An energy-equilibrium model for complex stress effect on fatigue crack initiation

Based on Tanaka and Mura’s fatigue model and Griffith theory for fracture,an energy-equilibrium model was proposed to explain the complex stress effect on fatigue behavior.When the summation of the elastic strain energy release and the stored strain energy of accumulated dislocations reach the surface energy of a crack,the fatigue crack will initiate in materials.According to this model,for multiaxial stress condition,the orientation of the crack initiation and the initiation life can be deduced from the energy equilibrium equation.For the uniaxial fatigue loading with mean stress,the relation between the maximum stress or the minimum stress and the stress amplitude is in agreement with an ellipse equation on the constant life diagram.If the ratio of the mean stress to stress amplitude is less than a critical value-0.17,and the stress amplitude keeps constant,the fatigue crack initiation life will decrease with the increase of the compress mean stress.In this model,the mean stress does not cause damage accumulation with the fatigue cycles in crack initiation.For this reason,the loading sequence of different load levels would induce the cumulative damage to deviate from the Palmgren-Miner cumulative damage rule.The procedure of estimating the damage under random loading is also discussed.     

A one-dimensional continuous model for carbon nanotubes

The two-dimensional (2D) continuous elastic energy model for isotropic tubes is reduced to a one-dimensional (1D) curvature elastic energy model strictly. This 1D model is in accordance with the Kirchhoff elastic rod theory. Neglecting the in-plane strain energy in this model, it is suitable to investigate the nature features of carbon nanotubes (CNTs) with large deformations and can also reduce to the string model in [Z.C. Ou-Yang et al., Phys. Rev. Lett. 76, 4055 (1997)] when the deformation is small enough. For straight chiral shapes, this general model indicates that the difference of the chiral angle between two equilibrium states is about π/6, which is consistent with the lattice model. It also reveals that the helical shape has lower energy for per atom than the straight shape has in the same condition. By solving the corresponding equilibrium shape equations, the helical tube solution is in good agreement with the experimental result, and super helical shapes are obtained and we hope they can be found in future experiments.     

Closed-form CRLB and LPI power allocation strategies for MIMO radars with unneglectable clutter

This paper studies clutter’s effect on MIMO radar performance through obtaining closed-form Cramer Rao lower bounds (CRLBs) for the range and velocity parameters versus the powers assigned to the transmit antennas which resulted in more calculation’ complexity. To verify extracted CRLBs, the maximum likelihood estimation’s error variance (MLEEV) of range and velocity were derived in attendance of clutter. Based on obtained closed-form CRLBs, four optimized power allocation (PA) strategies are proposed which consider measurement error statistics as the objective function or constraints to improve radar performance. So, the calculated closed-form CRLBs are simplified to the closed-forms versus assigned powers to the transmitters. Simulation results verify the proposed CRLBs’ accuracy, and improvements have been made by proposed power allocations.     

A nonlinear magneto-thermo-elastic coupled hysteretic constitutive model for magnetostrictive alloys

This paper presents a general hysteretic constitutive law of nonlinear magneto-thermo-elastic coupling for magnetostrictive alloys. The model considered here is thermodynamically motivated and based on the Gibbs free energy function. A nonlinear part of the elastic strain arising from magnetic domain rotation induced by the pre-stress is taken into account. Furthermore, the movement of the domain walls is incorporated to describe hysteresis based on Jiles–Atherton's model. Then a set of closed and analytical expressions of the constitutive law for the magnetostrictive rods and films are obtained, and the parameters appearing in the model can be determined by those measurable experiments in mechanics and physics. Comparing this model with other existing models in this field, the quantitative results show that the relationships obtained here are more effective to describe the effects of the pre-stress or in-plane residual stress and ambient temperature on the magnetization or the magnetostriction hysteresis loops.     

Effects of carbon nanotube structures on mechanical properties

This paper describes a structural mechanics approach to modelling the mechanical properties of carbon nanotubes (CNTs). Based on a model of truss structures linked by inter-atomic potentials, a closed-form elastic solution is obtained to predict the mechanical properties of single-walled carbon nanotubes (SWNTs). Moreover, the elastic modulus of multi-walled carbon nanotubes (MWNTs) is also predicted for a group of the above mentioned SWNTs with uniform interval spacing. Following the structural mechanics approach, the elastic modulus, Poissons ratio, and the deformation behaviors of SWNTs were investigated as a function of the nanotube size and structure. Poissons ratio of SWNTs shows a chirality dependence, while the elastic modulus is insensitive to the chirality. The disposition of the strain energy of bonds shows quite a difference between the zigzag and armchair tubes subjected to axial loading. A zigzag tube is predicted to have a lower elongation property than an armchair tube. PACS 62.20-x; 62.20.Dc; 62.25+g     

石墨烯/柔性基底复合结构双向界面切应力传递问题的理论研究

界面力学性能是影响石墨烯/柔性基底复合结构整体力学性能的关键因素,因此对该结构界面切应力传递机理的研究十分必要.考虑了石墨烯和基底泊松效应的影响,本文提出了二维非线性剪滞模型.对于基底泊松比相比石墨烯较大的情况,利用该模型理论研究了受单轴拉伸石墨烯/柔性基底结构的双向界面切应力传递问题.在弹性粘结阶段,导出了石墨烯双向正应变和双向界面切应力的半解析表达式,分析了不同位置处石墨烯正应变和界面切应力的分布规律.导出了石墨烯/柔性基底结构发生界面滑移的临界应变,结果表明该临界应变低于利用经典一维非线性剪滞模型得到的滑移临界应变,并且明显受到石墨烯宽度尺寸以及基底泊松比大小的影响.基于二维非线性剪滞模型建立有限元模型(FEM),研究了界面滑移阶段石墨烯双向正应变和双向界面切应力的分布规律.与一维非线性剪滞模型的结果对比表明,当石墨烯宽度较大时,二维模型和一维模型对石墨烯正应变、界面切应力以及滑移临界应变的计算结果均存在较大差别,但石墨烯宽度很小时,二维模型可近似被一维模型代替.最后,通过与拉曼实验结果的对比,验证了二维非线性剪滞模型的可靠性,并得到了石墨烯/聚对苯二甲酸乙二醇酯(PET)基底结构的界面刚度(100 TPa/m)和界面剪切强度(0.295 MPa).     

Mechanical properties of single- and double-walled carbon nanotubes under hydrostatic pressure

Based on a molecular mechanics coupled with atomistic-based continuum theory, a closed-form formula is presented to examine the elastic properties of single- and double-walled carbon nanotubes subjected to hydrostatic pressure. Following the present model, the effects of the armchair and zigzag CNT structures on the pressure behavior are theoretically investigated. The computational result indicates that the bulk modulus is less sensitive to the chiral structures except for very small tube diameters. Moreover, closed-end nanotubes under hydrostatic pressure exhibit a larger bulking modulus than open ended nanotubes. The cap of the zigzag tubes has a larger effect on the bulk modulus when compared to the armchair tubes, especially in small diameter nanotubes. The predicted strain and the bulk modulus are in good agreement with existing theoretical results. PACS 61.46.+w; 62.20.Dc; 62.20.-x; 62.25.+g     

Dislocation energy and calculation from Peierls stress： a rigorous the lattice theory

In the classical Peierls--Nabarro (P-N) theory of dislocation, there is a long-standing contradiction that the stable configuration of dislocation has maximum energy rather than minimum energy. In this paper, the dislocation energy is calculated rigorously in the context of the full lattice theory. It is found that besides the misfit energy considered in the classical P-N theory, there is an extra elastic strain energy that is also associated with the discreteness of lattice. The contradiction can be automatically removed provided that the elastic strain energy associated with the discreteness is taken into account. This elastic strain energy is very important because its magnitude is larger than the misfit energy, its sign is opposite to the misfit energy. Since the elastic strain energy and misfit energy associated with discreteness cancel each other, and the width of dislocation becomes wide in the lattice theory, the Peierls energy, which measures the height of the effective potential barrier, becomes much smaller than that given in the classical P-N theory. The results calculated here agree with experimental data. Furthermore, based on the results obtained, a useful formula of the Peierls stress is proposed to fully include the discreteness effects.     

Three-dimensional phase field microelasticity theory of a multivoid multicrack system in an elastically anisotropic body: Model and computer simulations

The phase field microelasticity theory of a three-dimensional, elastically anisotropic system of voids and cracks is proposed. The theory is based on the equation for the strain energy of the continuous elastically homogeneous body presented as a functional of the phase field, which is the effective stress-free strain. It is proved that the stress-free strain minimizing the strain energy of this homogeneous modulus body fully determines the elastic strain and displacement of the body with voids and/or cracks. The proposed phase field integral equation describing the elasticity of an arbitrary system of voids and cracks is exact. The geometry and evolution of multiple voids and/or cracks are described by the phase field, which is the solution of the time-dependent Ginzburg-Landau equation. Other defects, such as dislocations and precipitates, are trivially integrated into this theory. The proposed model does not impose a priori constraints on possible void and crack configurations or their evolution paths. Examples of computations of elastic equilibrium of systems with voids and/or cracks and the evolution of cracks under applied stress are considered.     

A general 3-D nonlinear magnetostrictive constitutive model for soft ferromagnetic materials

In this paper, a new general nonlinear magnetostrictive constitutive model is proposed for soft ferromagnetic materials, and it can predict magnetostrictive strain and magnetization curves under various pre-stresses. From the viewpoint of magnetic domain, it is based on the important physical fact that a nonlinear part of the elastic strain produced by magnetic domain wall motion under a pre-stress is responsible for the change of the maximum magnetostrictive strain in accordance with the pre-stress. Then the reduction of magnetostrictive strain from the maximum is caused by the domain rotation. Meanwhile, the magnetization under various pre-stresses in this model is introduced by magnetostrictive effect under the same pre-stress. A simplified 3-D model is put forward by means of linearizing the nonlinear function, i.e. the nonlinear part of the elastic strain produced by domain wall motion, and by using the quartic of magnetization to describe domain rotation. Besides, for the convenience of engineering applications, two-dimensional (plate or film) and one-dimensional (rod) models are also given for isotropic materials and their application ranges are discussed too. In comparison with the experimental data of Kuruzar and Jiles, it is found that this model can predict magnetostrictive strain and magnetization curves under various pre-stresses. The numerical simulation further illustrates that the new model can effectively describe the effects of the pre-stress or residual stress on the magnetization and magnetostrictive strain curves. Additionally, this model can be degenerated to the existing magnetostrictive constitutive model for giant magnetostrictive materials (GMM), i.e. a special soft ferromagnetic material.     

Prediction study of the structural and elastic properties for the cubic skutterudites LaFe4A12 (A = P,As and Sb) under pressure effect

We have performed accurate ab initio total energy calculations using the full-potential linear augmented plane wave plus local orbitals method with the local density approximation for the exchange–correlation potential to investigate the systematic trends for structural and elastic properties of the cubic LaFe₄A₁₂ skutterudites’ family depending on the type of A pnicogen atom (A stands for P, As and Sb). The calculated equilibrium lattice constants and internal free parameters are in good agreement with the experimental results. For the first time, the numerical estimates of the independent elastic constants and their pressure dependence are performed using the total energy variation as function of strain technique. Isotropic elastic parameters and related properties, namely bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, Lamé’s coefficients, average sound velocity and Debye temperature, are estimated in the framework of the Voigt–Reuss–Hill approximation for ideal polycrystalline LaFe₄A₁₂ aggregates.     

New bi-level programming model for routing and spectrum assignment in elastic optical network

The routing and spectrum assignment problems in elastic optical networks are well-known NP-hard problem, and are even more complex and challenging when the energy consumption is taken into account. To tackle this challenging problem, we establish a bi-level programming model with the energy consumption of the optical networks and the maximum index of used frequency slots as the leader’s and follower’s objectives to be minimized, respectively, which are used to determine the optimal schemes of routing and spectrum assignments. To solve the model effectively, a hybrid genetic algorithm framework integrating a heuristic algorithm into a genetic algorithm is proposed. We use heuristic algorithm to sort the connection requests and design a genetic algorithm with tailor-made crossover, mutation and local search operator to look for an optimal routing and spectrum assignment scheme. Finally, simulation experiments are conducted, and the experimental results indicate the effectiveness of the proposed model and algorithms.     

Cross-slip in face centred cubic metals: a general full stress-field dependent activation energy line-tension model

Cross-slip is a thermally activated process by which a screw dislocation changes its slip plane. Understanding and modelling the activation barrier of the cross-slip process as a free-energy barrier that depends on the stress conditions at the vicinity of the dislocation is crucial. In this work, we employ the line-tension model for the cross-slip of screw dislocations in face-centred cubic (FCC) metals in order to calculate the energy barrier when both Escaig stresses are applied on the primary and cross-slip planes and Schmid stress is applied on the cross-slip plane. We propose a closed-form expression for the activation energy for cross-slip in a large range of stresses, without any fitting parameters. The results of the proposed model are in good agreement with previous numerical results and atomistic simulations. We also show that, when Schmid stress is applied on the cross-slip plane, the energy barrier is decreased, and in particular, cross-slip can occur even when the Escaig stress in the primary plane is smaller than that on the cross-slip plane. The proposed closed-form expression for the activation energy can be easily implemented in dislocation dynamics simulations, owing to its simplicity and universality. This will allow cross-slip to be more accurately related to macroscopic plasticity.     

Elastic fields induced by non-elastic eigenstrains in a plane elliptical inhomogeneity existing in orthotropic media under uniform tension at infinity

This paper presents an analytical solution for the elastic fields induced by non-elastic eigenstrains in a plane elliptical inhomogeneity embedded in the orthotropic matrix under tension at infinity and inclined at any angle. The conformal transformation and complex function method for the anisotropic elastic material were used to determine the strain energies in the inhomogeneity and matrix, which were expressed by four undetermined coefficients characterizing the equilibrium boundary of the inhomogeneity due to the acting eigenstrains and external load. The use of the principle of the minimum potential energy led to analytical expressions for these coefficients and thus generated a closed-form solution for the elastic strain/stress fields. The resulting stress field in the inhomogeneity was examined and verified by checking the continuity conditions for the normal and shear stresses on the interior boundary of the matrix. Supported by the Program for New Century Excellent Talents in Universities (NCET) of the Ministry of Education of China (Grant No. NCET-04-0373) and the Program for Shanghai Pujiang Talents (Grant No. 05PJ14092)     

Vibrations of double-nanotube systems with mislocation via a newly developed van der Waals model

This study deals with transverse vibrations of two adjacent-parallel-mislocated single-walled carbon nanotubes (SWCNTs) under various end conditions. These tubes interact with each other and their surrounding medium through the intertube van der Waals (vdW) forces, and existing bonds between their atoms and those of the elastic medium. The elastic energy of such forces due to the deflections of nanotubes is appropriately modeled by defining a vdW force density function. In the previous works, vdW forces between two identical tubes were idealized by a uniform form of this function. The newly introduced function enables us to investigate the influences of both intertube free distance and longitudinal mislocation on the natural transverse frequencies of the nanosystem which consists of two dissimilar tubes. Such crucial issues have not been addressed yet, even for simply supported tubes. Using nonlocal Timoshenko and higher-order beam theories as well as Hamilton's principle, the strong form of the equations of motion is established. Seeking for an explicit solution to these integro-partial differential equations is a very problematic task. Thereby, an energy-based method in conjunction with an efficient meshfree method is proposed and the nonlocal frequencies of the elastically embedded nanosystem are determined. For simply supported nanosystems, the predicted first five frequencies of the proposed model are checked with those of assumed mode method, and a reasonably good agreement is achieved. Through various studies, the roles of the tube's length ratio, intertube free space, mislocation, small-scale effect, slenderness ratio, radius of SWCNTs, and elastic constants of the elastic matrix on the natural frequencies of the nanosystem with various end conditions are explained. The limitations of the nonlocal Timoshenko beam theory are also addressed. This work can be considered as a vital step towards better realizing of a more complex system that consists of vertically aligned SWCNTs of various lengths.     

Strain and piezoelectric fields in embedded quantum wire arrays

Utilizing a recently developed exact closed-form solution for a single polygonal quantum wire (QWR) inclusion problem, we theoretically investigate the elastic strain and electric fields induced by QWR arrays embedded in GaAs. We consider arrays ranging from 1×1 to 7×7 QWRs embedded in infinite substrates and up to 4×7 QWRs in half space substrates where the wires are near a surface. Our results for the infinite substrate indicate that although the elastic fields within any single QWR are similar to the fields in the other wires with only a weak dependence on the number of QWRs, the electric fields (both inside and outside the QWRs) can be significantly different for different array sizes. Due to the existence of the free surface, the half space solutions show that the elastic and electric fields both inside of and outside of the QWRs depend significantly on the number of QWRs, again with the electric field having the stronger dependence. A detailed analysis of the strain and electric fields for embedded QWR arrays is presented and the results could impact the design of proposed strain-modulated electronic devices.     

Velocity field of wave-induced local fluid flow in double-porosity media

Under the excitation of elastic waves,local fluid flow in a complex porous medium is a major cause for wave dispersion and attenuation.When the local fluid flow process is simulated with wave propagation equations in the double-porosity medium,two porous skeletons are usually assumed,namely,host and inclusions.Of them,the volume ratio of inclusion skeletons is low.All previous studies have ignored the consideration of local fluid flow velocity field in inclusions,and therefore they can not completely describe the physical process of local flow oscillation and should not be applied to the situation where the fluid kinetic energy in inclusions cannot be neglected.In this paper,we analyze the local fluid flow velocity fields inside and outside the inclusion,rewrite the kinetic energy function and dissipation function based on the double-porosity medium model containing spherical inclusions,and derive the reformulated Biot-Rayleigh(BR)equations of elastic wave propagation based on Hamilton’s principle.We present simulation examples with different rock and fluid types.Comparisons between BR equations and reformulated BR equations show that there are significant differences in wave response characteristics.Finally,we compare the reformulated BR equations with the previous theories and experimental data,and the results show that the theoretical results of this paper are correct and effective.     

Effects of surface and interface energies on the bending behavior of nanoscale multilayered beams

A modified continuum model of the nanoscale multilayered beams is established by incorporating surface and interface energies. Through the principle of minimum potential energy, the governing equations and boundary conditions are obtained. The closed-form solutions are presented and the overall Young's modulus of the beam is studied. The surface and interface energies are found to have a major influence on the bending behavior and the overall Young's modulus of the beam. The effect of surface and interface energies on the overall Young's modulus depends on the boundary condition of the beam, the values of the surface/interface elasticity constants and the initial surface/interface energy of the system. The results can be used to guide the determinations of the surface/interface elasticity properties and the initial surface/interface energies of the nanoscale multilayered materials through nanoscale beam bending experiments.     

Phase instabilities in small particles

In this review we consider the existing theories for the structure of small particles and the nature of morphological instabilities as the size is reduced. The various electron microscopic observations confirming the stability of a new phase, the so called ‘Multiply twinned structure’, in small particles is discussed. A theoretical model is presented to calculate the free energy surfaces for a series of asymmetric and single crystal structures using a modified Curie-Wulff construction for the surface energy, and a disclination model for the elastic strain energy. Depending on the activation barrier heights and the Boltzmann occupancy factors for the various local minima on the energy surface, the idea of ‘quasi-melting’ is introduced and compared with the structural instabilities in molecular clusters seen recently by various authors using computer simulations. A phase diagram for small particles as a function of size and temperature is presented and the effect of statistical fluctuations on stability is discussed. Finally a phenomenological discussion relating the phase instabilities to various melting and related phase transitions is given.     

基于绝对节点坐标法的大变形柔性梁几种动力学模型研究

对在平面内大范围转动的大变形柔性梁动力学进行了研究, 基于绝对节点坐标法建立了一种新的大变形柔性梁的非线性动力学模型. 该动力学模型中考虑了柔性梁的轴向拉伸变形和横向弯曲变形, 利用Green-Lagrangian应变张量计算柔性梁的轴向应变及应变能, 利用曲率的精确表达式计算柔性梁的横向弯曲变形能. 运用拉格朗日恒等式给出了柔性梁横向弯曲变形能新的表达式, 该变形能表达式更加简洁, 通过新的变形能表达式得到了新的弹性力模型, 由此得到的动力学方程可以精确地描述柔性梁的几何大变形问题. 通过与高次耦合模型以及ANSYS中BEAM188非线性梁单元模型的比较, 验证了本模型在计算大变形时的正确性以及高次耦合模型在处理大变形问题时的不足. 进一步研究发现, 新的广义弹性力模型可以适当地简化, 给出了两种简化模型, 根据不同模型的计算效率以及计算精度的比较确定了不同模型的适用范围.