Normal Stress Components Research Articles

Slow Motion of a Porous Sphere Translating Along the Axis of a Circular Cylindrical Pore Subject to a Stress Jump Condition

The coupled flow problem of an incompressible axisymmetrical quasisteady motion of a porous sphere translating in a viscous fluid along the axis of a circular cylindrical pore is discussed using a combined analytical–numerical technique. At the fluid–porous interface, the stress jump boundary condition for the tangential stress along with continuity of normal stress and velocity components are employed. The flow through the porous particle is governed by the Brinkman model and the flow in the outside porous region is governed by Stokes equations. A general solution for the field equations in the clear region is constructed from the superposition of the fundamental solutions in both cylindrical and spherical coordinate systems. The boundary conditions are satisfied first at the cylindrical pore wall by the Fourier transforms and then on the surface of the porous particle by a collocation method. The collocation solutions for the normalized hydrodynamic drag force exerted by the clear fluid on the porous particle is calculated with good convergence for various values of the ratio of radii of the porous sphere and pore, the stress jump coefficient, and a coefficient that is proportional to the permeability. The shape effect of the cylindrical pore on the axial translation of the porous sphere is compared with that of the particle in a spherical cavity; it found that the porous particle in a circular cylindrical pore in general attains a lower hydrodynamic drag than in a spherical envelope.

Fracture strength analysis of single-crystalline silicon cantilevers processed by focused ion beam

The fracture strength properties of single-crystalline Si micro-components fully processed via focused ion beam were successfully evaluated by an in situ nano-mechanical testing system. Fracture initiation of all tested specimen was completely brittle within the detection limit of the testing system. By using different types of cantilever specimens (smooth/notched), it was suggested that the fracture initiation along the {111} plane was controlled primarily by the critical normal stress component regardless of the magnitude of shear stress component. The average strength value for FIB-processed specimens (σc=8.1GPa) was found to be approximately the same as that of wet-etch-processed specimens while larger than that of dry-etch-processed specimens.

A phenomenological closure model of the normal dispersive stresses

[1] The spatial averaging of the momentum equation in obstructed environments generates dispersive stress terms that represent momentum flux induced by the spatial heterogeneity of the time-averaged flow. While previous studies ignored the dispersive stresses, recent evidences indicate that they may be significant, in particular within entry flow regions such as the leading edge of submerged vegetation in rivers and streams. The lack of available closure models makes it almost impossible to include the dispersive stresses in canopy flow models. Based on observations and theoretical considerations, we propose to model the normal component of the dispersive stress as a function of square of the double-averaged velocity. The model was tested by detailed particle image velocimetry measurements that were obtained inside and around a modeled vegetation patch, made of randomly distributed vertical thin glass plates. It was found that the normal dispersive stresses are scaled with two parameters: the relative area covered by wakes and the relative magnitude of the recirculation (negative) velocity inside the wake zones. The results indicate that prediction of the dispersive stresses is more sensitive to the wake area parameterization than that of the recirculation zone velocities. It is therefore concluded that when parameterization of the relative wake area is available, the normal dispersive stresses can be modeled and included in future flow simulations.

A micromechanical approach to volumetric and surface growth in the framework of shape optimization

We herewith adopt the physically and micromechanically motivated point of view that growth (resp. resorption) occurs as the expansion (resp. contraction) of initially small tissue elements distributed within a host surrounding matrix, due to the interfacial motion of their boundary. We postulate that the shape of the tissue element evolves in such a way as to minimize a certain functional amongst all possible admissible shapes. The driving force for the motion of the interface describing the surface growth models at the scale of the growing tissue elements is obtained from the identification of the driving force resulting from the shape derivative of the functional to be minimized. The shape derivative expresses as a surface integral involving the surface growth velocity and a conjugated driving force, in line with Hadamard’s structure theorem. Focusing on the total potential energy, the motion of the interface is described within the framework of gradient flows, whereby the interfacial velocity is related to a driving force identified to the jump of the normal component of Eshelby stress at the interface of the growing tissue elements. This formalism is exemplified in the situation of the avascular growth of spheroidal tumors and to bone external remodeling. This brings a dual viewpoint to the macroscopic volumetric growth models which consider production of new mass as a hidden mechanism occurring at a smaller scale, and traduced by a local increase of either density or volume. Volumetric growth at a macroscopic scale appears as the averaging of surface growth mechanisms occurring at the microscopic scale of the growing tissue elements.

Thermal residual stresses in in-plane functionally graded clamped hollow circular plates subjected to an edge heat flux

This study carries out the thermal residual stress analyses of functionally graded clamped hollow circular plates for in-plane constant inner and outer edge heat fluxes. The material properties of the functionally graded plates were assumed to vary with a power law along an in-plane direction not through the plate thickness direction. The transient heat conduction and Navier equations describing the two-dimensional thermoelastic problem were discretized using finite difference method, and the set of linear equations were solved using the pseudo singular value method. In order to determine the effect of the plate material properties on the thermal deformation and stress states the circular plates were designed in the way that their material compositions can vary from a pure ceramic (C) outer edge to a pure metal (M) inner edge and vice versa, such as ceramic-to-metal or metal-to-ceramic circular plates. The compositional gradient and direction affected considerably both in-plane temperature levels and heat transfer period whereas similar temperature distributions existed. The displacement components exhibited similar symmetrical distributions and were at lower levels in the metal-rich compositions. The normal strain components had similar distributions to those of the displacement components and were critical around both the inner and outer edges. A metal-rich composition resulted in lower normal strain levels. The equivalent strain distributions were always critical around the heat flux edge and became highest for a ceramic-rich composition. The normal stress components and equivalent stresses were critical in the ceramic-rich regions and the equivalent stress exhibited a sudden increase near the pure ceramic-edge subjected to the heat flux. The lower stress levels were also observed for a metal-rich composition variation. The ceramic material, a good thermal insulator, makes a metal-to-ceramic and a ceramic-to-metal material system suitable for outer and inner edge heat fluxes, respectively in practice. The metal-rich material compositions (with [Formula: see text] and 10.0) can prevent the local cracks in the ceramic-rich regions induced by high heat gradients.

Size Dependence of Residual Thermal Stresses in Micro Multilayer Ceramic Capacitors by Using Finite Element Unit Cell Model Including Strain Gradient Effect

The residual thermal stresses induced by the high-temperature sintering process in multilayer ceramic capacitors (MLCCs) are investigated by using a finite-element unit cell model, in which the strain gradient effect is considered. The numerical results show that the residual thermal stresses depend on the lateral margin length, the thickness ratio of the dielectrics layer to the electrode layer, and the MLCC size. At a given thickness ratio, as the MLCC size is scaled down, the peak shear stress reduces significantly and the normal stresses along the length and thickness directions change slightly with the decrease in the ceramic layer thickness t d as t d > 1 μm, but as t d < 1 μm, the normal stress components increase sharply with the increase in t d. Thus, the residual thermal stresses induced by the sintering process exhibit strong size effects and, therefore, the strain gradient effect should be taken into account in the design and evaluation of MLCC devices

Evaluation of disturbance function for geosynthetic–soil interface considering chemical reactions based on cyclic direct shear tests

Various geosynthetics for reinforcement, protection and encapsulation are widely applied to civil structures and waste landfill sites. The use of geosynthetics inevitably involves the coupled behaviors of different materials which include large displacement and strain-softening behaviors, etc. Current research indicates that the behavior of geosynthetic–soil systems depend on the shear strength of the interface governed by several intrinsic and environmental factors, such as moisture, normal stress, chemical conditions, and thermal components, etc.In this study, the effects of acidity and basicity from leachate and waste are intensively considered in order to build up the chemical reaction mechanism of the shear strength of the interface under cyclic loading based on an experimental inspection. The Multi-Purpose Interface Apparatus (M-PIA) has been newly manufactured, and cyclic direct shear tests for submerged geosynthetic–soil specimens under different chemical conditions have been performed. A Focused Ion Beam (FIB) analysis has also been performed to induce the reason for the variation in the disturbance function and to verify the hypothesis on the decay-proof ability of geosynthetics.Consequently, a new approach to reflect the chemical effect of geosynthetics has been applied by suggesting the use of new disturbance function parameters in the Disturbed State Concept. The basic schematic of the Disturbed State Concept (DSC) constitutive model is employed; then, new disturbance function parameters are proposed to describe the chemical degradation of the geosynthetic–soil interface under dynamic conditions. Furthermore, based on the FIB results, it is be deduced that the variation in the disturbance function mainly results from the different types of decay in the soil minerals.

Combined high-energy synchrotron X-ray diffraction and computed tomography to characterize constitutive behavior of silica sand

The deformation behavior of silica sand particles under one-dimensional (1D) loading compression was investigated using nondestructive 3D synchrotron micro-computed tomography (SMT) and three dimensional X-ray diffraction (3DXRD). High-resolution SMT images were used to monitor particle-to-particle interactions, and the onset and propagation of fracture mechanism in a column composed of three silica sand particles. Particle-averaged lattice strain tensors within individual sand particles were measured using the 3DXRD technique and were then used to calculate the stress tensor components via the general elastic stress–strain relationship. The normal stress component in the axial direction (σzz) exhibited a nearly linear increasing trend in all sand particles. Shear stress components were in general small relative to the normal stress components and displayed no systematic trend. Knowing lattice strains, stresses, and particle kinematic behavior, one can formulate and develop a micromechanics-based constitutive model to fully characterize strength properties and deformation characteristics of granular materials.

Molecular Dynamics Simulation of Tensile Properties of Nano-Layered Materials

Mechanical properties of nanolayered materials were simulated using molecular dynamics method. Elastic modulus was especially focused in this study, and the effect of layer width and the interval of the layers on the deformation behavior were discussed. Tension was imposed by adding a mono-axial strain in the x direction at a constant rate, while the other two normal components of stress were controlled to be zero. The influence of the dimension was preliminarily checked to avoid the model-size dependency, and the suitable size was determined as a cube with 12 unit cells in the x, y and z directions. First, a single nanolayer was set in the model, and the layer width was varied. The obtained elastic modulus showed almost linear dependency with the layer width. Then the interval of the layer was varied, and it revealed that the elastic moduli depend on the cross-sectional ratio of the layered material rather than the layer interval.

Measurements of the budgets of the subgrid-scale stress and temperature flux in a convective atmospheric surface layer

AbstractThe dynamics of the subgrid-scale (SGS) stress and scalar flux in the convective atmospheric surface layer are studied through the budgets of the SGS turbulence kinetic energy (TKE), the SGS stress and the SGS temperature flux using field measurements from the Advection Horizontal Array Turbulence Study (AHATS). The array technique, which employs sensor arrays to perform filter operations to obtain the SGS velocity and temperature, is extended to include pressure sensors to measure the fluctuating pressure, enabling separation of the resolvable- and subgrid-scale pressure, and therefore for the first time allowing for measurement of the pressure covariance terms and the full SGS budgets. The non-dimensional forms of the SGS budget terms are obtained as functions of the stability parameter$z/ L$and the ratio of the wavelength of the spectral peak of the vertical velocity to the filter width,${\Lambda }_{w} / {\Delta }_{f} $. The results show that the SGS TKE budget is a balance among the production, transport and dissipation. The SGS shear stress budget and the SGS temperature flux budgets are dominated by the production and pressure destruction, with the latter causing return to isotropy. The budgets of the SGS normal stress components are more complex. Most notably the pressure–strain-rate correlation includes two competing processes, return to isotropy and generation of anisotropy, the latter due to ground blockage of the large convective eddies. For neutral surface layers, return to isotropy dominates. For unstable surface layers return to isotropy dominates for small filter widths, whereas for large filter widths the ground blockage effect dominates, resulting in strong anisotropy. The results in the present study, particularly for the pressure–strain-rate correlation, have strong implications for modelling the SGS stress and flux using their transport equations in the convective atmospheric boundary layer.

Simple shear under large deformation: Experimental and theoretical analyses

Abstract The aim of the present work is to analyze the simple shear state of an incompressible hyperelastic solid under large deformation by experimental and theoretical approaches. The experimental procedure was performed using a single lap shear test and the displacement fields were determined by the Digital Image Correlation method. The applied force and the measured angular distortion were used to evaluate the shear stress and the amount of shear. Hence, a nonlinear stress-strain response was achieved. In addition, the normal stress components were obtained from the experimental data by assuming two hypotheses: the first one was based on a plane stress condition, while the normal component of the traction on the inclined surfaces was assumed to be zero on the second. Finally, to verify the presented results, the initial shear modulus of the hyperelastic material was estimated and compared with the value obtained using the data from a planar tensile test. The Lopez-Pamies strain energy function was used in the inverse analysis in order to estimate the material property, which was similar for both experimental tests.

Bolt support mechanism based on elastic theory

Mechanical model of anchorage surrounding rock considering tray effect was established based on elastic theory, in order to study the mechanism of bolt supporting. Elastic solutions of normal force at point in the interior of a semi-infinite solid were obtained by means of classical displacement function method in elasticity. The factors which influence stress of bolted surrounding rock, such as the length of bolt and tray effect, were analyzed. The absolute value of stress along bolt axes decreased rapidly with an increase in radical distance and the maximum appeared near ends of bolt. With increasing radical distance, the value of radical stress changed from positive to negative roughly and then increased to zero, with maximum at the middle of bolt. The evolution of hoop stress as radical distance increasing was similar with stress along bolt axes. With an increase in depth, the radical effect ranges of all normal stress components were reduced. These suggest that the effect from tray on stress along bolt axes of bolted surrounding rock could be neglected, except near surface of surrounding rock.

Transient wave propagation in non-homogeneous viscoelastic media

Propagation of transient pressure waves in nonhomogeneous viscoelastic media with a cylindrical hole of circular cross section is investigated by employing the theory of propagating surfaces of discontinuities. The non-homogeneities are assumed to depend on the radial distance from the axis of the cylindrical hole. The solutions for the normal stress components and the radial particle velocity are expressed as Taylor series expansions about the time of arrival of the wave front. Two types of boundary conditions are considered. The wall of the cylindrical hole is either subjected to uniform pressure or to uniform radial particle velocity both of which have arbitrary dependence on time. Then the solutions are reduced to the special case of homogeneous viscoelastic media. Numerical computations are carried out for a homogeneous standard linear solid and for a uniform pressure with a step distribution in time applied at the wall of the hole. These numerical results are compared with those obtained previously by other investigators who have employed the method of characteristics.

A triaxial tactile sensor without crosstalk using pairs of piezoresistive beams with sidewall doping

This paper reports on a triaxial tactile sensor using piezoresistive beams. The sensor chip is composed of two pairs of sidewall-doped Si beams for shear stress sensing and one pair of surface-doped Si beams for normal stress sensing. The sizes of the shear- and pressure-sensing beams are 180μm×15μm×20μm and 250μm×50μm×20μm (length×width×thickness), respectively. The sensor chip is embedded in a PDMS sheet 10mm×10mm×2mm in size. Because the simple beam structure can be fabricated easily, the proposed sensor is compatible with semiconductor device fabrication. The fabricated sensor was evaluated for normal and shear stress (0–400kPa and 0–100kPa, respectively). The responses of the corresponding beam pairs were found to be proportional to the magnitude of the applied stresses without the influence of the other stresses. The relationship between the angle of shear stress and the responses of each beam pair was also evaluated. Each beam pair detects only one axis's shear stress and showed little reaction to the other axes’ shear stress. As a result, the proposed sensor can measure the three axial components of normal and shear stress independently.

Residual stresses in laser welded ASTM A387 Grade 91 steel plates

Residual stresses in 9mm thick ASTM A387 Grade 91 steel plates, joined using constant power (8kW) low and high heat input laser welding processes, are characterised using neutron diffraction. The measured longitudinal and normal components of residual stress show a bimodal distribution across the welded joint with a low tensile or compressive trough at the weld centre flanked by high magnitude tensile peaks in parent metal adjacent to the heat affected zone boundaries. The width of the central trough and spread of the outboard tensile zones are significantly greater for the high heat input weld. In both cases, the stress distributions can be explained by the strains associated with the austenite to martensite solid-state transformation as the joint cools after welding.

Stokes flow past an assemblage of axisymmetric porous spherical shell-in-cell models: effect of stress jump condition

The quasisteady axisymmetrical flow of an incompressible viscous fluid past an assemblage of porous concentric spherical shell-in-cell model is studied. Boundary conditions on the cell surface that correspond to the Happel, Kuwabara, Kvashnin and Cunningham/Mehta-Morse models are considered. At the fluid-porous interfaces, the stress jump boundary condition for the tangential stresses along with continuity of normal stress and velocity components are employed. The Brinkman’s equation in the porous region and the Stokes equation for clear fluid are used. The hydrodynamic drag force acting on the porous shell by the external fluid in each of the four boundary conditions on the cell surface is evaluated. It is found that the normalized mobility of the particles (the hydrodynamic interaction among the porous shell particles) depends not only on the permeability of the porous shells and volume fraction of the porous shell particles, but also on the stress jump coefficient. As a limiting case, the drag force or mobility for a suspension of porous spherical shells reduces to those for suspensions of impermeable solid spheres and of porous spheres with jump.

Naturally Accepted Boundary Conditions for the Brazilian Disc Test and the Corresponding Stress Field

The stress field developed in the Brazilian disc is determined assuming that the disc is under the influence of a combination of two load distributions, namely normal (radial)- and shear (frictional)-stresses, both of them acting along two finite symmetric arcs of the disc periphery. The nature of the two distributions as well as the extent of the loaded arcs are obtained from the solution of the respective contact problem according to which the disc and the jaw are considered as a system of two elastic plane bodies in contact pressed against each other. Emphasis is given to the stresses due to friction since the stress field due to the specific distribution of radial pressure is already known. It is concluded that the role of friction cannot be ignored, especially in the immediate vicinity of the contact rim. Moreover, for high surface roughness the overall transverse normal stress component in this region becomes of tensile nature indicating increased possibility of premature local cracking (taking into account the low tensile strength of the materials tested using the Brazilian disc test). On the other hand, the stress field at the disc’s center is totally insensitive to both the exact distribution of radial pressure and also to the presence or absence of friction. It is thus indicated that in case fracture in the immediate vicinity of the contact rim is by some means suppressed (reducing for example drastically the coefficient of friction) the results of the Brazilian disc test correspond, in a satisfactory manner, to those predicted by Hondros’ classic approach.

Budget of Equations for Reynolds Stresses in a Turbulent Patch Arising from Internal Wave Breaking

Results of the direct numerical simulations are used to obtain statistical moments in a quasi-steady turbulent patch arising in a stably stratified flow above an obstacle after internal wave breaking. Temporal evolution and spatial behavior of the Reynolds-stress tensor components and budgets of the Reynolds-stress transport equations have been studied. Such an analysis is helpful to explore the turbulent patch and its energetic characteristics by means of statistical moments, to examine closure hypotheses in turbulence models, and to evaluate geophysically important quantites. In particular, the calculated global value of the mixing efficiency is about 0.2 as in oceanic applications. Moreover, simple algebraic relations are proposed between the turbulent kinetic energy and its dissipation rate. In the Reynolds stress tensor equation, the pressure-strain correlation term provides the redistribution of the normal stress components according to the linear returnto-isotropy approximation, whereas the dissipation tensor roughly follows the local-isotropy assumption

Elastic and Plastic Stress Analysis of Composite Beams under Distributed Load

An analytical elastic-plastic stress analysis is carried out on metal-matrix composite beams of arbitrary orientation, supported from two ends under a transverse uniformly distributed load. The composite layer consists of stainless steel fiber and aluminum matrix. The material is assumed to be perfectly plastic during the elastic–plastic solution. The intensity of the uniform force is chosen at a small value; therefore, the normal stress component is neglected in the elastic-plastic solution. The expansion of the plastic region and plastic stress component of σxare determined for orientation angles of 0, 30, 45, 60 and 90o. Plastic yielding occurs for 0 o and 90 o orientation angles on the lower and upper surfaces of the beam at the same distances from the mid-point. However, it starts first at the lower surface for 30, 45 and 60 o orientation angles.

A new nine‐node solid‐shell finite element using complete 3D constitutive laws

SUMMARYThe solid‐shell element presented in this paper has nine nodes: eight are classically located at the apexes and are fitted with three translational DOFs whereas the ninth is sited at the center and is endowed with only one DOF; a displacement along the ‘thickness’ direction. Indeed, to be used for modeling thin structures under bending effects, this kind of finite element has a favored direction where several integration points are distributed. Besides, there is solely one ‘in‐plane’ quadrature point to avoid locking phenomena and prohibitive CPU costs for large nonlinear computations. Because a reduced integration is not enough to completely prevent transverse shear locking, a shear–strain field is assumed. Compared with the other eight‐node ‘solid‐shell' bricks, the presence of a supplementary node has a main aim: getting a linear normal strain component which, along with a full three‐dimensional constitutive strain–stress behavior, allows to achieve similar results in bending cases as those obtained with the usual plane stress state hypothesis. For that, the ninth node DOF plays the role of an extra parameter essential for a quadratic interpolation of the displacement in the thickness direction. The advantage is that this DOF has a physical meaning and, for instance, a strength equivalent to a normal pressure can be prescribed. With a suitable nodal numbering, the band width is not significantly increased and meshes can easily be generated because the extra nodes are always located at element centers. To emphasize the peculiar features of such an element, a set of examples (linear and nonlinear) is carried out. Numerous comparisons with other elements show pretty good results in bending dominating problems while adding the event of a normal stress component in sheet metal forming simulations with double side contact. Copyright © 2012 John Wiley &amp; Sons, Ltd.