Three-dimensional stress analysis of textile composites: Part I. Numerical analysis

ObjectivesTo study the problem of determining the degree of stress at the apex of a wedge-shaped area in cases where the sides (or one of them) are covered with a thin flexible coating.MethodIt is assumed that the coating is not stretchable. On the other side of the wedge-shaped area, the same coating is assumed to be present; it is either fixed, stress-free or in smooth contact with a rigid base. Mathematically, the problem is reduced to the task of determining the roots of characteristic transcendental equations arising from the existence of a nontrivial solution to the system of linear homogeneous equations.ResultsValues for the specific characteristics of the radial component of a stress tensor are determined for different combinations of boundary conditions and solution angles. In particular, the angles at which the singular behaviour of stresses occurs are determined. The case is considered when a special boundary condition is given on the edge surface, simulating the overlay. Characteristic equations are obtained to determine the index of the degree dependency of the asymptotic solution in its vicinity for four variants of boundary conditions. In two cases, transcendental equations are obtained, which are solved numerically.ConclusionCalculations of the first positive roots of the equations depending on the angle of the edge solution and Poisson's ratio are presented. The values of the angles, at which the singular behaviour of stresses occurs, are determined. In the case of a combination of boundary conditions (III – IV), the singular stress behaviour is observed for the angle ???? = ????/8, while in the case of (III – III) this value is equal to ????/4.

A static laminated plate theory based on an assumed piecewise linear through-the-thickness in-plane stress distribution has been extended to include inertia effects. Based on this in-plane stress distribution assumption, outof-plane shear and normal stress component distributions were derived from the three-dimensional equations of motion, resulting in six nonzero stress components. Hamilton's variational principle was used to derive the plate equations of motion, the plate constitutive relationships, and the interface continuity equations. The governing equations were written in a form that is self-adjoint with respect to the convolution bilinear mapping. The resulting system of equations for a single lamina consists of 25 field equations in terms of 9 weighted displacement field variables, 10 stress and moment resultant field variables, and 6 out-of-plane shear and normal stress boundary field variables. For the laminated system, the mixed formulation enforces both traction and displacement continuity at lamina interfaces as it satisfies layer equilibrium. A finite element formulation based on a specialized form of the governing functional was developed. The method is illustrated with results of a free vibration analysis of sandwich and homogeneous plates for which exact solutions are available.

Theoretical aspects of fracture mechanics

The interlaminar stress components can cause delamination (separation of laminae), resulting in the failure of material before its elastic limit. Thus, the accurate prediction of the stress components in the composite laminates is vital for the prediction of onset and progress of delamination. Our aim is to analytically arrive at a close approximation solution for interlaminar stress components using recovery relations through 1-D analyses. In this study, the development of an efficient analytical approach to obtain the 3-D elasticity solutions by using recovery relations is achieved. In order to get these stress components accurately, a procedure combining VAM-based framework with approximation method is developed. The approximate method is based upon the stress distribution from more appropriate, sophisticated, and simple polynomials on the equilibrium equation of elasticity. The resulting solution satisfies all the boundary conditions and the compatibility. A parametric study is carried out to understand the nature of 3-D stress components along the thickness of various symmetric, quasi-isotropic, and antisymmetric stacking sequences by this approach. The effectiveness of our approach is demonstrated by comparing the results for interlaminar normal and shear stress components along the interface and through the thickness near free edge under axial strain with those of the available in literature and 3-D FEM for the symmetric, antisymmetric, angle-ply, and cross-ply laminates. This newly described approach shows a good agreement and the computational efficiency. This approach effectively predicts the 3-D stress components with great time-saving.

Stress intensity factors for spot welds between plates of unequal thickness

Introduction. Checking the soil of the subgrade and the layers of road pavement made of loosely cohesive materials by shear resistance is one of the three mandatory conditions for calculating road clothing according to strength criteria. The methodology for checking the soil of the subgrade and the sandy layers of the road pavement is constantly being modified, which is why changes concerning certain calculation details appear in each new version of the regulatory document. The purpose of this work is to analyze the advantages of the classical solution of A.M. Krivissky and to reveal the essence of the errors made in subsequent modifications of this calculation.Materials and methods. The analysis of solutions is carried out from the standpoint of compliance with the basics of mechanics. It is shown that the calculation of the total shear stress in the classical solution of A.M. Krivissky is performed in accordance with the principle of force superposition, which consists in calculating the components of the stress tensor from each force (time load and the own weight of the layer materials) separately, followed by summing the corresponding components. In this case, the active shear stresses from the temporary load and the own weight of the materials are calculated as the equivalent stress of the Mohr-Coulomb criterion. The calculation of these two components of the total shear stress is performed at the same value of the internal friction angle. Since the angle of inclination of the sliding surface to the main axes is determined by the sum or difference of 45 degrees and half of the internal friction angle, the tangential and normal stresses, which are components of the active shear stress, both from the temporary load and the own weight of the materials, are determined for the same shear surface rotated to the main axes at the same angle. In the current normative calculations, the active shear stresses from the temporary load and the own weight of the materials are determined at different angles of internal friction. This means that the active shear stresses from the temporary load and the own weight of the materials act on two different shear surface rotated to the main axes at different angles. Such stresses cannot be summed up or compared with each other. In addition to this error of the normative calculation methods, their other disadvantages are given.Results. As a result of a detailed analysis of the known modifications of the classical solution, obvious contradictions to the principles of continuum mechanics are established. As an alternative to modern calculation criteria for shear resistance, the article presents criteria for soil strength in which the shear stress exceeds the equivalent stress in the Mohr-Coulomb criterion. The principle of deducing formulas for calculating the first critical load and the total shear stress from the strength criteria under consideration is shown.Conclusion. Conclusions are drawn about the need to return to the classical solution obtained by specialists of the Leningrad School of the USSR, or to develop a fundamentally new solution based on a new plasticity condition in which the total shear stress exceeds the similar characteristic of the stress state of the original Mohr - Coulomb criterion.

Fluvial bank erosion rates are often quantified by assuming that the erosion rate is a function of the excess (above a critical threshold) boundary shear stress applied by the flow. Research has shown that the form roughness induced by natural topographic bank features, such as slumps, spurs and embayments, is the dominant component of the spatially‐averaged total shear stress, meaning that form roughness provides an important control on bank erosion rates. However, measuring the relative components of the total shear stress for a natural system is not straightforward. In this work we use the method of Kean and Smith to partition the form and skin drag components of river bank roughness using a time series (2005–2011) of high‐resolution topographic surveys of an eroding bank of the Cecina River in central Italy. This method approximates the form drag component of the roughness along a longitudinal bank profile as a series of user‐defined Gaussian curves. The extracted metrics are used in conjunction with an estimate of the outer region flow velocity to partition the form and skin drag components of the total boundary shear stress according to the Kean and Smith analytical solution. The relative magnitude of the form and skin shear stress at each survey date is analysed alongside DEMs of difference to reveal that intense episodes of erosion are followed by periods of quiescence. We show that this is due to the protection offered by increased form drag roughness following erosion. We conceptualise the dynamic feedbacks that exist between river discharge, bank erosion processes and bank form roughness, into a simple model of the self‐limiting nature of river bank erosion. Copyright © 2015 John Wiley & Sons, Ltd.

The singular behaviour at the free edges of the fibre-matrix interface is analysed for the fibre push-out test geometry based on the boundary element method. The fibre push-out test has been extensively used to measure the fibre-matrix interfacial properties in polymer, ceramic and metal matrix composites. There are two free edges in the fibre push-out specimen: one is at the loaded fibre end and the other at the supported fibre end. The singular stresses can be expressed as a function of singular exponent and singular stress intensity. It is shown that the singular exponents obtained at both fibre ends are characteristic of composite constituent properties, such as Young's moduli of fibre and matrix, and does not vary with specimen dimensions. The singular exponents are real and identical for the shear and radial stress components at fibre ends where the wedge angles are the same. The singular stress intensities are also implicit in material properties, and vary with specimen dimensions, such as fibre to matrix radius ratio, fibre aspect ratio and support hole size. An interfacial failure criterion is proposed here based on the average stress concept to determine the critical singular stress intensities in mode I and mode II loads.

Nonlocal hcp kernel functions based on ab initio calculations: Pertinent dislocation problems revisited

Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior in solid mechanics, only of late has there been much in the way of corresponding identifications of flow-induced stress singularities in fluid mechanics. These recent asymptotic identifications are for a single incompressible viscous fluid: Here the asymptotic approach is extended to apply to a configuration entailing two such fluids. For this configuration, various specifications leading to power or log singularities are determined. These results demonstrate that flow-induced stress singularities can occur in a structural container at a location where no singularities are identified within solid mechanics alone.

In order to explore the nature of cyclic loading in seabed soil deposits due to travelling waves, an analysis was made to determine the stresses in an elastic half-space subjected to continuously distributed sinusoidal loads on the surface. The result of the analysis showed that the cyclic loading generates an alternate changeover of two components of shear stresses, i. e., the horizontal shear stress and the stress difference between the vertical normal stress and horizontal normal stresses. It was further shown that the alternate changeover in stresses as above takes place in such a way that the principal stress axes continuously rotates while holding the deviator stress (difference between two principal stresses) at a constant level. In an attempt to simulate the actual stress conditions as above, a triaxial torsion shear test apparatus was manufactured, and controlled combinations of torsional and vertical stresses were applied so that the same nature of cyclic loads as described above could be applied to hollow cylindrical sand specimens prepared in the test apparatus. The test results showed that, even when the amplitude of the combined shear stress (deviator stress) is maintained constant, the plastic deformation as represented by the pore water pressure build-up could take place in the sand, if the rotation of the principal stress axes is executed during the cyclic loading test, and consequently the cyclic strength of sand is reduced, as compared to the cyclic strength obtained from the conventional type of cyclic triaxial test apparatus.

The endothelium is a single cell layer that plays a critical role in determining the health and function of blood vessels. Endothelial function is shaped by shear stress, the frictional force exerted by the speed of blood flow, and the thickness (viscosity) of the blood. Exposure to shear stress that reverses direction back-and-forth impairs endothelial function in young men. Whether women are equally susceptible to this perturbation and the isolated impact of a low level of shear stress with and without reversal of shear had not been investigated. Hypoxia, the low levels of oxygen that are experienced at high altitude, has been shown to influence flow reversal and impair endothelial function. However, no previous study had accounted for the changes in blood thickness, and hence shear stress that occur at high altitude. This may be especially important in the context of excessive erythrocytosis, a high-altitude disease characterized by exceptionally thick blood and increased cardiovascular risk. This thesis examined (i) whether there are sex differences in the impact of exposure to low and reversing shear stress on endothelial function; (ii) whether isolated low shear stress impairs endothelial function; (iii) the impact of reversing shear stress on endothelial function in short-term exposure to low levels of oxygen and after trekking to 5050 m in the Himalayas; and (iv) the role of high levels of blood viscosity on endothelial function in high-altitude natives in Cerro de Pasco, Peru (4330 m), with excessive erythrocytosis. We identified that (i) premenopausal women have some protection against reductions in endothelial function after being exposed to reversing shear stress; (ii) isolated low shear stress impaired endothelial function; (iii) short-term exposure to low levels of oxygen and sustained high-altitude exposure reduced endothelial function, while superimposing reversing shear stress had no effect; and (iv) high levels of hemoglobin and blood viscosity contributed to lower endothelial function in Andean high-altitude natives with excessive erythrocytosis. Altogether, this dissertation advances our understanding of how the components of shear stress (the pattern, magnitude, and blood viscosity) impact endothelial function in humans under normoxic (normal levels of oxygen) and hypoxic (low levels of oxygen, such as high-altitude) conditions.

In this work, we present a new solution representation for the Helmholtz transmission problem in a bounded domain in ℝ2with a thin and periodic layer of finite length. The layer may consists of a periodic pertubation of the material coefficients or it is a wall modelled by boundary conditions with an periodic array of small perforations. We consider the periodicity in the layer as the small variableδand the thickness of the layer to be at the same order. Moreover we assume the thin layer to terminate at re-entrant corners leading to a singular behaviour in the asymptotic expansion of the solution representation. This singular behaviour becomes visible in the asymptotic expansion in powers ofδwhere the powers depend on the opening angle. We construct the asymptotic expansion order by order. It consists of a macroscopic representation away from the layer, a boundary layer corrector in the vicinity of the layer, and a near field corrector in the vicinity of the end-points. The boundary layer correctors and the near field correctors are obtained by the solution of canonical problems based, respectively, on the method of periodic surface homogenization and on the method of matched asymptotic expansions. This will lead to transmission conditions for the macroscopic part of the solution on an infinitely thin interface and corner conditions to fix the unbounded singular behaviour at its end-points. Finally, theoretical justifications of the second order expansion are given and illustrated by numerical experiments. The solution representation introduced in this article can be used to compute a highly accurate approximation of the solution with a computational effort independent of the small periodicityδ.

An efficient iterative solver and high-resolution computations of the Oldroyd-B fluid flow past a confined cylinder

Failure of an electronic package generally initiates from the interface corners, due to the stress and strain singular behaviors near the corners. Since the solder materials are viscous elastic and even maybe viscous plastic, the singular behavior near the solder joint corner is thereby time-dependent, and is quite different from that of an elastic one. It is necessary to clarify such a singular behavior for the strength and life evaluation of an electronic package. This paper firstly has deduced the approximated viscous elastic singular fields theoretically based on the principle of correspondence and the Laplace transformation techniques, and secondly has investigated the viscous plastic singular behavior of an elastic-plastic interface corner by the analogue method; finally the numerical analysis of an electronic package has been carried out to show the details of the singular behaviors.