Material characterization by dual sharp indenters

In a recent study, Le [Le, M.-Q., 2008. A computational study on the instrumented sharp indentations with dual indenters. International Journal of Solids and Structures, 45 (10), 2818–2835.] demonstrated that the yield strength Y can be replaced by the loading curvature C and hence the reduced elastic modulus-loading curvature ratio $E^1/C$ and strain hardening exponent n can be used to govern characteristic parameters of indentation load–depth curves. Extending Le’s approach and regarding dimensional analysis, it is found that $C/Y\text{and}{E}^1/Y$ can be used to investigate fundamental issues in instrumented sharp indentation. Based on extensive finite element analysis, a set of dimensionless functions are constructed for cone indenters of half included angles of 60° and 70.3°. Dimensionless relationships with respect to dual indenters are further explored. Several features of hardness are also considered. An inverse analysis procedure is suggested to estimate material properties, giving good inverse results for experimental data from the literature and representative materials. Sensitivity of inverse solution are studied and discussed. The results show that the proposed dual indenter method is quite robust and can be applied to a wide range of materials.     

Improved reverse analysis for material characterization with dual sharp indenters

It was illustrated by the author in the previous work that combinations between material properties and indentation parameters can be used as mixed parameters in dimensionless functions to capture the indentation response of materials to single and dual sharp indenters. These issues are further extended in the present study. A parametric finite element analysis was performed to investigate the conical indentation response of elasto-plastic solids. Frictional effects are studied. Conical indenters of half-included angles from 50° to 88° are considered to examine several fundamental features of instrumented sharp indentation within the frame work of limit analysis. Regarding dimensional analysis, it is found that a Taylor series expansion according to the elastic indentation work-total indentation work ratio W_e/W_t can be used to improve dimensionless functions. Within this context, a new set of dimensionless functions is explicitly constructed for hardness and indentation parameters of single and dual indenters. Based on formulated functions, a reverse analysis with dual sharp indenters, which was previously proposed by the author, is improved to extract mechanical properties of materials.     

A computational study on the instrumented sharp indentations with dual indenters

Finite element analysis was performed to investigate the indentation response of elasto-plastic solids for conical indenters of half included angles of 60° and 70.3°. The interdependence indentation parameters resulting from a single indentation load–depth curve is considered. Regarding dimensional analysis, several dimensionless relationships are constructed as functions of the reduced elastic modulus-loading curvature ratio E¹/C and the strain hardening exponent n. Further, the duality between corresponding parameters with dual indenters is explored. Finally, a new method based on dual indenters is proposed to extract the strain hardening exponent and the reduced elastic modulus of an indented material. The accuracy of this method is verified and discussed with experimental data from the literature and representative materials.     

Switchable dry adhesive based on shape memory polymer with hemispherical indenters for transfer printing

Transfer printing based on switchable adhesive is essential for developing unconventional systems, including flexible electronics, stretchable electronics, and micro light-emitting diode (LED) displays. Here we report a design of switchable dry adhesive based on shape memory polymer (SMP) with hemispherical indenters, which offers a continuously tunable and reversible adhesion through the combination of the preloading effect and the thermal actuation of SMP. Experimental and numerical studies reveal the fundamental aspects of design, fabrication, and operation of the switchable dry adhesive. Demonstrations of this adhesive concept in transfer printing of flat objects (e.g., silicon wafers), three-dimensional (3D) objects (e.g., stainless steel balls), and rough objects (e.g., frosted glasses) in two-dimensional (2D) or 3D layouts illustrate its unusual manipulation capabilities in heterogeneous material integration applications.     

Complete solutions for rotating plane rigid indenters

Summary Complete solution classes are presented of rotating rough rigid indenters in plane strain collapse theory. Examples are given of nonuniqueness of surface tractions associated with such rough indenters.

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Sommario Si presentano classi complete di soluzioni per penetratori rigidi scabri rotanti, secondo la teoria del collasso in deformazioni piane. Si danno esempi di non unicità di trazione superficiale associata con tali penetratori.

     

基于对偶四元数的卫星信息一致性控制

为了解决航天器控制信息一致性问题,提出了利用对偶四元数来描述对象的位置及姿态信息,实现位置与姿态的统一表述。同时利用信息一致性理论,通过设计航天器间的信息传递模型来解决分布式航天器间的状态同步问题。采用对偶四元数及信息一致性理论为工具,分别给出了位姿同步及跟踪两种控制方法并针对两种信息拓扑模型,以空间交会对接问题进行仿真实验,实验结果表明,在500s以内,卫星的位置及姿态实现了同步及跟踪控制。     

UZAWA TYPE ALGORITHM BASED ON DUAL MIXED VARIATIONAL FORMULATION

ＩｎｔｒｏｄｕｃｔｉｏｎＦｏｒｔｈｅｓｏｌｕｔｉｏｎｏｆｔｈｅｅｌａｓｔｉｃｐｒｏｂｌｅｍ ,ｔｈｅｍｏｓｔｉｍｐｏｒｔａｎｔａｄｖａｎｔａｇｅｏｆｔｈｅｍｉｘｅｄｆｉｎｉｔｅｅｌｅｍｅｎｔｍｅｔｈｏｄｓｌｉｅｓｉｎｔｈｅｃｏｍｐｕｔｉｎｇｏｆｓｔｒｅｓｓａｎｄｄｉｓｐｌａｃｅｍｅｎｔａｎｄｓｏｏｎｓｉｍｕｌｔａｎｅｏｕｓｌｙ .Ｆｏｒｔｈｅｃｏｎｔａｃｔｐｒｏｂｌｅｍｉｎｅｌａｓｔｉｃｉｔｙ ,ａｎｅｗｄｕａｌｍｉｘｅｄｖａｒｉａｔｉｏｎａｌｆｏｒｍｕｌａｔｉｏｎａｎｄｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎ…     

基于双磁偶极子的螺线管磁场建模分析

针对低频交变磁场定位中,螺线管磁场分布的单磁偶极子模型在近场误差较大,定位精度差的问题,提出了一种基于双磁偶极子的螺线管磁场分布建模方法。首先通过分析磁偶极子在空间中的磁场分布规律,将螺线管等效为两个对称的磁偶极子阵列的叠加,建立了螺线管的磁偶极子阵列模型。然后引入模型误差的目标函数,利用模拟退火算法计算最优模型参数。最后根据磁场分布模型,将磁偶极子阵列简化为磁偶极子,在保证定位精度的同时,简化了模型,便于定位解算。实验结果表明,在近场条件下,双磁偶极子模型的最大误差仅为0.003m,相对传统的单磁偶极子模型,最大定位误差下降了90.26%,在远场条件下,单磁偶极子模型与双磁偶极子模型的最大误差近似。     

Sliding of two smooth indenters on a viscoelastic foundation in the presence of friction

The axisymmetric contact problem of sliding of two solid parabolic indenters on a viscoelastic half-space with constant velocity is considered. Shear stresses modeling the adhesive component of the friction force act in the contact area. The model of the foundation material is described by an integral operator with an exponential kernel characterized by one relaxation time. The problem is solved by the boundary element method. The dependences of the contact characteristics on the sliding velocity, the normal load, and the distance between the centers of the indenters is analyzed. The results can be used to study the effect of the roughness elements modeled by two indenters on the contact characteristics and the deformation component of the friction force.     

基于双模型的光纤陀螺温度补偿方法（英文）

基于Sagnac效应的光纤陀螺(FOG),因其自身的优点广泛地应用在捷联惯性导航系统中(SINS)。然而,温度对FOG的影响包括常值影响和随机影响,仍是制约光纤陀螺性能的关键因素之一。针对不同性质的漂移,首先建立基于相关性分析的多项式模型补偿常值漂移;然后结合时间序列分析的方法,利用Kalman滤波抑制经多项式模型补偿后残差信号中的随机成分,进一步提高FOG的精度。单轴光纤陀螺试验结果表明,传统的单多项式补偿模型,FOG的零偏稳定性能由0.05(°)/h仅提高到0.04(°)/h;采用常值和随机的双补偿模型,FOG的零偏稳定性能由0.05(°)/h提高到了0.01(°)/h。证明了双温度建模与补偿方法的有效性,在工程上有一定的参考价值。     

Indentation by nominally flat or conical indenters with rounded corners

Axisymmetric indentation of a flat surface is considered: specifically, the case of flat-ended indenter with rounded edges, and the case of a shallow cone with a rounded tip. Analytical solutions are obtained for the normal and sequential tangential loading, in both full or partial slip conditions (with the Cattaneofn9Mindlin approximation) , and for the complete interior stress field in all these conditions.Implications for strength of the contact are discussed with reference to metallic or brittle materials, with the intention to shed more light in particular to the understanding of common fretting fatigue or indentation testings with nominally flat or conical indenters. It is found that the strength of the contact, which is nominally zero for perfectly sharp flat or conical indenters, is well defined even for a small radius of curvature. This is particularly true for the flat indenter, for which the strength is even significantly higher than for the classical Hertzian indenter for a wide range of geometrical and loading conditions, rendering it very attractive for design purposes.     

Nonlinear energy harvesting with dual resonant zones based on rotating system

An electromagnetic nonlinear energy harvester(NEH) based on a rotating system is proposed, of which the host system rotates at a constant speed and vibrates harmonically in the vertical direction. This kind of device exhibits several resonant phenomena due to the combinations of the rotating and the vibration frequencies of the host system as well as the cubic nonlinearity of the NEH. The governing equation of motion for the NEH is derived, and the dynamic responses and output power are investig...     

一种基于降维对偶四元数的多源导航系统信息融合方法

以陆用载体为研究背景,提出了一种基于降维对偶四元数的多源导航系统信息融合方法。以SINS作为公共参考系统,在分别获得推力、引力及位置对偶四元数误差方程基础上,搭建SINS/GPS/地磁的降维联邦Kalman滤波器模型。一方面,结合载体匀速、加速、转弯、爬坡四种运动状态,利用奇异值分解对系统状态量进行可观测性分析;另一方面,开展该降维对偶四元数导航框架下的惯性/GPS、惯性/地磁子滤波器分级设计,以获得最佳状态维数与导航解算效率。仿真与实验结果表明,降维后的组合导航系统计算量仅为全状态的3.34%,且参数估算结果的"解的集中性"更好。     

基于对偶四元数的双星编队相对位姿测量

为了描述编队卫星中主从星的相对位置和姿态信息,提出了基于对偶四元数的编队卫星相对位姿测量算法。以双星编队飞行的位姿运动为主线,运用对偶四元数工具,充分发挥其能以最简洁的形式表示一般性刚体运动的优点,对卫星轨道和姿态进行分析并建立了对偶四元数位姿模型。同时设计类GPS测量技术来测量编队卫星的相对位置和姿态,该技术载波相位波长和伪码码元比GPS的更短,可获得更高精度的相对测量信号。由于状态方程和观测方程的非线性特征,使用UKF滤波来消除随机噪声对量测过程的干扰。实验结果表明,所设计的算法能够有效估计系统误差,卫星的位置误差和四元数误差收敛于零,验证了该算法的有效性。     

The equivalent axisymmetric model for Berkovich indenters in power-law hardening materials

Nix and Gio [Nix, W.D., Gao, H.J., 1998. Indentation size effects in crystalline materials: a law for strain gradient plasticity. Journal of the Mechanics and Physics of Solids 46, 411–425] established an important relation between the micro-indentation hardness and indentation depth for axisymmetric indenters. For the Berkovich indenter, however, this relation requires an equivalent cone angle. Qin et al. [Qin, J., Huang, Y., Xiao, J., Hwang, K.C., 2009. The equivalence of axisymmetric indentation model for three-dimensional indentation hardness. Journal of Materials Research 24, 776–783] showed that the widely used equivalent cone angle from the criterion of equal base area leads to significant errors in micro-indentation, and proposed a new equivalence of equal cone angle for iridium. It is shown in this paper that this new equivalence holds for a wide range of plastic work hardening materials. In addition, the prior equal-base-area criterion does not hold because the Berkovich indenter gives much higher density of geometrically necessary dislocations than axisymmetric indenter. The equivalence of equal cone angle, however, does not hold for Vickers indenter.     

A fast 3D dual boundary element method based on hierarchical matrices

In this paper a fast solver for three-dimensional BEM and DBEM is developed. The technique is based on the use of hierarchical matrices for the representation of the collocation matrix and uses a preconditioned GMRES for the solution of the algebraic system of equations. The preconditioner is built exploiting the hierarchical arithmetic and taking full advantage of the hierarchical format. Special algorithms are developed to deal with crack problems within the context of DBEM. The structure of DBEM matrices has been efficiently exploited and it has been demonstrated that, since the cracks form only small parts of the whole structure, the use of hierarchical matrices can be particularly advantageous. Test examples presented show that, with the proposed technique, substantial increase in number of elements over the crack surfaces leads only to moderate increases in memory storage and solution time.     

The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape

The contact of an indenter of arbitrary shape on an elastically anisotropic half space is considered. It is demonstrated in a theorem that the solution of the contact problem is the one that maximizes the load on the indenter for a given indentation depth. The theorem can be used to derive the best approximate solution in the Rayleigh-Ritz sense if the contact area is a priori assumed to have a certain shape. This approach is used to analyze the contact of a sphere and an axisymmetric cone on an anisotropic half space. The contact area is assumed to be elliptical, which is exact for the sphere and an approximation for the cone. It is further shown that the contact area is exactly elliptical even for conical indenters when a limited class of Green's functions is considered. If only the first term of the surface Green's function Fourier expansion is retained in the solution of the axisymmetric contact problem, a simpler solution is obtained, referred to as the equivalent isotropic solution. For most anisotropic materials, the contact stiffness determined using this approach is very close to the value obtained for both conical and spherical indenters by means of the theorem. Therefore, it is suggested that the equivalent isotropic solution provides a quick and efficient estimate for quantities such as the elastic compliance or stiffness of the contact. The “equivalent indentation modulus”, which depends on material and orientation, is computed for sapphire and diamond single crystals.     

基于对偶变量变分原理的完整约束系统保辛算法

基于对偶变量变分原理,选择积分区间两端位移为独立变量,构造了求解完整约束哈密顿动力系统的高阶保辛算法。首先,利用拉格朗日多项式对作用量中的位移、动量及拉格朗日乘子进行近似;然后,对作用量中不包含约束的积分项采用Gauss积分近似,对作用量中包含约束的积分项采用Lobatto积分近似,从而得到近似作用量;最后,在此近似作用量的基础上,利用对偶变量变分原理,将求解完整约束哈密顿动力系统问题转化为一组非线性方程组的求解。算法具有保辛性和高阶收敛性,能够在位移的插值点处高精度地满足完整约束。算法的收敛阶数及数值性质通过数值算例验证。     

Analytical solutions to edge effect of composite laminates based on symplectic dual system

In the symplectic space composed of the original variables, displacements, and their dual variables, stresses, the symplectic solution for the composite laminates based on the Pipes-Pagano model is established in this paper. In contrast to the traditional technique using only one kind of variables, the symplectic dual variables include displacement components as well as stress components. Therefore, the compatibility conditions of displacement and stress at interfaces can be formulated simultaneously. After being introduced into the symplectic dual system, the uniform schemes, such as the separation of variables and symplectic eigenfunction expansion method, can be implemented conveniently to analyze composite laminate problems. An analytical solution for the free edge effect of composite laminates is obtained, showing the effectiveness of the symplectic dual method in analyzing composite laminates.