Irreducible expressions for isotropic functions of two tensors

Polynomial expressions are given for scalar-valued, skew-symmetric second-order-tensor-valued and symmetric second-order-tensor-valued isotropic functions of two skew-symmetric second-order tensors, of one skew-symmetric and one symmetric second-order tensor and of two symmetric second-order tensors. It is shown that all terms of degree α, β in two tensors R, S (say) appearing in a given expression are linearly independent and that this is the case for all values of α and β.     

带转角自由度的三角形三棱柱单元

本文提出了一个带转角自由度平面三角形单元、两个带转角自由度空间三棱柱单元。对平面单元每个结点有两个线位移自由度、一个转角自由度；对空间单元每个结点有三个线位移自由度、三个转角自由度。这些单元列式简单，其中两个无多余零能模式，数值计算表明，它们的计算精度高。     

基于并联机构中医推拿机器人机型研究

 在对中医推拿手法运动学研究的基础上，依据中医推拿手法运动学特征并结合并联机构的特点，提出基于并联机构中医推拿机器人机型及输出矩阵。对基于三平移三转动并联机构、三平移两转动并联机构、两平移三转动并联机构、两平移两转动并联机构、两平移一转动并联机构的中医推拿机器人进行了概念设计，并利用Pro/E软件构建出各机型虚拟样机。最后从动平台输出矩阵、控制解耦性、结构对称性、工作空间及转动能力等方面对各机型进行了分析总结。为各中医推拿机器人的实际应用提供了理论依据。     

Dual orthotropic damage–effect tensors with complementary structures

This paper deals with secant constitutive relations of orthotropic elastic damage based on the so-called damage–effect tensors, namely the fourth-order operators that define the linear transformations between nominal and effective stress and strain quantities. The damage–effect tensors are expressed by orthotropic representations in terms of symmetric second-order damage tensor variables. The paper provides a set of new dual orthotropic damage–effect tensors that possess complementary structures in the dual compliance- and stiffness-based derivations. More specifically, each orthotropic damage–effect tensor of the solution set possesses an inverse (its dual counterpart) that displays the structure of the (major) transpose of the tensor obtained by replacing the adopted second-order damage tensor variables with their inverses.     

Dynamics of inelastically colliding spheres with Coulomb friction: Relaxation of translational and rotational energy

We investigate the free cooling of inelastic rough spheres in the presence of Coulomb friction. Depending on the coefficients of normal restitution ε and Coulomb friction μ, we find qualitatively different asymptotic states. For nearly complete normal restitution (ε close to 1) and large μ, friction does not change the cooling properties qualitatively compared to a constant coefficient of tangential restitution. In particular, the asymptotic state is characterized by a constant ratio of rotational and translational energies, both decaying according to Haff's law. However, for small ε and small μ, the dissipation of rotational energy is suppressed, so that the asymptotic state is characterized by constant rotational energy while the translational energy continues to decay as predicted by Haff's law. Introducing either surface roughness for grazing collisions or cohesion forces for collisions with vanishing normal load, causes the rotational energy to decay according to Haff's law again in the asymptotic long-time limit with, however, an intermediate regime of approximately constant rotational energy. Received: 19 November 1999     

Spectral analysis of the rotational component of seismic ground motion

An algorithm for the spectrum of the rotational component of surface ground motion during earthquake is derived. To obtain the rotation the total motion is decomposed into the wave components. Then the rotational motion is obtained in terms of the horizontal and vertical components treated as non-stationary random processes. The evolutionary spectrum of the rotational acceleration is a function of respective translational spectra, their co-spectrum and respective wave parameters. The analysis shows a shift of the higher frequency components in the rotational spectrum. The rotation is a function of the time derivative of translational components.     

Hybrid Hydrogel-Magnet Actuators with pH-Responsive Hydrogels for Gastrointestinal Microrobots

Limited space on millimeter-scale devices for biomedical applications makes it challenging to incorporate bulky actuators and power for onboard mechanical actuation. Stimuli-responsive hydrogels, such as pH-responsive hydrogels, provide a solution to automatically sense and actuate in the gastrointestinal tract. However, hydrogels are often nonload bearing and slow in actuation. To overcome these challenges, a new type of hybrid actuator is developed which utilizes a pH-responsive hydrogel with magnets to trigger magnetic springs (i.e., permanent magnets with repulsive, spring-like forces) to quickly initiate rotational and translational movements at pH > 6. The agar-poly(acrylic acid) hydrogel undergoes a large volume transition at pH > 6 and exhibits large nominal blocking stress of 610–819 kPa for a 3–4 mm diameter cylinder hydrogel. Moreover, the scaling of hydrogel force and response times are experimentally confirmed. Based on the hydrogel properties, an analytical hydrogel model is developed to predict hydrogel force and displacement under varying magnetic loads and wall constraints in simulated gastric fluid (SGF, pH 1.2) and simulated intestinal fluid (SIF, pH 6.8), and the experimental data validate the model. Finally, an innovative hybrid hydrogel-magnet actuator that triggers rotational and translational motion without external activation is demonstrated.     

Families of continuous spin tensors and applications in continuum mechanics

A new method is proposed for generating families of continuous spin tensors associated with families of corotational rates of second-order tensors using isotropic tensor functions of the same tensor arguments and different forms of continuous antisymmetric scalar spin functions of scalar arguments. Tensor functions are represented in terms of eigenprojections of a symmetric tensor S, which is one of the arguments of these functions. Each member of the generated family is represented as the sum of some basic spin tensor associated with the basic corotational tensor rate and the above-mentioned tensor function, whose structure is matched to the structure of the tensor function required to construct the twirl tensor of the triad of orthonormal eigenvectors of the tensor S (but this twirl tensor itself does not belong to the family of continuous spin tensors). The developed method is used in continuum mechanics to generate two families of continuous spin tensors associated with two families of objective corotational rates: Lagrangian and Eulerian. In these families, isotropic tensor functions are constructed using Lagrangian and Eulerian tensor arguments of the kinematic type, respectively. It is shown that if the same scalar spin function is used in deriving tensor functions of Lagrangian and Eulerian tensor arguments, then the corotational tensor rates associated with the generated spin tensors are objective (Lagrangian and Eulerian) counterparts of each other. It is shown that the spin tensors associated with the classical Eulerian corotational tensor rates (Zaremba–Jaumann, Green–Naghdi, d-rate) and their Lagrangian counterparts (including material rate) belong to the generated families of continuous spin tensors. It is also shown that both of these families of continuous spin tensors are subfamilies of the families of material spin tensors derived by Xiao et al. (J Elast 52:1–41, 1998). It is noted that the twirl tensors of the Lagrangian and Eulerian triads associated with the Gurtin–Spear corotational rates of tensors belong to the families of material spin tensors but do not belong to the families of continuous spin tensors. The final section gives expressions of continuous spin tensors from families associated with the families of Lagrangian and Eulerian corotational tensor rates which are appropriate for applications.     

Application of higher-order tensor theory for formulating enhanced continuum models

Summary In this paper attention is focussed on the derivation of higher-order isotropic tensors and their application in the formulation of enhanced continuum models. A mathematical theory will be discussed which relates formal orthogonal invariant polynomial functions to isotropic tensors. Using this theory, the second-order to the sixth-order isotropic tensor will be derived. When the tensor order increases, the derivation procedure clearly reveals a repeatable character. Thereafter, an example will be given of how the higher-order isotropic tensors can be used in the formulation of an enhanced continuum model. It will be demonstrated that symmetry conditions significantly reduce the number of material parameters.     

Revealing Rotational Modes of Functionalized Gold Nanorods on Live Cell Membranes

A full understanding of cell mechanics requires knowledge of both translational and rotational dynamics. The single particle orientation and rotational tracking (SPORT) technique is combined here with correlation analysis to identify the fundamental rotational modes: in‐plane rotation and out‐of‐plane tilting, as well as other more complex rotational patterns, from the vast image data captured at a temporal resolution of 5 ms for single gold nanorod probes in live cell imaging experiments. The unique capabilities of visualizing and understanding rotational motions of functional nanoparticles on live cell membranes allow correlation of the rotational and translational dynamics in unprecedented detail and provide new insights into complex membrane processes. Particles with functionalized surfaces, which interact with the membrane in fundamentally different ways, can exhibit distinct rotational modes and are, for the first time, directly visualized, and these show the early events for membrane approach and attachment.     

Translational and rotational dynamics of methane in ZSM-5 zeolite: A quasi-elastic neutron scattering study

The translational and rotational motions of methane adsorbed at different loadings in NaZSM-5 have been studied by quasi-elastic neutron scattering at two temperatures: 200 and 250 K. The translational motion does not simply follow Fick's law, but a jump diffusion model with a Gaussian distribution of jump lengths satisfactorily simulates the experimental results. The diffusion coefficient that is obtained for long-range translational motion does not vary much on the loading in the range that was studied: it is of ⋍ 2.7 × 10⁻⁵ cm² s⁻¹ at 200 K and ⋍ 5.5 × 10⁻⁵ cm² s⁻¹ at 250 K. Good agreement is found between the neutron and n.m.r. results for this motion, but large discrepancies are observed with the macroscopic measurements. The rotational motion is well described by an isotropic rotational diffusion model, and this motion is found to be much slower in the zeolite than in physisorbed layers or in bulk solid methane.     

带转角自由度的四边形六面体单元

本文提出了三个带转角自由度单元，其中一个平面四边形单元，两个空间六面体单元。对平面单元每个结点有两个线位移自由度、一个转角自由度；对空间单元，每个结点有三个线位移自由度、三个转角自由度。这些单元列式简单，其中两个无多余零能模式，数值计算表明，它们的计算精度高。     

On improved hybrid finite elements with rotational degrees of freedom

A set of three new hybrid elements with rotational degrees-of-freedom (d.o.f.'s) is introduced. The solid, 8-node, hexahedron element is developed for solving three-dimensional elasticity problems. This element has three translational and three rotational d.o.f.'s at each node and is based on a 42-parameter. three-dimensional stress field in the natural convected co-ordinate system. For two-dimensional, plane elasticity problems, an improved triangular hybrid element and a quadrilateral hybrid element are presented. These elements use two translational and one rotational d.o.f. at each node. Three different sets of five-parameter stress fields defined in a natural convected co-ordinate system for the entire element are used for the mixed triangular element. The mixed quadrilateral element is based on a nine-parameter complete linear stress field in natural space. The midside translational d.o.f.'s are expressed in terms of the corner nodal translations and rotations using appropriate transformations. The stiffness matrix is derived based on the Hellinger–Reissner variational principle. The elements pass the patch test and demonstrate an improved performance over the existing elements for prescribed test examples.     

Direct simultaneous measurement of rotational and translational accomodation coefficients

When molecules of a low density diatomic gas strike a solid surface both translational energy and the internal energy modes of rotation and vibration will contribute the energy exchange that occurs. Theoretical studies indicate that accomodation coefficient for rotational energy should be less than that for translational energy, and this is confirmed by experimental results. The experimental apparatus described in this paper uses the electron bream fluorescence detector to measure simultaneously both rotational and translational energy accommodation coefficients of room temperature nitrogen reflecting from a solid surface. A bakeable ultra high vacuum system was built to provide a clean vacuum environment for control of the solid surface properties. In addition to being the only known direct measurement of rotational accomodation coefficient the system offers an advantage over some previous methods of translational accommodation measurement in that there are few restrictions on solid surface temperature or composition.     

The asymptotic behaviour of second-order stochastic Volterra series models of slow drift response

The paper presents a detailed study of the structure and asymptotic behaviour of a second-order stochastic Volterra series model of the slow drift response of large volume compliant offshore structures subjected to random seas. A long standing challenge has been to develop efficient and accurate methods for calculating the response statistics of compliant offshore structures to random seas. Recent work has revealed that the statistical properties of the response process, which consist of a linear, first-order component and a nonlinear, second-order component, is surprisingly complex. The goal of the research work presented here is to complement efforts to develop numerical procedures to calculate the statistics of the response process.     

Random pulsations in a coarsely disperse fluidized bed

A simple model of a uniform isotropic bed of large particles fluidized by a gas is offered which allows one to estimate the intensity of the chaotic translational and rotational motion of the particles. The influence of the pulsations on the observed macroscopic properties of the bed is discussed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 6, pp. 1089–1097, December, 1978.     

Measurement of the chi (2) tensors of KTiOPO4, KTiOAsO4, RbTiOPO4, and RbTiOAsO4 crystals

We use the separated-beams method to measure the second-order nonlinear optical tensors of the crystals KTiOPO4, KTiOAsO4, RbTiOPO4, and RbTiOAsO4 for second-harmonic generation of 1064-nm light. Our results agree well with most previous measurements but have improved precision.     

Dynamics of ethane and propane in zeolite ZSM-5 studied by quasi-elastic neutron scattering

Quasi-elastic neutron scattering has been used to study the dynamics of ethane and propane in zeolite ZSM-5. The experiments were performed at different loadings for the two alkanes and at different temperatures for propane. The long-range translational motion of the molecules has been observed and has been interpreted with a jump diffusion model, the mean jump lengths being of the order of 10 Å, slightly decreasing with increasing loading. The self-diffusion coefficients of ethane are about 2 × 10⁻⁹ m² s⁻¹ at 300 K, those of propane at the same temperature being smaller by a factor of two. An activation energy of 5 kJ mol⁻¹ is obtained for the self-diffusion of propane. These results are in good agreement with the pulsed-field gradient n.m.r. measurements. In addition to the translational motion, a rotational motion of the two molecules is also observed; it is described by an uniaxial rotational diffusion model and rotational diffusion constants are derived.     

Dislocation-disclination transformations and the reverse Hall-Petch effect in nanocrystalline materials

A relay-race dislocation-disclination model of plastic shear development in nanocrystalline materials is proposed, which is based on the mechanism of switching between translational and rotational deformation modes. The dependence of the external deforming stress on the grain size is calculated. It is shown that the switching from the translational to rotational deformation mode and back explains the reverse Hall-Petch effect in nanocrystalline materials.