Showing papers on "Torsion (mechanics) published in 2001"

Advanced Mechanics of Materials

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Corrugated long-period fiber gratings as strain, torsion, and bending sensors

Abstract: We present a novel corrugated long-period fiber grating whose transmission spectra are highly sensitive to the applied tensile strain, torsion, and bending due to the periodical index modulation created and changed by these mechanic forces. The induced index modulation can also be experimentally characterized by using a built-in fiber Bragg grating (FBG). The long period fiber gratings possess the following unique properties when used as sensors. As a tensile strain sensor, its resonance loss varies but resonance wavelength remains stable. As a torsion sensor, the wavelength varies with the applied twist rate. As a bending sensor, the cladding-mode resonance grows with the bending curvature.

Torsion and bending of micron-scaled structures

Abstract: Typical microelectromechanical systems (MEMS) devices and packages are composed of micron-scaled structures. Experimental investigations on the effect of size on the deformation behavior of simple structures have shown that the deformation behavior of metals and polymers is size dependent. The size dependence in small structures is attributed to the contribution of nonnegligible strain gradients. In this work, torsion and bending of micron-sized rods and plates were analyzed by using a two-parameter model of strain-gradient plasticity. Microrod torsion and microplate bending experimental data were analyzed to determine the magnitude of the strain-gradient material parameters. The parametric analyses showed that conventional analysis is applicable only when the size of the structure is significantly larger than the material parameters, which are typically in the micron range. Strain-gradient analysis of micron-sized rod revealed that the presence of strain gradient increased the torque by three to nine times at the same twist. For MEMS structures with micron-sized features, conventional structural analysis without strain gradient is potentially inadequate, and strain-gradient analysis must be conducted to determine the elastoplastic behavior in the micron scale.

Shear strength and fatigue properties of human cortical bone determined from pure shear tests.

Abstract: Shear properties of bone have been inferred from torsion tests. However, torsion often causes spiral fracture planes that correspond to tensile rather than shear failure. We measured the shear properties of human cortical bone in both longitudinal and transverse directions using pure shear tests. Shearing applied transverse to the bone long axis caused fracture along a 45 degrees plane that coincided with maximum tension. This fracture pattern is similar to spiral fractures caused by torsion. Shear strength along the bone axis was 51.6 MPa or about 35% less than that determined using torsion tests. Fatigue tests of human cortical bone in pure shear were conducted. The results agreed well with previous measurements of cortical bone fatigue life in tension and compression, when normalized to strength. Using tibial shear strain magnitudes measured previously for human volunteers, we estimated the fatigue life of cortical bone for different activities, and speculate that shear fatigue failure is a probable cause of tibial stress fractures resulting from impact loading.

Geometric classification of the torsion tensor in space-time

Abstract: Torsion appears in literature in quite different forms. Generally, spin is considered to be the source of torsion, but there are several other possibilities in which torsion emerges in different contexts. In some cases a phenomenological counterpart is absent, in some other cases torsion arises from sources without spin as a gradient of a scalar field. Accordingly, we propose two classification schemes. The first one is based on the possibility to construct torsion tensors from the product of a covariant bivector and a vector and their respective space-time properties. The second one is obtained by starting from the decomposition of torsion into three irreducible pieces. Their space-time properties again lead to a complete classification. The classifications found are given in a U_4, a four dimensional space-time where the torsion tensors have some peculiar properties. The irreducible decomposition is useful since most of the phenomenological work done for torsion concerns four dimensional cosmological models. In the second part of the paper two applications of these classification schemes are given. The modifications of energy-momentum tensors are considered that arise due to different sources of torsion. Furthermore, we analyze the contributions of torsion to shear, vorticity, expansion and acceleration. Finally the generalized Raychaudhuri equation is discussed.

Geometric classification of the torsion tensor of space-time

Abstract: Torsion appears in literature in quite different forms. Generally, spin is considered to be the source of torsion, but there are several other possibilities in which torsion emerges in different contexts. In some cases a phenomenological counterpart is absent, in some other cases torsion arises from sources without spin as a gradient of a scalar field. Accordingly, we propose two classification schemes. The firstone is based on the possibility to construct torsion tensors from the product of a covariant bivector and a vector and their respective space-time properties. The secondone is obtained by starting from the decomposition of torsion into three irreducible pieces. Their space-time properties again lead to a complete classification. The classifications found are given in a U4, a four dimensional space-time where the torsion tensors have some peculiar properties. The irreducible decomposition is useful since most of the phenomenological work done for torsion concerns four dimensional cosmological models. In the second part of the paper two applications of these classification schemes are given. The modifications of energy-momentum tensors are considered that arise due to different sources of torsion. Furthermore, we analyze the contributions of torsion to shear, vorticity, expansion and acceleration. Finally the generalized Raychaudhuri equation is discussed.

Multiaxial fatigue of welded joints under constant and variable amplitude loadings

Abstract: Flange-tube joints from fine grained steel StE 460 with unmachined welds were investigated under biaxial constant and variable amplitude loading (bending and torsion) in the range of 10 3 to 5 x 10 6 cycles to crack initiation and break-through, respectively. In order not to interfere with residual stresses they were relieved by a heat treatment. In-phase loading can be treated fairly well using the conventional hypotheses (von Mises or Tresca) on the basis of nominal, structural or local strains or stresses. But the influence of out-of-phase loading on fatigue life is severely overestimated if conventional hypotheses are used. However, the hypothesis of the effective equivalent stress that is introduced leads to fairly good predictions for constant as well as for random variable amplitude loads. Therefore, the knowledge of local strains or stresses is necessary. They are determined by boundary element analyses that are dependent on weld geometry. This hypothesis considers the fatigue-life-reducing influence of out-of-phase loading by taking into account the interaction of local shear stresses acting in different surface planes of the material. Further, size effects resulting from weld geometry and loading mode were included. Damage accumulation under a Gaussian spectrum can be assessed for in- and out-of-phase combined bending and torsion using an allowable damage sum of 0.35.

Gradient-enhanced computational homogenization for the micro-macro scale transition

Abstract: Predicting the macroscopic behaviour of materials on the basis of the mechanics of their microstructure, has been a subject of intensive research in the past decade. A large class of homogenization techniques has been developed to obtain macroscopic descriptions which represent microstructural features. Among these, closed-form homogenization techniques used to obtain macroscopic constitutive relations with their associated effective parameters, are probably best known. This paper focuses on micro-macro coupled homogenization formulations in which a two-level coupled boundary value problem is set up. Such a formulation is particularly efficient for an evolving highly nonlinear and heterogenous microstructure. A higher-order micro-macro framework is established here, which accounts for size effects and more complex microstructural deformation modes. This curichment opens up new possibilities for the future use of these two-level computational homogenization methods.

Geometric torsion in idiopathic scoliosis: three-dimensional analysis and proposal for a new classification.

Abstract: Study design Three-dimensionally reconstructed spines of 62 subjects with idiopathic scoliosis were reviewed for three-dimensional pattern classification based on the measurement of geometric torsion. Objectives To evaluate the relevance of geometric torsion as a three-dimensional index of scoliosis, and to develop a three-dimensional classification of deformity for idiopathic scoliosis as opposed to the current classifications based on two-dimensional frontal views. Summary of background data Attempts have been made to measure the geometric torsional shape of scoliotic curves represented curvilinearly. However, the geometric torsion phenomenon has never been properly analyzed and thus has never been precisely defined. Methods Standardized stereoradiographs of 62 patients with idiopathic scoliosis were obtained and used to generate three-dimensional reconstructions. A continuous parametric form of the curved line that passes through the vertebrae was created by least square fitting of Fourier series functions. Frenet's formulas then were used to calculate the geometric torsion. Results Analysis of geometric torsion associated with 94 major scoliotic curves allowed three basic categories of torsion curve patterns to be identified. Scoliotic spines with multiple major curves are described by a combination of basic torsion patterns, one for each curve. Conclusions A three-dimensional analysis of the spine in terms of geometric torsion has defined three distinct patterns of torsion in a group of scoliotic curves. Geometric torsion had extreme values at the levels of upper and lower vertebrae, but zero or nearly zero values at the levels of the apices. The torsional phenomenon can be unidirectional or bidirectional in both single and double major curves.

Length scales in the static and dynamic torsion of a circular cylindrical micro-bar

Abstract: The static and dynamic torsion of a circular cylindrical micro-bar is analyzed within the couple stress theory The static shear stresses and natural frequencies are solved for the circular cylinder with couple stresses The maximum shear stress will eventually drop and the natural frequencies will increase with the cylinder radius close to the material length scale

Axial-vector torsion and the teleparallel Kerr spacetime

Abstract: In the context of the teleparallel equivalent of general relativity, we obtain the tetrad and the torsion fields of the stationary axisymmetric Kerr spacetime It is shown that, in the slow rotation and weak-field approximations, the axial-vector torsion plays the role of the gravitomagnetic component of the gravitational field, and is thus responsible for the Lense-Thirring effect

A review of multiaxial fatigue of weldments: experimental results, design code and critical plane approaches

Abstract: A survey of biaxial (bending or tension and torsion) constant amplitude fatigue of welded connections is presented. Re-analysis of 233 experimental results from eight different studies has been performed based on hot spot stresses and three potential damage parameters: maximum principal stress range; maximum shear stress range; and a modified critical plane model for welds. Of the three methods, the critical plane model was most successful in resolving the data to a single S–N line. The design curve for all toe failures based on the critical plane model was FAT 97 with a slope of 3. By excluding butt welds and including only fillet welds that failed at the weld toe, the design curve was increased to FAT 114 with a slope of 3. However, observed scatter was 70–100% larger than that observed in uniaxial loaded specimens analysed using the hot spot approach.

Flexural–torsional post-buckling analysis of thin-walled elements with open sections

Abstract: The post-buckling analysis of thin-walled elements under compression is investigated. A nonlinear model is developed by using nonlinear relationships between curvatures and bending moments. Warping and shortening effects are considered in the torsion equilibrium equation. Based on Galerkin's method, a nonlinear algebraic system is obtained for simply supported boundary conditions. The three resulting equations in bending and torsion are highly coupled and the Newton–Raphson algorithm with displacement control is adopted for the solution. The post-buckling equilibrium curves are obtained for various sections shapes, such as bisymmetric and monosymmetric sections. The importance of the shortening effect is outlined.

Numerical studies on the identification of the material parameters of Rivlin's hyperelasticity using tension-torsion tests

Abstract: This paper deals with the identification of material parameters of elasticity relations based on Rivlin's hyperelasticity for incompressible material response, where the free energy evolves as a polynomial in the first and second invariant of the right Cauchy-Green tensor. This elasticity relation has the advantage of incorporating the material parameters linearily. The numerical studies are applied to tension, torsion and combined tension-torsion tests with cylindrical carbon black-filled rubber specimens represented in Haupt and Sedlan [1] and [2]. In the identification process the analytical solution of the resulting boundary value problem leads to a linear least square solution. In this article attention is focused on the numerical solution of several models proposed in the literature and their behavior for both a large and a small number of test data.

On Saint-Venant’s Problem for an Inhomogeneous, Anisotropic Cylinder—Part I: Methodology for Saint-Venant Solutions

Abstract: In this paper, the first in a series of three, a procedure based on semi-analytical finite elements is presented for constructing Saint-Venant solutions for extension, bending, torsion, and flexure of a prismatic cylinder with inhomogeneous, anisotropic cross-sectional properties. Extension-bending-torsion involve stress fields independent of the axial coordinate and their displacements may be decomposed into two distinct parts which are called the primal field and the cross-sectional warpages herein. The primal field embodies the essence of the kinematic hypotheses of elementary bar and beam theories and that for unrestrained torsion. The cross-sectional warpages are independent of the axial coordinate and they are determined by testing the variationally derived finite element displacement equations of equilibrium with the primal field. For flexure, a restricted three-dimensional stress field is in effect where the stress can vary at most linearly along the axis. Integrating the displacement field based for extension-bending-torsion gives that for the flexure problem. The cross-sectional warpages for flexure are determined by testing the displacement equations of equilibrium with this displacement field. In the next paper, the cross-sectional properties such as the weighted-average centroid, center of twist and shear center are defined based on the Saint-Venant solutions established in the present paper and numerical examples are given. In the third paper, end effects or the quantification of Saint-Venant's principle for the inhomogeneous, anisotropic cylinder is considered.

An angle-based design approach for rectangular electrostatic torsion actuators

Abstract: In this paper, we develop a fast, angle-based design approach for rectangular electrostatic torsion actuators based on several simple equations. This approach is significantly more straightforward than the usual full calculation or simulation methods. The main results of the simplified approach are verified by comparing them with analytical calculations and MEMCAD simulations with fractional difference smaller than 3% for torsion mode dominant actuators. Also, good agreement is found by comparison with the measured behavior of a microfabricated full-plate device.

Design of a variable twist tilt-rotor blade using shape memory alloy (SMA) actuators

Abstract: This paper presents research aimed at actively altering the twist distribution of a tiltrotor blade between hover and forward flight. Three different concepts-extension-twist coupled composites, bimoment actuation and discrete SMA torque tube actuation - are considered, and the torque tube appears the most feasible. Parametric design of the torque tube and attachment technique is presented with actuation torque, heat transfer and bandwidth issues being considered to arrive at the configuration of the tube. The effect of heat treatment of the SMA in tuning the actuation characteristics is discussed. A dramatic improvement in the actuation cooling time is demonstrated through the use of active cooling using thermodelectric modules. An extension of the one-dimensional formulation of Brinson's model to the torsional case is presented. The model is shown to have good correlation with room temperature characteristics. The criterion for impedance matching between the actuator and the host structure is derived. The torsional actuator is tested both under no load and acting against a restoring spring and shows repeatable actuation characteristics.

A torsion sensor made of a corrugated long period fibre grating

Abstract: Based on the photoelastic effect, the strain distribution within a corrugated long period fibre grating (LPFG) subjected to tensile stress and twisting will cause a periodic index variation, which may result in resonant couplings between fibre core and cladding modes. The resonance wavelength corresponding to the peak loss is directly sensitive to the torsional angle per unit length; thus a novel torsion sensor can be made from the corrugated long period fibre grating. We also present a phenomenological theory based on the scattering matrix formalism to qualitatively explain the mode coupling behaviour in the corrugated grating.

Influence of shear deformation on restrained torsional warping of pultruded FRP bars of open cross-section

Abstract: Pultruded FRP bars of open cross-section possess relatively low transverse shear moduli in relation to their axial and flexural moduli. This can result in shear deformation constituting a significant proportion of the total deformation induced by non-uniform bending, and a reduction in the buckling loads of members subjected to axial compression and bending. Herein an approximate theory for quantifying the influence of shear deformation on the restrained torsional warping of pultruded FRP bars of open cross-section is presented. Contrary to expectations the theory indicates that the influence of shear deformation on the restrained warping torsional stiffness of such members is not significant. The theory is validated by a series of bending and torsion tests on three pultruded FRP I-beams.