In understanding how a radially symmetrical actin cytoskeleton spontaneously evolves into a chiral system, here we construct a torsional clutch-filament model for one radial fiber. The model analysis indicates that when actin filaments in growth tend to actively drive the radial fiber to only rotate counter-clockwise, certain amount of passive elastic energy also builds up within the radial fiber upon filament growth, the release of which tends to drive it to rotate clockwise. The competition between these two sources would eventually determine the cellular swirling direction, which can be counter-clockwise or clockwise. The model prediction is in consistency with recent experimental findings. This work provides understanding into how the cellular chirality can be modulated by varied molecular components associated with the cytoskeleton.

The mechanics of mode-III defect initiation and quasi-static growth is examined by analyzing a torqued cylindrical bar separated at its midsection by a nonuniform, nonlinear cohesive interface. The exact analysis is based on the elasticity solution to the problem of a cylinder subjected to nonuniform shear traction at one end and an equilibrating torque at the other. The formulation leads to a pair of interfacial integral equations governing the relative rigid body rotation and the interfacial separation field. The cohesive interface is assumed to be modeled by three Needleman-type traction–separation relations characterized by a shear strength, a characteristic force length and, depending on the specific law, other parameters. Axisymmetric penny, edge, and annular interface defects are modeled by a strength function which varies with radial interface coordinate. Infinitesimal strain equilibrium solutions are sought by eigenfunction approximation of the solution of the governing interfacial integral equations. Results show that for increasing remote torque, at small values of force length, brittle behavior occurs that corresponds to sharp crack growth. At larger values of force length, ductile response occurs similar to a linear “spring” interface. Both behaviors ultimately give rise to the failure of the interface. Results for the stiff, strong interface under a small applied torque show excellent agreement with the static fracture mechanics solution of Benthem and Koiter (1973, “Asymptotic Approximations to Crack Problems,” Mechanics of Fracture, Vol. 1, G.C. Sih, ed., Noordhoff, Leyden, pp. 131–178) for the edge cracked, torsionally loaded cylindrical bar. Extensions of the theory are carried out for (i) the bi-cylinder problem and (ii) the decohesive, frictional interface problem.

The shear stress–strain response of an aluminum alloy is measured to a shear strain of the order of one using a pure torsion experiment on a thin-walled tube. The material exhibits plastic anisotropy that is established through a separate set of biaxial experiments on the same tube stock. The results are used to calibrate Hill's quadratic anisotropic yield function. It is shown that because in simple shear the material axes rotate during deformation, this anisotropy progressively reduces the material tangent modulus. A parametric study demonstrates that the stress–strain response extracted from a simple shear test can be influenced significantly by the anisotropy parameters. It is thus concluded that the material axes rotation inherent to simple shear tests must be included in the analysis of such experiments when the material exhibits anisotropy.

To take into account the flexibility resulting from sectional deformations of a thin-walled box beam, higher-order beam theories considering warping and distortional degrees of freedom (DOF) in addition to the Timoshenko kinematic degrees have been developed. The objective of this study is to derive the exact matching condition consistent with a 5-DOF higher-order beam theory at a joint of thin-walled box beams under out-of-plane bending and torsion. Here we use bending deflection, bending/shear rotation, torsional rotation, warping, and distortion as the kinematic variables. Because the theory involves warping and distortion that do not produce any force/moment resultant, the joint matching condition cannot be obtained just by using the typical three equilibrium conditions. This difficulty poses considerable challenges because all elements of the 5 × 5 transformation matrix relating the field variables of one beam to those in another beam should be determined. The main contributions of the investigation are to propose additional necessary conditions to determine the matrix and to derive it exactly. The validity of the derived joint matching transformation matrix is demonstrated by showing good agreement between the shell finite element results and those obtained by the present box beam analysis in various angle box beams.

A helical spring that is constrained to no rotation has a compliance that is typically more than 95% of the compliance of springs constrained to free rotation when restricted to symmetric wires made from materials with Poisson’s ratio between 0 and 1/2. It is shown that the shape of the spring wire can be designed so the spring will not twist when it is extended nor extend when it is twisted. The constrained spring versus a freely rotating spring with the helix angle equal to π / 4 has the largest reduction in compliance in the limits of beam theory. Spring compliances for torsion and extension with quite complex helical spring geometries are found to be related by a dimensionless ratio of compliances in a very simple equation that only depends on Poisson’s ratio and the helical, spring angle, ψ . Springs made from materials with negative Poisson’s ratio, however, can have a very substantial reduction in compliance; the no rotation compliance is zero when Poisson’s ratio is −1. There are large changes in spring compliances for springs with geometric coils that are elongated rectangles or flattened ellipses.

For one-dimensional quasi-crystals, the refined theory of thick plates is explicitly established from the general solution of quasi-crystals and the Luré method without employing ad hoc stress or deformation assumptions. For a homogeneous plate, the exact equations and solutions are derived, which consist of three parts: the biharmonic part, the shear part, and the transcendental part. For a nonhomogeneous plate, the exact governing differential equations and solutions under pure normal loadings and pure shear loadings, respectively, are obtained directly from the refined plate theory. In an illustrative example, explicit expressions of analytical solutions are obtained for torsion of a rectangular quasi-crystal plate.

This work deals with refined theories for beams with an increasing number of displacement variables. Reference has been made to the asymptotic and axiomatic methods. A Taylor-type expansion up to the fourth-order has been assumed over the section coordinates. The finite element governing equations have been derived in the framework of the Carrera unified formulation (CUF). The effectiveness of each expansion term, that is, of each displacement variable, has been established numerically considering various problems (traction, bending, and torsion), several beam sections (square, annular, and airfoil-type), and different beam slenderness ratios. The accuracy of these theories have been evaluated for displacement and stress components at different points over the section and along the beam axis. Error-type parameters have been introduced to establish the role played by each generalized displacement variable. It has been found that the number of terms that have to be retained for each of the considered beam theories is closely related to the addressed problem; different variables are requested to obtain accurate results for different problems. It has, therefore, been concluded that the full implementation of CUF, retaining all the available terms, would avoid the need of changing the theory when a problem is changed (geometries and/or loading conditions), as what happens in most engineering problems. On the other hand, CUF could be used to construct suitable beam theories in view of the fulfillment of prescribed accuracies.

Based on the finite-deformation shell theory for carbon nanotubes established from the interatomic potential and the continuum model for van der Waals (vdW) interactions, we have studied the buckling of double-walled carbon nanotubes subjected to compression or torsion. Prior to buckling, the vdW interactions have essentially no effect on the deformation of the double-walled carbon nanotube. The critical buckling strain of the double-wall carbon nanotubes is always between those for the inner wall and for the outer wall, which means that the vdW interaction decelerates buckling of one wall at the expenses of accelerating the buckle of the other wall.

A random mass of loose fibers interacting by fiber-fiber contact is considered. As proposed in a previous paper, the elastic response is modeled based on the statistical mechanics of bending and torsion of fiber segments between fiber-fiber contact points. Presently we show how the statistical approach can be used to account for a distribution of fiber diameters rather than just a single diameter. The resulting expression has the same form and the same set of parameters as its single-diameter counterpart, except for two dimensionless reduction factors, which depend on the fiber diameter distribution only and reduce to unity for monodisperse fibers. Uniaxial compressibility experiments are performed on several materials with different bimodal fiber diameter distributions and are compared to model predictions. Even though no additional parameters were introduced to model the effect of mixed fiber diameters, the behavior is accurately predicted. Notably, the effect of the nonuniform fiber diameter is strong: A mixture of two fiber diameters differing by a factor of 2 can reduce the response by an order of magnitude, compared to the case of uniform diameter.

A finite element dynamic instability analysis of stiffened shell panels with cutout subjected to uniform in-plane harmonic edge loading along the two opposite edges is presented in this paper. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the shell panels and the stiffeners, respectively. As the usual formulation of degenerated beam element is found to overestimate the torsional rigidity, an attempt has been made to reformulate it in an efficient manner. Moreover the new formulation for the beam element requires five degrees of freedom per node as that of shell element. Bolotin method is applied to analyze the dynamic instability regions. Numerical results of convergence studies are presented and comparison is made with the published results from literature. The effects of various parameters such as shell geometry, radius of curvature, cutout size, stiffening scheme, and dynamic load factors are considered in dynamic instability analysis of stiffened shell panels with cutout. The free vibration and static stability (buckling) results are also presented. With the consideration of radius of curvatures the panels reduce from deep shell case to shallow shell case and finally become flat plate.

A theoretical study of a slender engineering structure with lateral and angular deflections is investigated under the action of flow-induced vibrations. This aero-elastic instability excites and couples the system’s bending and torsion modes. Semiactive means due to open-loop parametric excitation are introduced to stabilize this self-excitation mechanism. The parametric excitation mechanism is modeled by time-harmonic variation in the concentrated mass and/or moment of inertia. The conditions for full suppression of the self-excited vibrations are determined analytically and compared with numerical results of an example system. For the first time, example systems are presented for which parametric antiresonance is established at the parametric combination frequency of the sum type.

In this work, the classic theory of Timoshenko beams is revisited using screw theory. The theory of screws is familiar from robotics and the theory of mechanisms. A key feature of the screw theory is that translations and rotations are treated on an equal footing and here this means that bending, torsion, and extensions can all be considered together in a particularly simple manner. By combining forces and torques into a six-dimensional vector called a wrench, Hooke’s law for the Timoshenko beam can be written in a very simple form. From here simple expressions can be found for the kinetic and potential energy densities of the beam. Hence equations of motion for small vibrations of the beam can be easily derived. The screw theory also leads to a new understanding of the boundary conditions for beams. It is demonstrated that simple boundary conditions are closely related to mechanical joints. In order to set up the boundary conditions for a beam attached to a joint, a system of wrenches dual to the screws representing the freedoms of the joint must be found. Finally, a screw version of the Rayleigh–Ritz numerical method is introduced. An example is investigated in which the boundary conditions on the beam lead to vibrational modes of the beam involving bending, torsion, and extension at the same time.

Based on the finite-deformation shell theory for carbon nanotubes established from the interatomic potential in Part I of this paper, we have studied the instability of carbon nanotubes subjected to different loadings (tension, compression, internal and external pressures, and torsion). Similar to the conventional shells, carbon nanotubes may undergo bifurcation under compression/torsion/external pressure. Our analysis, however, shows that carbon nanotubes may also undergo bifurcation in tension and internal pressure, though the bifurcation modes for tension and compression are very different, and so are the modes for the internal and external pressures. The critical load for instability and bifurcation depends on the interatomic potential used.

Of particular interest is the experimental study of the complex dynamic plastic buckling of circular metallic shells and their energy absorption capacity. Initially proposed by Baleh and Abdul-Latif (2006), “Quasi-Stalic Biaxial Plastic Buckling of Tubular Structures used as an Energy Absorber,” ASME J. Appl. Mech., 74, pp. 638–635 , the novel idea, which aims to enhance the strength properties of materials, is extended for studying the biaxial plastic dynamic buckling behavior of circular shells. It can be assumed that changes in local deformation mechanisms, which reflect this enhancement in the strength properties, are mainly governed by the loading path complexity. The question of whether the performance of dynamic axially crushed tubes could be further improved by using the developed device (the absorption par compression-torsion plastique (ACTP)) generating a biaxial loading path (combined compression and torsion) from a uniaxial loading. A key point emerging from this study is that the structure impact response (i.e., the plastic flow mechanism and the absorbed energy) is influenced by the loading rate coupled with the biaxial loading complexity. In this study, three different metallic circular shells made from copper, aluminum, and mild steel, having distinct geometrical parameters, are extensively investigated. The obtained results show that the higher the biaxial loading complexity provided by the ACTP applied, the greater the energy absorbed by the copper, aluminum, and mild-steel structures. Thus, it is easy to demonstrate that the enhancement in the energy absorption, notably in the case of aluminum, is higher than 150%, in favor of the most complicated loading path (i.e., biaxial 45 deg case) compared to the classical uniaxial case. Moreover, the deformation mode for the tested materials is slightly sensitive to the torsion amplitude in dynamic loading, contrary to the quasistatic one.

Background . Many papers on the elastic stability of both thin-walled and massive (three-dimensional) bodies regard the bifurcation of equilibrium in the case of compressive loads. Although, the elastic instability may also occur under tensile stresses. Method of Approach . In the present paper on the basis of three-dimensional equations of the nonlinear elasticity the instability of a stretched infinite hollow cylinder under torsion and inflation is investigated. The bifurcational method of stability analysis is used. Results . The critical surfaces and stability region in the space of loading parameters are defined for a Biderman material and special model of incompressible medium, which possess essential material nonlinearity. The influence of a wall thickness on the instability of a hollow cylinder is analyzed. Conclusions . Based on the obtained results, a simple and efficient practical criterion of stability under tension is formulated. This criterion can be represented in the form of the Drucker postulate, given in terms of external loads.

The paper is devoted to formulation and analysis of a new model of structural fatigue that is a direct extension of the model of contact fatigue developed by Kudish (2000, STLE Tribol. Trans., 43, pp. 711–721 ). The model is different from other published models of structural fatigue ( Collins, J. A., 1993, Failure of Materials and Mechanical Design: Analysis, Prediction, Prevention, 2nd ed., Wiley, New York ) in a number of aspects such as statistical approach to material defects, stress analysis, etc. The model is based on fracture mechanics and fatigue crack propagation. The model takes into account local stress distribution, initial statistical distribution of defects versus their size, crack location, and orientation, and material fatigue resistance parameters. The assumptions used for the new model derivation are stated clearly and their validity is discussed. The model considers the kinetics of crack distribution by taking into account the fact that the crack distribution varies with the number of applied loading cycles due to crack growth. A qualitative and quantitative parametric analysis of the model is performed. Some analytical formulas for fatigue life as a function of the initial defect distribution, material fatigue resistance, and stress state are obtained. Examples of application of the model to predicting fatigue of beam bending and torsion and contact fatigue for tapered bearings is presented.

A theory is presented for the rate modeling of flexible granular solids based on affine average motion of interparticle contacts. We allow contacts to form and break continually but assume the existence of a finite friction coefficient rendering contacts force free as they form or break. The resulting constitutive equations are of the hypoelastic type. A specific model for the deformation of a fiber mass is then developed. The model improves on previous theories for fiber masses in at least two respects: First, it is more general in that it is not restricted to uniaxial compression, although it is restricted to predominantly compressive deformations histories, due to neglect of frictional dissipation. Second, by allowing torsion as well as bending of fibers, this theory covers a larger deformation range. Compression experiments are performed on carded slivers of PA6 fibers under various conditions. The measured response is found to be in close agreement with that predicted by the model.

In this paper, consideration is given to the dynamic response of a rotating cantilever twisted and inclined airfoil blade subjected to contact loads at the free end. Starting with the basic geometrical relations and energy formulation for a rotating Timoshenko beam constrained at the hub in a centrifugal force field, a system of coupled partial differential equations are derived for the combined axial, lateral and twisting motions which includes the transverse shear, rotary inertia, and Coriolis effects, as well. In the mathematical formulation, the torsion of the thin airfoil also considers a very general case of shear center not being coincident with the CG (center of gravity) of the cross section, which allows the equations to be used also for analyzing eccentric tip-rub loading of the blade. Equations are presented in terms of axial load along the longitudinal direction of the beam which enables us to solve the dynamic pulse buckling due to the tip being loaded in the longitudinal as well as transverse directions of the beam column. The Rayleigh–Ritz method is used to convert the set of four coupled-partial differential equations into equivalent classical mass, stiffness, damping, and gyroscopic matrices. Natural frequencies are computed for beams with varying “slenderness ratio” and “aspect ratio” as well as “twist angles.” Dynamical equations account for the full coupling effect of the transverse flexural motion of the beam with the torsional and axial motions due to pretwist in the airfoil. Some transient dynamic responses of a rotating beam repeatedly rubbing against the outer casing is shown for a typical airfoil with and without a pretwist.

Effective viscoelastic response of a unidirectional fiber composite with interfaces that may separate or slip according to uniform Needleman-type cohesive zones is analyzed. Previous work on the solitary elastic composite cylinder problem leads to a formulation for the mean response consisting of a stress-strain relation depending on the interface separation∕slip discontinuity together with an algebraic equation governing its evolution. Results for the fiber composite follow from the composite cylinders representation of a representative volume element (RVE) together with variational bounding. Here, the theory is extended to account for viscoelastic matrix response. For a solitary elastic fiber embedded in a cylindrical matrix which is an n th -order generalized Maxwell model in shear relaxation, a pair of nonlinear n th -order differential equations is obtained which governs the relaxation response through the time dependent stress and interface separation∕slip magnitude. When the matrix is an n th -order generalized Kelvin model in shear creep, a pair of nonlinear n th -order differential equations is obtained governing the creep response through the time dependent strain and interface separation∕slip magnitude. We appeal to the uniqueness of the Laplace transform and its inverse to show that these equations also apply to an RVE with the composite cylinders microstructure. For a matrix, which is a standard linear solid ( n = 2 ) , the governing equations are analyzed in detail paying particular attention to issues of bifurcation of response. Results are obtained for transverse bulk response and antiplane shear response, while axial tension with related lateral Poisson contraction and transverse shear are discussed briefly. The paper concludes with an application of the theory to the analysis of stress relaxation in the pure torsion of a circular cylinder containing unidirectional fibers aligned parallel to the cylinder axis. For this problem, the redistribution of shear stress and interface slip throughout the cross section, and the movement of singular surfaces, are investigated for an interface model that allows for interface failure in shear mode.