on the test results:(1) The impact disturbance has a significant interference effect on the shear creep failure of soft rock. With the increase of the impact disturbance energy, the accelerated creep duration and the total creep failure time of the soft rock are shortened, and shear creep failure strength decreases. (2) The impact energy can affect the spread characteristics of the shear failure surface of rock samples. The impact disturbance energy destroys the rock sample structure, resulting in an increase in the number of shear cracks. (3) The total deformation of the rock sample is positively correlated with the impact energy. The total deformation of the rock sample is positively correlated with the impact energy. With the increase of impact energy, the proportion of plastic deformation is larger and the proportion of elastic deformation is smaller.After applying a disturbance of 7.09J impact energy, the ratio of plastic deformation to total deformation is not less than 73.1%.According to the test results, a damage factor D based on impact energy is introduced, and a shear creep damage model of soft rock considering the impact disturbance effect is established. The BFGS algorithm and the 1stOpt general global optimization mathematical software are used to identify the model parameters. It is found that the established model can better describe the whole process of shale creep deformation under impact disturbance. This paper provides a certain theoretical basis for the long-term stability research of mine slope under blasting disturbance effect.
		2022 Vol. 43 (5): 646-657 [Abstract] ( 111 ) HTML (1 KB) PDF (0 KB) ( 81 )

	658	Effect of cladding structure on low frequency vibration band gap of light phononic crystals

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2022.022
		A new design method of light phononic crystal cladding structure is proposed based on the local resonance mechanism. With the help of the finite element method, the energy band structure and eigenmodes of a new type of phononic crystal are calculated. When the total notch degree of the cladding is fixed, the influence of the number and location of different cladding notches on the cut-off frequency of the first complete band gap is analyzed. Two new phononic crystal models, line connection and point connection, are designed to connect the cladding and the scatterer, and the first complete band gap with an initial frequency of 37.4Hz and 19.0Hz are obtained respectively. The eigenmodes of scatterers at the initial frequency of the first complete band gap are analyzed, and the generation mechanism of the very low initial frequency of the first complete band gap of the new phononic crystal is revealed. Furthermore, it is compared with the traditional method of reducing the initial frequency of the first complete band gap by increasing the mass of the scatterer. The results show that when the total notch degree of the cladding is fixed, a wider first complete band gap can be obtained by using the cladding arrangement with more notches and farther away from the connecting short plate. The proposed cladding and scatterer line connected and point connected phononic crystals not only obtain a very low first complete band gap initial frequency, but also significantly reduce the phononic crystal weight, breaking through the limitation of traditional phononic crystals to reduce the first complete band gap initial frequency by increasing the scatterer mass, It provides a reference for the research and design of light phononic crystals to obtain very low local resonant band gap initial frequency.
		2022 Vol. 43 (5): 658-668 [Abstract] ( 99 ) HTML (1 KB) PDF (0 KB) ( 90 )

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