Authors:Aizhong Lu; Ning Zhang; Guisen Zeng Abstract: Publication date: Available online 8 July 2017 Source:Acta Mechanica Solida Sinica Author(s): Aizhong Lu, Ning Zhang, Guisen Zeng When concentrated forces are applied at any points of the outer region of an ellipse in an infinite plate, the complex potentials are determined using the conformal mapping method and Cauchy's integral formula. And then, based on the superposition principle, the analytical solutions for stress around an elliptical hole in an infinite plate subjected to a uniform far-field stress and concentrated forces, are obtained. Tangential stress concentration will occur on the hole boundary when only far-field uniform loads are applied. When concentrated forces are applied in the reversed directions of the uniform loads, tangential stress concentration on the hole boundary can be released significantly. In order to minimize the tangential stress concentration, we need to determine the optimum positions and values of the concentrated forces. Three different optimization methods are applied to achieve this aim. The results show that the tangential stress can be released significantly when the optimized concentrated forces are applied.
Authors:M. Faraji Oskouie; R. Ansari; F. Sadeghi Abstract: Publication date: Available online 8 July 2017 Source:Acta Mechanica Solida Sinica Author(s): M. Faraji Oskouie, R. Ansari, F. Sadeghi The nonlinear vibrations of viscoelastic Euler-Bernoulli nanobeams are studied using the fractional calculus and the Gurtin-Murdoch theory. Employing Hamilton's principle, the governing equation considering surface effects is derived. The fractional integro-partial differential governing equation is first converted into a fractional ordinary differential equation in the time domain using the Galerkin scheme. Thereafter, the set of nonlinear fractional time-dependent equations expressed in a state-space form is solved using the predictor-corrector method. Finally, the effects of initial displacement, fractional derivative order, viscoelasticity coefficient, surface parameters and thickness-to-length ratio on the nonlinear time response of simply-supported and clamped-free silicon viscoelastic nanobeams are investigated.
Authors:A.K. Singh; A. Das; A. Lakshman; A. Negi; A. Chattopadhyay Abstract: Publication date: Available online 8 July 2017 Source:Acta Mechanica Solida Sinica Author(s): A.K. Singh, A. Das, A. Lakshman, A. Negi, A. Chattopadhyay The present article deals with the stresses developed in an initially stressed irregular viscoelastic half-space due to a load moving with a constant velocity at a rough free surface. Expressions for normal and shear stresses are obtained in closed form. The substantial effects of influence parameters, viz., depth (from the free surface), irregularity factor, maximum depth of irregularity, viscoelastic parameter, horizontal and vertical initial stresses, and frictional coefficient, on normal and shear stresses are investigated. Moreover, comparative study is carried out for three different cases of irregularity, viz., rectangular irregularity, parabolic irregularity and no irregularity, which is manifested through graphs.
Authors:A.M. Khludnev; T.S. Popova Abstract: Publication date: Available online 20 June 2017 Source:Acta Mechanica Solida Sinica Author(s): A.M. Khludnev, T.S. Popova The paper concerns an analysis of equilibrium problems for 2D elastic bodies with a thin Timoshenko inclusion crossing an external boundary at zero angle. The inclusion is assumed to be delaminated, thus forming a crack between the inclusion and the body. We consider elastic inclusions as well as rigid inclusions. To prevent a mutual penetration between the crack faces, inequality type boundary conditions are imposed at the crack faces. Theorems of existence and uniqueness are established. Passages to limits are investigated as a rigidity parameter of the elastic inclusion going to infinity.
Authors:Limei Xu; Hui Fan; Yufeng Zhou Abstract: Publication date: Available online 17 June 2017 Source:Acta Mechanica Solida Sinica Author(s): Limei Xu, Hui Fan, Yufeng Zhou In the present paper, we study the torsional wave propagation along a micro-tube with clogging attached to its inner surface. The clogging accumulated on the inner surface of the tube is modeled as an “elastic membrane” which is described by the so-called surface elasticity. A power-series solution is particularly developed for the lowest order of wave propagation. The dispersion diagram of the lowest-order wave is numerically presented with the surface (clogging) effect.
Authors:Guangyan Liu; Wei Zhu; Guangyan Huang Abstract: Publication date: Available online 15 June 2017 Source:Acta Mechanica Solida Sinica Author(s): Guangyan Liu, Wei Zhu, Guangyan Huang Two grades of Dyneema® composite laminates with the commercial designations of HB26 and HB50 were cut into blocks with or without an edge crack and compressed in the longitudinal fiber direction. The cracked and uncracked specimens show similar compressive responses including failure pattern and failure load. The two grades of Dyneema® composites exhibits different failure modes: a diffuse, sinusoidal buckling pattern for Dyneema® HB50 due to its weak matrix constituent and a kink band for Dyneema® HB26 due to its relatively stronger matrix constituent. An effective finite element model is used to simulate the collapse of Dyneema® composites, and the sensitivity of laminate compressive responses to the overall effective shear modulus, interlaminar shear strength, thickness and imperfection angle are investigated. The change of failure mode from kink band to sinusoidal buckling pattern by decreasing the interlaminar shear strength is validated by the finite element analyses.
Authors:Yuyang Lu; Yong Ni Abstract: Publication date: Available online 16 May 2017 Source:Acta Mechanica Solida Sinica Author(s): Yuyang Lu, Yong Ni Development of high-performance phase transformation electrodes in lithium ion batteries requires comprehensive studies on stress-mediated lithiation involving migration of the phase interface. It brings out many counter-intuitive phenomena, especially in nanoscale electrodes, such as the slowing down migration of phase interface, the vanishing of miscibility gap under high charge rate, and the formation of surface crack during lithiation. However, it is still a challenge to simulate the evolution of stress in arbitrarily-shaped nanoscale electrodes, accompanied with phase transformation and concurrent plastic deformation. This article gives a brief review of our efforts devoted to address these issues by developing phase field model and simulation. We demonstrate that the miscibility gap of two-phase state is affected not only by stress but also by surface reaction rate and particle size. In addition, the migration of phase interface slows down due to stress. It reveals that the plastic deformation generates large radial expansion, which is responsible for the transition from surface hoop compression to surface hoop tension that may induce surface crack during lithiation. We hope our effort can make a contribution to the understanding of stress-coupled kinetics in phase transformation electrodes.
Authors:Xiaojuan Jiao; Jianmin Ma Abstract: Publication date: Available online 11 May 2017 Source:Acta Mechanica Solida Sinica Author(s): Xiaojuan Jiao, Jianmin Ma The stress wave propagation law and dynamic buckling critical velocity are formulated and solved by considering a general axial connecting boundary for a slender elastic straight rod impacted by a rigid body. The influence of connecting stiffness on the critical velocity is investigated with varied impactor mass and buckling time. The influences of rod length and rod mass on the critical velocity are also discussed. It is found that greater connecting stiffness leads to larger stress amplitude, and further results in lower critical velocity. It is particularly noteworthy that when the connecting stiffness is less than a certain value, dynamic buckling only occurs before stress wave reflects off the connecting end. It is also shown that longer rod with larger slenderness ratio is easier to buckle, and the critical velocity for a larger-mass rod is higher than that for a lighter rod with the same geometry.
Authors:Yinfeng Li; Weiwei Zhang; Bill Guo; Dibakar Datta Abstract: Publication date: Available online 8 May 2017 Source:Acta Mechanica Solida Sinica Author(s): Yinfeng Li, Weiwei Zhang, Bill Guo, Dibakar Datta In this paper, the interlayer sliding between graphene and boron nitride (h-BN) is studied by molecular dynamics simulations. The interlayer shear force between h-BN/h-BN is found to be six times higher than that of Graphene/Graphene, while the interlayer shear between Graphene/h-BN is approximate to that of Graphene/Graphene. The Graphene/h-BN heterostructure shows several anomalous interlayer shear characteristics compared to its bilayer counterparts. For Graphene/Graphene and h-BN/h-BN, interlayer shears only exit along the sliding direction while interlayer shear for Graphene/h-BN is observed along both the translocation and perpendicular directions. Our results provide significant insight into the interlayer shear characteristics of 2D nanomaterials.
Authors:Senbo Xiao; Jianying He; Zhiliang Zhang Abstract: Publication date: Available online 6 May 2017 Source:Acta Mechanica Solida Sinica Author(s): Senbo Xiao, Jianying He, Zhiliang Zhang Anti-icing is crucial for numerous instruments and devices in low temperature circumstance. One of the approaches in anti-icing is to reduce ice adhesion strength, seeking spontaneous de-icing processes by natural forces of gravity or by winds. In order to enable tailored surface icephobicity design, research requires a good theoretical understanding of the atomistic interacting mechanisms between water/ice molecules and their adhering substrates. Herein, this work focuses on using atomistic modeling and molecular dynamics simulation to build a nanosized ice-cube adhering onto silicon surface, with different contact modes of solid-solid and solid-liquid-solid patterns. This study provides atomistic models for probing nanoscale ice adhesion mechanics and theoretical platforms for explaining experimental results.
Authors:Jin-Wu Jiang Abstract: Publication date: Available online 5 May 2017 Source:Acta Mechanica Solida Sinica Author(s): Jin-Wu Jiang The single-layer black phosphorus is characterized by its puckered configuration that possesses the hinge-like behavior, which leads to the highly anisotropic in-plane Poisson's ratios and the negative out-of-plane Poisson's ratio. We demonstrate that the hinge-like mechanism can be described by the angle-angle cross interaction, which, combined with the bond stretching and angle bending interactions, is able to provide a good description for the mechanical properties of single-layer black phosphorus. We also propose a nonlinear angle-angle cross interaction, which follows the form of Stillinger-Weber potential and can be advantageous for molecular dynamics simulations of single-layer black phosphorus under large deformation.
Authors:Feng Zhu; Yuxing Zhang; Bin Wang; Zhenghua Qian Abstract: Publication date: Available online 27 April 2017 Source:Acta Mechanica Solida Sinica Author(s): Feng Zhu, Yuxing Zhang, Bin Wang, Zhenghua Qian Wave propagation in a piezoelectric layered structure of a film bulk acoustic resonator (FBAR) is studied. The accurate results of dispersion relation are calculated using the proposed elastic electrode model for both electroded and unelectroded layered plates. The differences of calculated cut-off frequencies between the current elastic electrode model and the simplified inertial electrode model (often used in the quartz resonator analysis) are illustrated in detail, which shows that an elastic electrode model is indeed needed for the accurate analysis of FBAR. These results can be used as an accurate criterion to calibrate the 2-D theoretical model for a real finite-size structure of FBAR.
Authors:Jiuling Wang; Xinghua Shi Abstract: Publication date: Available online 6 April 2017 Source:Acta Mechanica Solida Sinica Author(s): Jiuling Wang, Xinghua Shi The rapid diffusion of nanoparticles (NPs) through mucus layer is critical for efficient transportation of NPs-loaded drug delivery system. To understand how the physical and surface properties of NPs affect their diffusion in mucus, we have developed a coarse-grained molecular dynamics model to study the diffusion of NPs in modeled mucus layer. Both steric obstruction and hydrodynamic interaction are included in the model capable of capturing the key characteristics of NPs’ diffusion in mucus. The results show that both particle size and surface properties significantly affect the diffusivities of NPs in mucus. Furthermore, we find rodlike NPs can gain a higher diffusivity than spherical NPs with the same hydrodynamic diameter. In addition, the disturbed environment can enhance the diffusivity of NPs. Our findings can be utilized to design mucus penetrating NPs for targeted drug delivery system.
Authors:Jiuling Wang; Xinghua Shi Abstract: Publication date: Available online 6 April 2017 Source:Acta Mechanica Solida Sinica Author(s): Jiuling Wang, Xinghua Shi The rapid diffusion of nanoparticles (NPs) through mucus layer is critical for efficient transportation of NPs-loaded drug delivery system. To understand how the physical and surface properties of NPs affect their diffusion in mucus, we have developed a coarse-grained molecular dynamics model to study the diffusion of NPs in modeled mucus layer. Both steric obstruction and hydrodynamic interaction are included in the model capable of capturing the key characteristics of NPs’ diffusion in mucus. The results show that both particle size and surface properties significantly affect the diffusivities of NPs in mucus. Furthermore, we find rodlike NPs can gain a higher diffusivity than spherical NPs with the same hydrodynamic diameter. In addition, the disturbed environment can enhance the diffusivity of NPs. Our findings can be utilized to design mucus penetrating NPs for targeted drug delivery system.
Authors:Cheng Chang; Xiaoyan Li; Zhiping Xu; Huajian Gao Abstract: Publication date: Available online 31 March 2017 Source:Acta Mechanica Solida Sinica Author(s): Cheng Chang, Xiaoyan Li, Zhiping Xu, Huajian Gao The application of silicon as ultrahigh capacity electrodes in lithium-ion batteries has been limited by a number of mechanical degradation mechanisms including fracture, delamination and plastic ratcheting, as a result of its large volumetric change during lithiation and delithiation. Graphene coating is one feasible technique to mitigate the mechanical degradation of Si anode and improve its conductivity. In this paper, first-principles calculations are performed to study the atomic structure, charge transfer and sliding strength of the interface between lithiated silicon and graphene. Our results show that Li atoms segregate at the (lithiated) Si-graphene interface preferentially, donating electrons to graphene and enhancing the interfacial sliding resistance. Moreover, the interfacial cohesion and sliding strength can be further enhanced by introducing single-vacancy defects into graphene. These findings provide insights that can guide the design of stable and efficient anodes of silicon/graphene hybrids for energy storage applications.
Authors:A-Li Chen; Li-Zhi Tian; Yue-Sheng Wang Abstract: Publication date: Available online 22 March 2017 Source:Acta Mechanica Solida Sinica Author(s): A-Li Chen, Li-Zhi Tian, Yue-Sheng Wang The localization factor is used to describe the band structures for P wave propagating normally in the nanoscaled nearly periodic layered phononic crystals. The localization factor is calculated by the transfer matrix method based on the nonlocal elastic continuum theory. Three kinds of nearly periodic arrangements are concerned, i.e., random disorder, quasi-periodicity and defects. The influences of randomly disordered degree of the sub-layer's thickness and mass density, the arrangement of quasi-periodicity and the location of defect on the band structures and cut-off frequency are analyzed in detail.
Authors:Huyi Wang; Wenjun Hu; Fengpeng Zhao Abstract: Publication date: Available online 22 March 2017 Source:Acta Mechanica Solida Sinica Author(s): Huyi Wang, Wenjun Hu, Fengpeng Zhao A complex rubber foam under quasi-static compression is simulated using the finite element method (FEM). The present work sets up the phenomenological constitutive model for the silicon rubber. The computerized tomography (CT) technique is utilized to reconstruct the real complex foam geometries. The quasi-static uniaxial compression on the foam is simulated in ABAQUS. The present work obtains the stress response as the nominal strain nearly reaches 80% and the foam exhibits hyper-elastic behavior. The FEM results achieve good agreements with the data obtained from the multi-scale simulation and the tests as the nominal strain is less than 60%.
Authors:Wei Shen; Renjun Yan; Nigel Barltrop; Kai Qin; Feng He Abstract: Publication date: Available online 22 March 2017 Source:Acta Mechanica Solida Sinica Author(s): Wei Shen, Renjun Yan, Nigel Barltrop, Kai Qin, Feng He In the as-welded condition the fatigue crack initiation period was considered non-existent and Linear Elastic Fracture Mechanics (LEFM) was used to calculate fatigue strength for a range of weld geometries. Fracture mechanics assessment of welded joints requires accurate solutions for stress intensity factor (SIF). However, the solutions for the SIF of complex welded joints are difficult to determine due to the complicated correction factors. Three methods for SIF prediction are discussed on fillet welded specimens containing continuous or semi-elliptical surface cracks, including the traditional correction method Mk , the approximate correction method Kt , and the suggested additional crack size method (ac+ae). The new additional crack parameter ae is used to replace the stress concentration effect of weld profile Mk , which simplifies the calculation process. Experimental results are collected to support fatigue strength assessment of the additional crack size method.
Authors:Yadong Zhou; Xiaochen Hang; Shaoqing Wu; Qingguo Fei; Natasa Trisovic Abstract: Publication date: Available online 22 March 2017 Source:Acta Mechanica Solida Sinica Author(s): Yadong Zhou, Xiaochen Hang, Shaoqing Wu, Qingguo Fei, Natasa Trisovic The panel-type structures used in aerospace engineering can be subjected to severe high-frequency acoustic loadings in service. This paper evaluates the frequency-dependent random fatigue of panel-type structures made of ceramic matrix composites (CMCs) under acoustic loadings. Firstly, the high-frequency random responses from the broadband random excitation will result in more stress cycles in a definite period of time. The probability density distributions of stress amplitudes will be different in different frequency bandwidths, though the peak stress estimations are identical. Secondly, the fatigue properties of CMCs can be highly frequency-dependent. The fatigue evaluation method for the random vibration case is adopted to evaluate the fatigue damage of a representative stiffened panel structure. The frequency effect through S-N curves on random fatigue damage is numerically verified. Finally, a parameter is demonstrated to characterize the mean vibration frequency of a random process, and hence this parameter can further be considered as a reasonable loading frequency in the fatigue tests of CMCs to obtain more reliable S-N curves. Therefore, the influence of vibration frequency can be incorporated in the random fatigue model from the two perspectives.
Authors:Veniamin D. Kubenko; Ihor V. Yanchevskyi Abstract: Publication date: Available online 22 March 2017 Source:Acta Mechanica Solida Sinica Author(s): Veniamin D. Kubenko, Ihor V. Yanchevskyi A numerical-analytical approach is described to investigate the process of impact interaction between a long smooth rigid body and the surface of a circular cylindrical cavity in elastic space. A non-stationary mixed initial boundary value problem is formulated with a priori unknown boundaries moving with variable velocity. The problem is solved using the methods of the theory of integral transforms, expansion of desired variables into a Fourier series, and the quadrature method to reduce the problem to solving a system of linear algebraic equations at each time step. Some concrete numerical computations are presented. The cylindrical body mass and radius impact on the profile of the transient process of contact interaction has been analysed.
Authors:Changda Wang; Xuejun Chen; Peijun Wei; Yueqiu Li Abstract: Publication date: Available online 22 March 2017 Source:Acta Mechanica Solida Sinica Author(s): Changda Wang, Xuejun Chen, Peijun Wei, Yueqiu Li The reflection elastic waves at the elastically supported boundary of a couple stress elastic half-space are studied in this paper. Different from the classical elastic solid, there are three kinds of elastic waves in the couple stress elastic solid, and two of them are dispersive. The boundary conditions of a couple stress elastic half-space include the couple stress vector and the rotation vector which disappear in the classical elastic solids. These boundary conditions are used to obtain a linear algebraic equation set, from which the amplitude ratios of reflection waves to the incident wave can be determined. Then, the reflection coefficients in terms of energy flux ratios are calculated numerically, and the normal energy flux conservation is used to validate the numerical results. Based on these numerical results, the influences of the boundary parameters, which reflect the mechanical behavior of elastic support, on the reflection energy partition are discussed. Both the incident longitudinal wave (the P wave) and incident transverse wave (the SV wave) are considered.
Authors:Liang Wang; Qunfeng Liu; Wenshan Yu; Shengping Shen Abstract: Publication date: Available online 22 March 2017 Source:Acta Mechanica Solida Sinica Author(s): Liang Wang, Qunfeng Liu, Wenshan Yu, Shengping Shen The shear responses of β-SiC are investigated using molecular dynamics simulation with the Tersoff interatomic potential. Results show a clear decreasing trend in critical stress, fracture strain and shear modulus as temperature increases. Above a critical temperature, β-SiC bulk just fractures after the elastic deformation. However, below the critical temperature, an interesting pattern in β-SiC bulk emerges due to the elongation of Si-C bonds before fracture. Additionally, the shear deformation of β-SiC at room temperature is found to be dependent on the strain rate. This study may shed light on the deformation mechanism dependent on temperature and strain rate.
Authors:Lin Pang; Gao Lin; Zhiqiang Hu Abstract: Publication date: Available online 22 March 2017 Source:Acta Mechanica Solida Sinica Author(s): Lin Pang, Gao Lin, Zhiqiang Hu A refined global-local approach based on the scaled boundary finite element method (SBFEM) is proposed to improve the accuracy of predicted singular stress field. The proposed approach is carried out in conjunction with two steps. First, the entire structure is analyzed by employing an arbitrary numerical method. Then, the interested region, which contains stress singularity, is re-solved using the SBFEM by placing the scaling center right at the singular stress point with the boundary conditions evaluated from the first step imposed along the whole boundary including the side-faces. Benefiting from the semi-analytical nature of the SBFEM, the singular stress field can be predicted accurately without highly refined meshes. It provides the FEM or other numerical methods with a rather simple and convenient way to improve the accuracy of stress analysis. Numerical examples validate the effectiveness of the proposed approach in dealing with various kinds of problems.
Authors:Jiangyi Chen; Junhong Guo Abstract: Publication date: Available online 22 March 2017 Source:Acta Mechanica Solida Sinica Author(s): Jiangyi Chen, Junhong Guo A cylindrical system of vector functions, the stiffness matrix method and the corresponding recursive algorithm are proposed to investigate the static response of transversely isotropic, layered magneto-electro-elastic (MEE) structures over a homogeneous half-space substrate subjected to circular surface loading. In terms of the system of vector functions, we expand the extended displacement and stresses, and deduce two sets of ordinary differential equations, which are related to the expansion coefficients. The solution to one of the two sets of these ordinary differential equations can be evaluated by using the stiffness matrix method and the corresponding recursive algorithm. These expansion coefficients are then integrated by adaptive Gaussian quadrature to obtain the displacements and stresses in the physical domain. Two types of surface loads, mechanical pressure and electric loading, are considered in the numerical examples. The calculated results show that the proposed technique is stable and effective in analyzing the layered half-space MEE structures under surface loading.
Authors:Zhizhong Yan; Yangyang Wang; Chuanzeng Zhang Abstract: Publication date: Available online 22 March 2017 Source:Acta Mechanica Solida Sinica Author(s): Zhizhong Yan, Yangyang Wang, Chuanzeng Zhang The localization characteristics of the in-plane elastic waves in locally resonant aperiodic phononic crystals are examined in this study. In particular, the phononic crystals generated according to the Thue-Morse, Rudin-Shapiro and Period-Doubling sequences are theoretically investigated by using the extended transfer matrix method. For comparison, the binary and ternary locally resonant systems are considered, and their band structures are characterized by using the localization factors. Moreover, the influences of structural arrangement, material combination, incidence angle, number of components, length ratio, and random disorder on the band structures are also discussed. Some novel and interesting phenomena are observed and discussed.
Authors:Tengwu He; Wanshen Xiao; Xiangdong Li; Yan Zhang Abstract: Publication date: Available online 16 February 2017 Source:Acta Mechanica Solida Sinica Author(s): Tengwu He, Wanshen Xiao, Xiangdong Li, Yan Zhang The problem of a screw dislocation interacting with a circular nano-inhomogeneity near a bimaterial interface is investigated. The stress boundary condition at the interface between the inhomogeneity and the matrix is modified by incorporating surface/interface stress. The analytical solutions to the problem in explicit series are obtained by an efficient complex variable method associated with the conformal mapping function. The image force exerted on the screw dislocation is also derived using the generalized Peach-Koehler formula. The results indicate that the elastic interference of the screw dislocation and the nano-inhomogeneity is strongly affected by a combination of material elastic dissimilarity, the radius of the inclusion, the distance from the center of inclusion to the bimaterial interface, and the surface/interface stress between the inclusion and the matrix. Additionally, it is found that when the inclusion and Material 3 are both harder than the matrix (μ1 > μ2 and μ3 > μ2), a new stable equilibrium position for the screw dislocation in the matrix appears near the bimaterial interface; when the inclusion and Material 3 are both softer than the matrix (μ1 < μ2 and μ3 < μ2), a new unstable equilibrium position exists close to the bimaterial interface.
Authors:Yu Xiang; Honghua Jiang; Jing Lu Abstract: Publication date: Available online 16 February 2017 Source:Acta Mechanica Solida Sinica Author(s): Yu Xiang, Honghua Jiang, Jing Lu Based on the classical theory of thin plate and Biot theory, a precise model of the transverse vibrations of a thin rectangular porous plate is proposed. The first order differential equations of the porous plate are derived in the frequency domain. By considering the coupling effect between the solid phase and the fluid phase and without any hypothesis for the fluid displacement, the model presented here is rigorous and close to the real materials. Owing to the use of extended homogeneous capacity precision integration method and precise element method, the model can be applied in higher frequency range than pure numerical methods. This model also easily adapts to various boundary conditions. Numerical results are given for two different porous plates under different excitations and boundary conditions.
Authors:S. Sahmani; M.M. Aghdam; M. Bahrami Abstract: Publication date: Available online 13 February 2017 Source:Acta Mechanica Solida Sinica Author(s): S. Sahmani, M.M. Aghdam, M. Bahrami The objective of the present investigation is to predict the nonlinear buckling and postbuckling characteristics of cylindrical shear deformable nanoshells with and without initial imperfection under hydrostatic pressure load in the presence of surface free energy effects. To this end, Gurtin-Murdoch elasticity theory is implemented into the first-order shear deformation shell theory to develop a size-dependent shell model which has an excellent capability to take surface free energy effects into account. A linear variation through the shell thickness is assumed for the normal stress component of the bulk to satisfy the equilibrium conditions on the surfaces of nanoshell. On the basis of variational approach and using von Karman-Donnell-type of kinematic nonlinearity, the non-classical governing differential equations are derived. Then a boundary layer theory of shell buckling is employed incorporating the effects of surface free energy in conjunction with nonlinear prebuckling deformations, large deflections in the postbuckling domain and initial geometric imperfection. Finally, an efficient solution methodology based on a two-stepped singular perturbation technique is put to use in order to obtain the critical buckling loads and postbuckling equilibrium paths corresponding to various geometric parameters. It is demonstrated that the surface free energy effects cause increases in both the critical buckling pressure and critical end-shortening of a nanoshell made of Silicon.
Authors:Q.F. Lü; M.L. Deng; W.Q. Zhu Abstract: Publication date: Available online 10 February 2017 Source:Acta Mechanica Solida Sinica Author(s): Q.F. Lü, M.L. Deng, W.Q. Zhu A stochastic averaging method of quasi integrable and resonant Hamiltonian systems under excitation of fractional Gaussian noise (fGn) with the Hurst index 1/2 < H < 1 is proposed. First, the definition and the basic property of fGn and related fractional Brownian motion (fBm) are briefly introduced. Then, the averaged fractional stochastic differential equations (SDEs) for the first integrals and combinations of angle variables of the associated Hamiltonian systems are derived. The stationary probability density and statistics of the original systems are then obtained approximately by simulating the averaged SDEs numerically. An example is worked out to illustrate the proposed stochastic averaging method. It is shown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of original system agree well.
Authors:Jianlin Chen; Zheng Li; Kezhuang Gong Abstract: Publication date: Available online 10 February 2017 Source:Acta Mechanica Solida Sinica Author(s): Jianlin Chen, Zheng Li, Kezhuang Gong Based on Lamb wave analysis of propagation in plate-like structures, a damage detection method is proposed that not only locates the position of the damage accurately but also estimates its size. Similar damage detection methods focus only on localization giving no quantitative estimation of extent. To improve detection, we propose two predictive circle methods for size estimation. Numerical simulations and experiments were performed for an aluminum plate with a hole. Two PZT configurations of different sizes were designed to excite and detect Lamb waves. From cross-correlation analysis, the damage location and extent can be determined. Results obtained using the proposed method enable a better quantitative resolution in detection, and the size of the inspection area influences the accuracy of damage identification. The closer to the damage, the more accurate the results are. The method proposed can be developed into a multiple-step detection method for multi-scale analysis with prospective accuracy.
Authors:He Dan; Yang Wanli; Chen Wanji Abstract: Publication date: Available online 10 February 2017 Source:Acta Mechanica Solida Sinica Author(s): He Dan, Yang Wanli, Chen Wanji In this study, a size-dependent composite laminated skew Mindlin plate model is proposed based on a new modified couple stress theory. This plate model can be viewed as a simplified couple stress theory in engineering mechanics. Governing equations and related boundary conditions are derived based on the principle of minimum potential energy. The Rayleigh–Ritz method is employed to obtain the numerical solutions of the center deflections of simply supported plates with different ply orientations. Numerical results show that the normalized center deflections obtained by the proposed model are always smaller than those obtained by the classical one, i.e. the present model can capture the scale effects of microstructures. Moreover, a phenomenon is revealed that the ply orientation would make a significant influence on the magnitude of scale effects of composite laminated plates at micro scale. Additionally, the present model of thick skew plate can be degenerated to the model of Kirchhoff plate based on the modified couple stress theory by adopting the assumptions in Bernoulli-Euler beam and material isotropy.
Authors:Farzad Ebrahimi; S.H.S. Hosseini Abstract: Publication date: Available online 10 February 2017 Source:Acta Mechanica Solida Sinica Author(s): Farzad Ebrahimi, S.H.S. Hosseini This paper deals with the study of the temperature effect on the nonlinear vibration behavior of nanoplate-based nano electromechanical systems (NEMS) subjected to hydrostatic and electrostatic actuations. Using Eringen's nonlocal elasticity and Gurtin–Murdoch theory, the nonlocal plate model is derived through Hamilton's principle. The governing equation which is extremely nonlinear due to the geometrical nonlinearity and electrostatic attraction forces is solved numerically using the differential quadrature method (DQM). The accuracy of the present method is verified by comparing the obtained results with the experimental data and those in the literature and very good agreement is obtained. Finally a comprehensive study is carried out to determine the influence of temperature on the nonlinear vibration characteristics of NEMS have made of two different materials including aluminum (Al) and silicon (Si) and some conclusions are drawn.
Authors:Qiao Wang; Wei Zhou; Yonggang Cheng; Gang Ma; Xiaolin Chang; Qiang Huang Abstract: Publication date: Available online 10 February 2017 Source:Acta Mechanica Solida Sinica Author(s): Qiao Wang, Wei Zhou, Yonggang Cheng, Gang Ma, Xiaolin Chang, Qiang Huang An adaptive cell-based domain integration method (CDIM) is proposed for the treatment of domain integrals in 3D boundary element method (BEM). The domain integrals are computed in background cells rather than volume elements. The cells are created from the boundary elements based on an adaptive oct-tree structure and no other discretization is needed. Cells containing the boundary elements are subdivided into smaller sub-cells adaptively according to the sizes and levels of the boundary elements; and the sub-cells outside the domain are deleted to obtain the desired accuracy. The method is applied in the 3D potential and elasticity problems in this paper.
Authors:Jacques Luk-Cyr; Daniel Paquet; Jacques Lanteigne; Henri Champliaud; Aurelian Vadean Abstract: Publication date: Available online 9 February 2017 Source:Acta Mechanica Solida Sinica Author(s): Jacques Luk-Cyr, Daniel Paquet, Jacques Lanteigne, Henri Champliaud, Aurelian Vadean In this paper, a novel unified plasticity methodology is proposed to allow the coupling of rate- and temperature-sensitivity of engineering alloys as well as the non-linear kinematic hardening behaviour often observed during cyclic loading. The proposed methodology is general in the sense that an arbitrary constitutive model may be chosen for the viscoplastic part, as well as the cyclic part. We adapt our model with a physically-motivated viscoplasticity flow rule and a nonlinear kinematic hardening model. In contrast with other unified plasticity models, the simplified theory involves few material parameters that can be readily calibrated from standard mechanical tests. The capabilities of the proposed theory are demonstrated for a hot rolled annealed 304L stainless steel supplied by VI-Metal Peckover. The model is tested with stress-strain curves obtained from standard tensile and cyclic uniaxial tests at various strain amplitudes and strain-rates, and good accuracy of the response is obtained for strains up to 15%, within a temperature range of 293 − 673 K. We note that the cyclic plasticity model in our adapted theory can be readily enhanced with ratchetting, mean stress relaxation, strain amplitude history, Masing effects or other complex capabilities.
Authors:Jiashi Yang Abstract: Publication date: Available online 9 February 2017 Source:Acta Mechanica Solida Sinica Author(s): Jiashi Yang This paper presents a derivation of the equations of linear momentum, angular momentum, and energy of an electroelastic body using a composite particle consisting of two differential elements based on Tiersten's two-continuum model. The differential derivation shows the physics involved in a way different from the integral approach in the literature. Like the integral approach, it also produces the expressions of the electric body force, couple, and power which are fundamental to the development of the nonlinear macroscopic theory of an electroelastic body.
Authors:Y.P. Chen; Y.Y. Cai Abstract: Publication date: Available online 9 February 2017 Source:Acta Mechanica Solida Sinica Author(s): Y.P. Chen, Y.Y. Cai A semi-implicit elastic/crystalline viscoplastic finite element (FE) method based on a “crystallographic homogenization” approach is formulated for a multi-scale analysis. In the formulation, the asymptotic series expansion is introduced to define the displacement in the micro-continuum. This homogenization FE analysis is aimed at predicting the plastic deformation induced texture evolution of polycrystalline materials, the constituent microstructure of which is represented by an assembly of single crystal grains. The rate dependent crystal plasticity model is adopted for the description of microstructures. Their displacements are decomposed into two parts: the homogenized deformation defined in the macro-continuum and the perturbed one in the micro-continuum. This multi-scale formulation makes it possible to carry out an alternative transition from a representative micro-structure to the macro-continuum. This homogenization procedure satisfies both the compatibility and the equilibrium in the micro-structure. This developed code is applied to predict the texture evolution, and its performance is demonstrated by the numerical examples of texture evolution of FCC polycrystalline metals.
Authors:Zhaoling Wang; Hao Li; Zhengnan Yin; Heng Xiao Abstract: Publication date: Available online 9 February 2017 Source:Acta Mechanica Solida Sinica Author(s): Zhaoling Wang, Hao Li, Zhengnan Yin, Heng Xiao The objective of this study is two-fold. Firstly, new finite strain elastoplasticity models are proposed from a fresh standpoint to achieve a comprehensive representation of thermomechanical behavior of metals and alloys over the whole deformation range up to failure. As contrasted with the usual elastoplasticity models, such new models of much simpler structure are totally free, in the sense that both the yield condition and the loading-unloading conditions need not be introduced as extrinsic coercive conditions but are automatically incorporated as inherent constitutive features into the models. Furthermore, the new models are shown to be thermodynamically consistent, in a further sense that both the specific entropy function and the Helmholtz free energy function may be presented in explicit forms, such that the thermodynamic restriction stipulated by Clausius-Duhem inequality for the intrinsic dissipation may be identically satisfied. Secondly, it is then demonstrated that the thermo-coupled fatigue failure behavior under combined cyclic changes of stress and temperature may be derived as direct consequences from the new models. This novel result implies that the new model can directly characterize the thermo-coupled fatigue failure behavior of metals and alloys, without involving any usual damage-like variables as well as any ad hoc additional criteria for failure. In particular, numerical examples show that, under cyclic changes of temperature, the fatigue characteristic curve of fatigue life versus temperature amplitude may be obtained for the first time from model prediction both in the absence and in the presence of stress. Results are in agreement with the salient features of metal fatigue failure.
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