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2018 Vol. 39, No. 2 Published: 2018-04-28

	113	Nonlinear Buckling Mechanics of Film-Substrate Systems: Recent Progress

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2018.008
		The High residual compressive stress in thin film-substrate systems usually causes structural and functional failures via buckling instability. Surface instability, evolution and pattern formation in buckled films have become hot topics in the field of nonlinear mechanics. Such buckling instabilities depend on not only the mechanical properties of both the film and the substrate but also the interfacial properties between them, exhibiting multiple modes such as wrinkling, buckle-delamination, crease, etc. This paper briefly reviews the formation conditions of these buckling modes, their influencing factors and post-buckling morphologies. The first part focuses on the formations of one-dimensional wrinkling, wrinkle branching, anisotropic wrinkles, localized wrinkles and wrinkles on curved substrates. The second part introduces the formation and growth of one-dimensional buckle-delamination, telephone-cord buckles, and network-like blisters. The effects of substrate curvature, interface sliding and ridge cracking are also discussed. The final part introduces the formation mechanism and critical conditions of other advanced buckling modes such as crease, folding and ridge.
		2018 Vol. 39 (2): 113-138 [Abstract] ( 627 ) HTML (1 KB) PDF (0 KB) ( 314 )

	139	Mechanical Properties and Application of the Star-shaped Cellular Auxetic Material

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2017.015
		Auxetic material, which has a negative Poisson’s ratio, has been widely studied in recent decades. According to the existed research results, the mechanical properties of auxetic material are mainly determined by its micro structure. The star-shaped auxetic material structure shows outstanding advantages in vibration isolation and energy harvesting. Based on structural mechanics and plane geometry method, theoretical expressions for Poisson’s ratio, relative density and elastic modulus of the star-shaped structure are presented in this paper. The finite element models are built to verify the accuracy of the analytical expressions. While the numerical results of Poisson’s ratio and relative density are highly consistent with the theoretical predictions, the theoretical expression can only show the trend of the elastic modulus approximately. Then a vibration isolation marine base made of this auxetic structure is designed based on the analytical expressions and numerical simulation results of the star-shaped structure. Different Poisson’s ratios, layer numbers and cell thicknesses of the star-shaped structure are set to analyze its damping effect on the proposed Auxetic material, which has a negative Poisson’s ratio, has been widely studied in recent decades. According to the existed research results, the mechanical properties of auxetic material are mainly determined by its micro structure. The star-shaped auxetic material structure shows outstanding advantages in vibration isolation and energy harvesting. Based on structural mechanics and plane geometry method, theoretical expressions for Poisson’s ratio, relative density and elastic modulus of the star-shaped structure are presented in this paper. The finite element models are built to verify the accuracy of the analytical expressions. While the numerical results marine base. Mathematical modelling and numerical simulation show that Poisson’s ratio, layer number and cell thickness all make a significant difference in the dynamic response of the whole auxetic marine isolation system. The maximum von Mises stress and the vibration level difference are calculated to characterize the strength and the damping effects of the auxetic marine bases, respectively. According to the numerical analysis results, the optimized vibration isolation marine base with sound isolation performance and qualified static mechanical properties can be obtained by setting the Poisson’s ratio of the star-shaped structure as , and properly decreasing its layer number and cell thickness. The dynamic properties showing in the numerical simulations agree with the theoretical predictions of the elastic modulus as well. Therefore, these results should have an important significance in designing and optimizing the real star-shaped cellular auxetic vibration isolation marine bases.
		2018 Vol. 39 (2): 139-151 [Abstract] ( 508 ) HTML (1 KB) PDF (0 KB) ( 440 )

	152	An Efficient High-order Meshfree Method for Thin Plate Bending Analysis

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2017.027
		In comparison with the traditional finite element method, meshfree methods possess several appealing advantages such as the high-order smoothness of the nodal shape functions, the convenience to construct high-order approximation, etc. However, the nodal shape functions of high-order meshfree methods are non-polynomial rational functions, and this leads to the difficulty to accurately evaluate the domain integration of the weak form. The high-order Gauss integration commonly used in meshfree analysis requires a lot of integration points, and thus it is computationally inefficient. Besides, it is also not accurate enough. In this paper, a curvature smoothing scheme which is consistent to high-order (cubic) approximation is first proposed for the meshfree analysis of thin plate bending problems. Accordingly, a numerical integration scheme based on the curvature smoothing is developed for background triangular integration cells, and the number of quadrature points is dramatically reduced. The key of the developed method is that the second-order derivatives of nodal shape functions used in the computation of the stiffness matrix are obtained by using the divergence theorem among the shape functions, the first- and the second-order derivatives, instead of directly taking derivatives of nodal shape functions. Numerical results show that the high-order meshfree method based on the standard Gauss integration scheme is not accurate enough. It cannot reproduce the pure bending and linear bending modes exactly and leads to severe numerical oscillation in the resulting bending moment contours. The proposed high-order meshfree method based on consistent curvature smoothing technique is capable of efficiently and conveniently solving thin plate bending problems. Especially, it can exactly reproduce the pure bending and linear bending modes. Compared with the standard Gauss integration and the dominated constant curvature smoothing methods, the proposed method possesses remarkable superiorities in computational efficiency, accuracy and bending moment distributions, so it is recommended in meshfree analysis of thin plate bending.
		2018 Vol. 39 (2): 152-169 [Abstract] ( 253 ) HTML (1 KB) PDF (0 KB) ( 465 )

	162	Stick-slip Friction Model for Elastic-plastic Contact of Rough Surfaces

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2018.001
		A tangential stick-slip friction model for the contact of rough surfaces is proposed in this paper. The elastically- and plastically-deformed asperities are considered simultaneously to model the rough surfaces. For the elastically-deformed asperities, the classic solutions of the Hertz elastic contact model and the Mindlin micro-slip model are used to model the relation between load and deformation. For the plastically-deformed asperities, the fully-plastic contact theory of Abbott and Firestone, and the Fujimoto tangential contact model are implemented. The relation between tangential load and deformation of rough surfaces is formulated using the GW (Greenwood, J.A. and Williamson, J.B.P) probability statistics approach. The proposed model is compared with the model where only elastically-deformed asperities are considered. The effect of plastic index on the tangential behavior of rough surfaces is also investigated. A comparison of the results with the fully-elastic contact model shows that the proposed model can better describe the nonlinear relationship between the tangential load of contact and the deformation of rough surfaces. The model is more physically-based as a supplement to the plastic contact theory, with the consideration of the contribution of elastically-deformed and plastically-deformed asperities to the total tangential load of contact resulted from different contact forces. In the micro-slip regime, the tangential load is mainly affected by the elastic deformation; while within the macro-slip regime, the tangential behavior is mainly dominated by the plastic deformation. The total tangential load of rough surfaces is the resultant of the stick and slip contacts. With the increase of tangential deformation, the slip contact force increases to the critical macro-slip force, while the stick contact force increases first and then decreases to zero, which shows the evolutional process from the micro-slip regime to the macro-slip regime. With the increase of the plastic index, the relationship between tangential load and deformation is mainly controlled by the plastically-deformed asperities evolved from the elastically-deformed asperities. A tangential stick-slip friction model for the contact of rough surfaces is proposed in this paper. The elastically- and plastically-deformed asperities are considered simultaneously to model the rough surfaces. For the elastically-deformed asperities, the classic solutions of the Hertz elastic contact model and the Mindlin micro-slip model are used to model the relation between load and deformation. For the plastically-deformed asperities, the fully-plastic contact theory of Abbott and Firestone, and the Fujimoto tangential contact model are implemented. The relation between tangential load and deformation of rough surfaces is formulated using the GW (Greenwood, J.A. and Williamson, J.B.P) probability statistics approach. The proposed model is compared with the model where only elastically-deformed asperities are considered. The effect of plastic index on the tangential behavior of rough surfaces is also investigated. A comparison of the results with the fully-elastic contact model shows that the proposed model can better describe the nonlinear relationship between the tangential load of contact and the deformation of rough surfaces. The model is more physically-based as a supplement to the plastic contact theory, with the consideration of the contribution of elastically-deformed and plastically-deformed asperities to the total tangential load of contact resulted from different contact forces. In the micro-slip regime, the tangential load is mainly affected by the elastic deformation; while within the macro-slip regime, the tangential behavior is mainly dominated by the plastic deformation. The total tangential load of rough surfaces is the resultant of the stick and slip contacts. With the increase of tangential deformation, the slip contact force increases to the critical macro-slip force, while the stick contact force increases first and then decreases to zero, which shows the evolutional process from the micro-slip regime to the macro-slip regime. With the increase of the plastic index, the relationship between tangential load and deformation is mainly controlled by the plastically-deformed asperities evolved from the elastically-deformed asperities.
		2018 Vol. 39 (2): 162-169 [Abstract] ( 330 ) HTML (1 KB) PDF (0 KB) ( 405 )

	170	The Elucidation of Thickness Effect of Three-dimensional Fracture Toughness by Using the Finite Element Method

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2017.022
		Due to the extensive applications of metal structures with large thickness in character, the corresponding fracture toughness of structure is needed for the accurate assessment of structural failure. However, the dimension of cracked components along the direction of three-dimensional crack-tip line has significant impact on the fracture toughness of material, which is generally known as the “thickness effect”. The present research focuses on predicting the fracture toughness of material with arbitrary thickness by combining the finite element method (FEM) calculations with experimental data. First, the critical loads of a group of specimens of thin thickness at fracture are recorded by the three-point bending tests performed on single-edge notched beam SENB specimens. The critical energy release rate (ERR) of material is achieved by using the cohesive zone model (CZM) and virtual crack closure technique (VCCT). Second, the critical ERR is applied as a material constant in the FEM models. The maximum ERR criterion is applied to predict the critical load while crack initiates. The variations of several representative crack-tip fracture parameters (K, J-integral, T-stress and the out-of-plane constraint factor Tz) with respect to the thickness of specimen are calculated using the FEM, and the corresponding analysis is addressed subsequently. Finally, another three groups of X70 SEB specimens are tested to verify accuracy of the FEM results through comparison. The present work provides a reliable method to study the thickness effect on the fracture toughness of material, based on which, fracture toughness of metal material with arbitrary thickness can be predicted. Furthermore, the thickness and fracture toughness of material can be correlated through several three-point bending tests on thin SENB specimens, and the corresponding results can be depicted by a curve or mathematical expression. The present work will be beneficial to the reduction in experimental cost and structure integrity assessment.
		2018 Vol. 39 (2): 170-181 [Abstract] ( 352 ) HTML (1 KB) PDF (0 KB) ( 451 )

	182	The Statistic Tensile Strength and Failure Probability of Nb3Sn Strands under Considering Filament Fragmentation Characteristics

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2017.023
		Nb3Sn superconducting composite strands have wide applications high magnetic field engineering, their tensile strength is a key parameter to assure and access the safety of long-time service. Using the Curtin-Zhou model which is on the basis of the Weibull/Poisson statistics as well as the shear lag theory, the fragmentation of filament in composite strands can be well described, and an analytical model is proposed to obtain the statistic tensile strength and the failure probability. The computation results indicate that when the initial damage parameter is rising, the statistic tensile strength is dropping sharply; at the service temperature 4.2 K, when Weibull modulus is equal to 8, the tensile strength decays from 900MPa to about 480MPa, which coincides well with the experimental results; as the initial damage parameter is near 1, the normalized variance reaches to its maximum value. For Nb3Sn superconducting composite strands, the filament initial damage and Weibull modulus both have strong influence on their statistic tensile strength and failure probability.
		2018 Vol. 39 (2): 182-188 [Abstract] ( 206 ) HTML (1 KB) PDF (0 KB) ( 378 )

	189	Simulation of Boundary Conditions at a Wettable Solid Wall Based on the SPH Method

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2017.020
		Due to the special structure of surface and material properties, solid wall always shows adsorption of water at the interface, and this feature is particularly evident to small water droplets. Surface wettability is used to reflect the magnitude of adsorption force. A Lagrange wettable solid surface boundary condition is presented. It is assumed that the hydrophilia and capillary action of solid wall particles are unified as an adsorption force acting on the liquid particles of supported domains. The adsorption force is deemed relevant to fluid pressure, saturation and surface hydrophilia. To investigate the adsorption phenomenon, several interactions between single droplet and wettable solid surface are simulated by a stress-correction Smoothed Particle Hydrodynamics (SPH) model. First, deformation processes of static droplets on different wettable solid surfaces are simulated to rate the relationship between the droplet’s static contact angle and the wettability coefficient. Then, droplet impact on wettable solid surface is studied to investigate the influence of wettability on the deformation of droplet. Finally, the propagation of stress wave on solid surface during the deformation is analyzed. Droplet’s impacting movement is divided into four stages: collision, spreading, retraction and rebound. Research shows that: according to the changing characteristics of droplet’s static contact angle, the mentioned boundary condition can clearly reflect the wettability of solid surface. Simulation of droplet impact on wettable solid surface shows good agreement with the experimental result. During the rebound stage, a sufficiently large wettability will cause droplet to deform into liquid column. The pressure wave of solid surface propagates and decays along with the spreading and retraction of droplet. Only at the end of the rebound stage, when the droplet is about to detach from the solid surface, tension plays a leading role. For the rest of time, the solid surface is under pressure. The study has improved the theory of interaction between free surface fluid and solid surface, which provides a reference for further study on the effects of free surface fluid and granular materials.
		2018 Vol. 39 (2): 189-196 [Abstract] ( 378 ) HTML (1 KB) PDF (0 KB) ( 367 )

	197	Simulation of Boundary Conditions at a Wettable Solid Wall Based on the SPH Method

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2017.028
		Due to the special structure of surface and material properties, solid wall always shows adsorption of water at the interface, and this feature is particularly evident to small water droplets. Surface wettability is used to reflect the magnitude of adsorption force. A Lagrange wettable solid surface boundary condition is presented. It is assumed that the hydrophilia and capillary action of solid wall particles are unified as an adsorption force acting on the liquid particles of supported domains. The adsorption force is deemed relevant to fluid pressure, saturation and surface hydrophilia. To investigate the adsorption phenomenon, several interactions between single droplet and wettable solid surface are simulated by a stress-correction Smoothed Particle Hydrodynamics (SPH) model. First, deformation processes of static droplets on different wettable solid surfaces are simulated to rate the relationship between the droplet’s static contact angle and the wettability coefficient. Then, droplet impact on wettable solid surface is studied to investigate the influence of wettability on the deformation of droplet. Finally, the propagation of stress wave on solid surface during the deformation is analyzed. Droplet’s impacting movement is divided into four stages: collision, spreading, retraction and rebound. Research shows that: according to the changing characteristics of droplet’s static contact angle, the mentioned boundary condition can clearly reflect the wettability of solid surface. Simulation of droplet impact on wettable solid surface shows good agreement with the experimental result. During the rebound stage, a sufficiently large wettability will cause droplet to deform into liquid column. The pressure wave of solid surface propagates and decays along with the spreading and retraction of droplet. Only at the end of the rebound stage, when the droplet is about to detach from the solid surface, tension plays a leading role. For the rest of time, the solid surface is under pressure. The study has improved the theory of interaction between free surface fluid and solid surface, which provides a reference for further study on the effects of free surface fluid and granular materials.
		2018 Vol. 39 (2): 197-202 [Abstract] ( 303 ) HTML (1 KB) PDF (0 KB) ( 300 )

	203	Stability Analysis of an Axially Compressed Hyper-elastic Tube with Confined Boundary

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2017.021
		Seals play an important role in modern engineering applications, especially in the oil and gas industry. Compression of a rubber tube where the outer boundary is confined is an important procedure when sealing a packer. Instability leading to a buckling profile may cause the seal to fail. Generally speaking, the rubber tube (or packer) undergoes a relatively large deformation during the whole sealing procedure. In this paper, we study the bifurcations of a hyper-elastic tube with confined outer boundary in the framework of the exact theory of nonlinear elasticity. Due to the restriction, the initial deformed state is no longer homogeneous, the basic state of which is first characterized by solving the equilibrium equation. Then the incremental governing equations and boundary conditions are established for an axial mode and a linear bifurcation analysis is carried out. The bifurcation condition is numerically solved using the determinant method. Then the bifurcation curves are obtained when the geometric parameters are specified. It is found that the critical axial mode number is always finite. In addition, the relation between the critical bifurcation stretch (or stress) and wall thickness of the tube is obtained, from which it is found that a thin-walled tube is more stable compared with a thick-walled one. According to the relation between the axial stretch and stretch on the inner surface, our results may provide insight into designing the gap between the base pipe and the oil pipe in order to avoid instability. On the other hand, we provide the formulae of contact stress in terms of the applied axial stress for both boundaries when a seal is finished, which correct an existing result in literature and also validate the accuracy of results based on the theory of linear elasticity. Finally, the stability analysis for a packer designed by the CNOOC EnerTech-Drilling & Production Company is conducted and the lowest stress to achieve a full seal is given.
		2018 Vol. 39 (2): 203-212 [Abstract] ( 279 ) HTML (1 KB) PDF (0 KB) ( 385 )

	213	Local-level-set-based Algorithm Combined with Bi-directional Evolutionary Feature Used for Topology Optimization

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2017.019
		The PDE-based local level set method (LLSM) has higher computational efficiency than the conventional level set methods (LSMs) with global models. Nevertheless, the LLSM possesses no mechanism to nucleate new holes in the material domain for two-dimensional structures. A local-level-set-based algorithm is needed to be developed, with the ability of hole nucleation and bi-directional evolutionary features during topology optimization. A novel algorithm is proposed by combining the LLSM with the bi-directional evolutionary structural optimization (BESO) method. Two kinds of local level set models are constructed in this algorithm: one adopts the proposed discrete level set functions (DLSFs); the other chooses the local level set function (LLSF) of the LLSM. Firstly, a proposed bi-directional evolutionary algorithm using the DLSFs is implemented according to the optimization criteria of the BESO method until a stable topological solution is found. Then the LLSM is applied to further evolve the local details of topology and the shape of structure. The DLSFs are treated as nodal design variables in the bi-directional evolutionary algorithm. As nodal sensitivities, topological derivatives are taken instead of elemental sensitivities of the BESO method. The Shepard interpolation is selected in the sensitivity filtering to fit for the node-based variables and sensitivities. This algorithm transforms the final DLSFs into the initial LLSF by iteratively solving a distance-regularized equation (DRE). To increase computational efficiency of the LLSM, the DRE is included in the LLSM instead of the reinitialization equation. To eliminate the unnecessary diffusion effect, a new and balanced formulation of the diffusion term is introduced into the DRE. Despite that parts of the diffusion rates in the DRE are negative, a conditionally stable difference scheme under reverse diffusion constraints is formulated to ensure the numerical stability of DRE. Typical examples are used to demonstrate the effectiveness of the proposed algorithm, and the numerical results show higher convergence. The bi-directional evolutionary algorithm can not only nucleate new holes inside the design domain but also prevent multiple local minima of topology optimization. The LLSM is able to further improve the convergence to obtain at least one local optimal solution.
		2018 Vol. 39 (2): 213-222 [Abstract] ( 267 ) HTML (1 KB) PDF (0 KB) ( 364 )

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