Shear Axis Research Articles

Numerical model of formation of a 3-D strike-slip fault system

The initiation and the initial evolution of a strike-slip fault are modeled within an elastoplasticity constitutive framework taking into account the evolution of the hardening modulus with inelastic straining. The initial and boundary conditions are similar to those of the Riedel shear experiment. The models first deform purely elastically. Then damage (inelastic deformation) starts at the model surface. The damage zone propagates both normal to the forming fault zone and downwards. Finally, it affects the whole layer thickness, forming flower-like structure in cross-section. At a certain stage, a dense set of parallel Riedel shears forms at shallow depth. A few of these propagate both laterally and vertically, while others die. The faults first propagate in-plane, but then rapidly change direction to make a larger angle with the shear axis. New fault segments form as well, resulting in complex 3-D fault zone architecture. Different fault segments accommodate strike-slip and normal displacements, which results in the formation of valleys and rotations along the fault system.

Hazelnut kernels (Corylus avellana L.) mechanical and acoustic properties determination: Comparison of test speed, compression or shear axis, roasting, and storage condition effect

The aim of this work was to compare different texture test conditions for the evaluation of instrumental mechanical and acoustic properties of raw and roasted hazelnut (Corylus avellana L.) kernels cv. Tonda Gentile Trilobata (TGT). A comparison of compression and shear tests, test speed (0.2, 1.0, 10.0 mm/s), and analyzed axis (x, y, z) combinations was performed. Joint mechanical and acoustic emission acquisitions were used for the first time on hazelnut kernels. The compression test method using 1.0 mm/s speed and analyzed on the x-axis showed the lowest variability of the results. These conditions were then used to evaluate raw kernels during 12 months of storage, conducted in-shell (at ambient temperature) and shelled (refrigerated, vacuum, frozen, with nitrogen modified atmosphere). The main differences among storage conditions were evidenced in rupture force, rupture slope and acoustic maximum peak parameters.

Influence of time-dependence on failure of echelon rock joints through a novel DEM model

This article investigates the time-dependent influence on the shear failure behaviour of parallel rock joints in the echelon arrangement due to chemical weathering, which can be treated as a generalised time-dependency of the rock material. A time-dependent parameter α, identifying the accumulated relative mass removal of bonding material, has been implemented into a novel distinct element method bond contact model. This model is based on a series of mechanical test on bonded aluminium rods with different bond geometries. The numerical direct shear test results of echelon rock joints characterised by different values of α show that increasing time-dependent parameter α can lead to a lower crack initiation and peak stresses. This is accompanied by a growing ratio of the microscopic compressive–shear–torsional (CST) bond failure number of bond failures to the total number of failures, except for the case without weathering influence. High values of α render the material bridge a weaker part to be cut through, generating a large number of CST bond breakages along the central shear axis.

Formation of flower structures in a geological layer at a strike-slip displacement in the basement

Formation of dislocations in a geological layer at a strike-slip displacement in its basement is studied by three-dimensional (3D) numerical modeling. It is shown that the pattern of strain localization is determined by the initial stress state or thickness of the deformed layer as well as by the Poisson ratio and strength of the medium. Three types of fracture zones are observed. Shear bands of the first type are dominated by the propeller-like surfaces of Riedel R-shears, which merge into a single main fault with feathering structures. In the second type of dislocation zones, the primary role is played by the surfaces oriented at an angle of ∼40° to the shear axis in the horizontal projections. After reaching the free surface, these discontinuities are cut by a V-shaped fault. In this case, the pattern of dislocations most closely corresponds to the flower structures. The third type is a trough, which may accommodate the formation of yet another strain localization zone along its axial part—a vertical fault.

Single particle motion in a sheared colloidal dispersion

The motion of a spherical Brownian “probe” particle addressed by an external force immersed in shear flow of a colloidal dispersion of spherical neutrally buoyant “bath” particles is quantified. The steady-state nonequilibrium microstructure of bath particles around the probe—induced by the applied force and ambient shear—is calculated to first order in the volume fraction of bath particles, ϕ. The distortion to the equilibrium microstructure caused by the moving probe is characterized by a Péclet number Pef (a dimensionless pulling force), and the distortion due to the shear flow is represented by another Péclet number Pes (a dimensionless shear rate). Matched asymptotic expansions are employed to quantify the microstructure at small Péclet numbers; specifically, within the distinguished limits Pes3/2≪Pef≪Pes1/2≪1. The nonequilibrium microstructure is subsequently utilized to compute the average rectilinear velocity of the probe through O(ϕPes3/2Us), for an arbitrary orientation of the external force to the shear flow. Here, Us is the Stokes velocity of the probe in a pure Newtonian fluid. It is also shown that to O(ϕPes3/2Us) the torque-free probe simply rotates with the ambient shear; a modification to the angular velocity of the probe is at most O(ϕPesPefUs). In particular, a probe forced along the flow axis of shear is demonstrated to experience a cross-streamline drift velocity of O(ϕPesUs), to leading order, which acts to propel the particle to streamlines of the ambient shear that move in the same direction as the external force. A mathematical connection between this result and cross-streamline drift of a particle in a Newtonian fluid at small, but nonzero, Reynolds numbers is drawn. The magnitude of the cross-streamline drift velocity is found to be sensitive to the degree of hydrodynamic interactions between the probe and bath particles, which are tuned via an excluded-annulus model. It is also demonstrated that a probe forced along the vorticity axis of the shear experiences a shear-driven enhancement in rectilinear velocity of O(ϕPes3/2Us), to leading order: This nonanalytic dependence originates from the microstructural deformation in the shear dominated (outer) region far from the probe. A connection of this finding to recent work on particle sedimentation in orthogonal shear flow of viscoelastic liquids is discussed.

Effects of changes in muscle activation level and spine and hip posture on erector spinae fiber orientation.

During lumbar flexion, the fiber orientation of the lumbar erector spinae (LES) muscle becomes oriented more along the spine compressive axis. It is unknown how changes in LES activation effect fiber orientation. Ultrasound images of LES were collected during 2 sets of experimental conditions: (1) varying levels of LES activation while lying prone; and (2) varying spine and hip angles while seated. Electromyographic activity and lumbar spine and hip angles were also recorded. As LES activation increased, increases in fiber orientation (signifying increased orientation along the posterior shear axis) were found (P<0.001). Compared with the relaxed sitting posture, decreases in fiber orientation were found with full spine flexion and combined spine and hip flexion (P<0.001), but there were no changes with full hip flexion alone. Activation magnitude and spine posture both affect LES fiber orientation, thus modifying its ability to protect the spine against anterior shear forces.

Torsional irregularity in multi-story structures

The purpose of this study is first to determine the conditions for excessive torsional irregularity and then to discuss the validity of code provisions. A parametric investigation is performed on six groups of typical struc- tures with varying shear wall positions, story, and axis numbers. It is found that torsional irregularity coefficients increase as the story numbers decrease, i.e., maximum irregularity coefficients occur for single-story structures. They reach maximum values when the asymmetrical shear walls are placed as close as possible to the centers of mass. However, the results obtained for floor rotations are quite contradictory. A new provisional definition for torsional irregularity coefficient based on floor rotations is proposed.

Deformation and fracture structures in strike-slip faulting

The paper presents the results of 3D numerical modeling of fault formation due to strike-slip displacement of basement blocks on the example of model rock massifs differing in thickness. It is shown that the material thickness and initial stress state substantially influence the form of fracture structures arising in strike-slip faulting. The formation of a vertical fault with feathering Riedel fractures is characteristic of high-strength material and small thickness. If the material thickness is large, there arises a complex spatial flower structure with inclined fractures oriented in the horizontal plane at an angle of ∼40° to the shear axis. The inclined fractures represent strain localization bands or so-called shear bands developing as pairs of “flakes” that resemble opened oyster valves. A main fault with clearly defined feathering fractures of different orientations is formed from the top down once these strain localization bands reach a free surface.

On principal shear axes for correction factors in Timoshenko beam theory

Compelling arguments with substantiating data are presented to explain why there is no role for principal shear axes in shear correction factors of Timoshenko beam theory. This article supplies more details to the explanation in a previous paper on this issue.

Influence of microfillers on molecular alignment and tensile stress fracture in thermotropic liquid crystalline polymer

This research focuses on the influence of microfillers on mechanical properties, molecular orientation, and fracture behavior of reinforced thermotropic liquid crystalline polymers (LCPs). The LCPs are random copolyesters based on 1,4-hydroxybenzoic acid (B) and 2,6-hydroxynaphthoic acid (N) with composition 73:27 mol%. Glass fibers, graphite, and mineral fillers were used as microfillers. The influence of filler was investigated, up to 30 wt % filler concentration. Tensile tests revealed that the strain at failure of the neat LCP occurred within 3% deformation. The addition of microfillers initially decreased the Young’s modulus and the strain at failure below that of the neat LCP. However, the combination of graphite/glass fibers did increase the Young’s modulus, and increased the yield stress but at the cost of reducing, significantly, the strain at failure. The x-ray patterns of the molded neat LCP showed that the molecular chains were preferentially oriented along the injection molding axis. However, addition of microfillers randomized the molecular orientation, as measured by the order parameter, P–2, where glass fiber-based fillers were more effective to reduce P–2. The reduction in molecular alignment appeared to be the key property to deteriorate Young’s modulus along the shear axis. Moreover, the reduction in modulus could be compensated by adding more microfillers and offers the benefit of homogenizing the mechanical properties. Analysis of fractured samples suggests that the main mechanism for fracture was the loss of adhesion between the microfillers and the polymer matrix, this effect being more evident when using glass fiber.

Nucleation and Crystal Growth in Sheared Granular Sphere Packings

We investigate the nucleation of ordered phases, their symmetries, and distributions in dense frictional hard sphere packings as a function of particle volume fraction ϕ, by imposing cyclic shear and constant applied pressure conditions. We show, with internal imaging, that the nucleating crystallites in the bulk consist of 10-60 spheres with hexagonal close packed (hcp) order and nonspherical shape, that are oriented preferentially along the shear axis. Above ϕ=0.62±0.005, crystallites with face centered cubic (fcc) order are observed with increasing probability, and ordered domains grow rapidly. A polycrystalline phase with domains of fcc and hcp order is observed after hundreds of thousands of shear cycles.

External biofidelity in lateral impact measurement of global and local forces

A study was conducted to develop high-resolution external biofidelity data for the response of post-mortem human surrogates (PMHS) in side-impact loading. This study implemented stationary PMHS (N = 3) impacted by a wall moving at a constant velocity. The wall was subdivided into 15 impact plates, each instrumented to record the normal and shear forces as well as reaction moments about the shear axes. A method to determine the time-history of the centre of pressure (COP) of each load plate was developed and validated in both quasi-static and dynamic loading conditions. A validation test demonstrated that the COP can be predicted to within 1 cm for loads generally achieved by the shoulder and pelvis. The repeatability of COP was very good for the pelvis, where maximum variation was 1.44 cm, but higher for the thorax (3.4 cm) and shoulder (4.1 cm). Patterns of COP motion on the pelvis plate were consistent for all subjects.

Shear Deformation Effect in Flexural-torsional Vibrations of Composite Beams by Boundary Element Method (BEM)

In this paper a boundary element method (BEM) is developed for the general flexural-torsional vibration problem of Timoshenko beams of arbitrarily shaped composite cross-section taking into account the effects of warping stiffness, warping and rotary inertia and shear deformation. The composite beam consists of materials in contact, each of which can surround a finite number of inclusions. The materials have different elasticity and shear moduli with same Poisson’s ratio and are firmly bonded together. The beam is subjected to arbitrarily transverse and/or torsional distributed or concentrated loading, while its edges are restrained by the most general linear boundary conditions. The resulting initial boundary value problem, described by three coupled partial differential equations, is solved employing a boundary integral equation approach. Besides the effectiveness and accuracy of the developed method, a significant advantage is that the displacements as well as the stress resultants are computed at any cross-section of the beam using the respective integral representations as mathematical formulae. All basic equations are formulated with respect to the principal shear axes coordinate system, which does not coincide with the principal bending one in a non-symmetric cross-section. To account for shear deformations, the concept of shear deformation coefficients is used. Six boundary value problems are formulated with respect to the transverse displacements, to the angle of twist, to the primary warping function and to two stress functions and solved using the Analog Equation Method, a BEM-based method. Both free and forced vibrations are examined. Several beams are analyzed to illustrate the method and demonstrate its efficiency and wherever possible its accuracy.

Shear deformation effect in flexural-torsional buckling analysis of beams of arbitrary cross section by BEM

In this paper a boundary element method is developed for the general flexural-torsional buckling analysis of Timoshenko beams of arbitrarily shaped cross section. The beam is subjected to a compressive centrally applied concentrated axial load together with arbitrarily axial, transverse and torsional distributed loading, while its edges are restrained by the most general linear boundary conditions. The resulting boundary value problem, described by three coupled ordinary differential equations, is solved employing a boundary integral equation approach. All basic equations are formulated with respect to the principal shear axes coordinate system, which does not coincide with the principal bending one in a nonsymmetric cross section. To account for shear deformations, the concept of shear deformation coefficients is used. Six coupled boundary value problems are formulated with respect to the transverse displacements, to the angle of twist, to the primary warping function and to two stress functions and solved using the Analog Equation Method, a BEM based method. Several beams are analysed to illustrate the method and demonstrate its efficiency and wherever possible its accuracy. The range of applicability of the thin-walled theory and the significant influence of the boundary conditions and the shear deformation effect on the buckling load are investigated through examples with great practical interest.

Much ado about shear correction factors in Timoshenko beam theory

Many shear correction factors have appeared since the inception of Timoshenko beam theory in 1921. While rational bases for them have been offered, there continues to be some reluctance to their full acceptance because the explanations are not totally convincing and their efficacies have not been comprehensively evaluated over a range of application. Herein, three-dimensional static and dynamic information and results for a beam of general (both symmetric and non-symmetric) cross-section are brought to bear on these issues. Only homogeneous, isotropic beams are considered. Semi-analytical finite element (SAFE) computer codes provide static and dynamic response data for our purposes. Greater clarification of issues relating to the bases for shear correction factors can be seen. Also, comparisons of numerical results with Timoshenko beam data will show the effectiveness of these factors beyond the range of application of elementary (Bernoulli–Euler) theory. An issue concerning principal shear axes arose in the definition of shear correction factors for non-symmetric cross-sections. In this method, expressions for the shear energies of two transverse forces applied on the cross-section by beam and three-dimensional elasticity theories are equated to determine the shear correction factors. This led to the necessity for principal shear axes. We will argue against this concept and show that when two forces are applied simultaneously to a cross-section, it leads to an inconsistency. Only one force should be used at a time, and two sets of calculations are needed to establish the shear correction factors for a non-symmetrical cross-section.

Geometry of the Nojima Fault at Nojima-Hirabayashi, Japan – I. A Simple Damage Structure Inferred from Borehole Core Permeability

The 1995 Kobe (Hyogo-ken Nanbu) earthquake, M=7.2, ruptured the Nojima fault in southwest Japan. We have studied core samples taken from two scientific drillholes that crossed the fault zone SW of the epicentral region on Awaji Island. The shallower hole, drilled by the Geological Survey of Japan (GSJ), was started 75 m to the SE of the surface trace of the Nojima fault and crossed the fault at a depth of 624 m. A deeper hole, drilled by the National Research Institute for Earth Science and Disaster Prevention (NIED) was started 302 m to the SE of the fault and crossed fault strands below a depth of 1140 m. We have measured strength and matrix permeability of core samples taken from these two drillholes. We find a strong correlation between permeability and proximity to the fault zone shear axes. The half-width of the high permeability zone (approximately 15 to 25 m) is in good agreement with the fault zone width inferred from trapped seismic wave analysis and other evidence. The fault zone core or shear axis contains clays with permeabilities of approximately 0.1 to 1 microdarcy at 50 MPa effective confining pressure (10 to 30 microdarcy at in situ pressures). Within a few meters of the fault zone core, the rock is highly fractured but has sustained little net shear. Matrix permeability of this zone is approximately 30 to 60 microdarcy at 50 MPa effective confining pressure (300 to 1000 microdarcy at in situ pressures). Outside this damage zone, matrix permeability drops below 0.01 microdarcy. The clay0rich core material has the lowest strength with a coefficient of friction of approximately 0.55. Shear strength increases with distance from the shear axis. These permeability and strength observations reveal a simple fault zone structure with a relatively weak fine-grained core surrounded by a damage zone of fractured rock. In this case, the damage zone will act as a high-permeability conduit for vertical and horizontal flow in the plane of the fault. The fine-grained core region, however, will impede fluid flow across the fault.

Fundamental Deformations in Asymmetric Continuum

Abstract The complexity of processes in a seismic source zone has inspired us to reconsider a class of basic motions and deformations in an asymmetric continuum, including simple motions (translation and rotation, named spin) and simple deformations. Simple deformations include the axial nuclei, that is, point extension/compression, and the shear nuclei related to string-string point deformations. The point deformation is further redefined as another kind of rotational motion, called twist, representing oscillations of the main shear axes and their amplitudes. Some remarks are added on the recording systems used to measure these motions and deformations.

Shear deformation effect in flexural–torsional vibrations of beams by BEM

In this paper, a boundary element method is developed for the general flexural–torsional vibration problem of Timoshenko beams of arbitrarily shaped cross section taking into account the effects of warping stiffness, warping and rotary inertia and shear deformation. The beam is subjected to arbitrarily transverse and/or torsional distributed or concentrated loading, while its edges are restrained by the most general linear boundary conditions. The resulting initial boundary value problem, described by three coupled partial differential equations, is solved employing a boundary integral equation approach. Besides the effectiveness and accuracy of the developed method, a significant advantage is that the displacements as well as the stress resultants are computed at any cross-section of the beam using the respective integral representations as mathematical formulae. All basic equations are formulated with respect to the principal shear axes coordinate system, which does not coincide with the principal bending one in a nonsymmetric cross section. To account for shear deformations, the concept of shear deformation coefficients is used. Six boundary value problems are formulated with respect to the transverse displacements, to the angle of twist, to the primary warping function and to two stress functions and solved using the Analog Equation Method, a BEM based method. Both free and forced vibrations are examined. Several beams are analysed to illustrate the method and demonstrate its efficiency and wherever possible its accuracy.

Flexural-torsional buckling analysis of composite beams by BEM including shear deformation effect

In this paper, a boundary element method is developed for the general flexural-torsional linear buckling analysis of Timoshenko beams of arbitrarily shaped composite cross-section. The composite beam consists of materials in contact, each of which can surround a finite number of inclusions. The materials have different elasticity and shear moduli with same Poisson’s ratio and are firmly bonded together. The beam is subjected to a compressive centrally applied load together with arbitrarily axial, transverse and/or torsional distributed loading, while its edges are restrained by the most general linear boundary conditions. The resulting boundary value problem, described by three coupled ordinary differential equations, is solved employing a boundary integral equation approach. Besides the effectiveness and accuracy of the developed method, a significant advantage is that the method can treat composite beams of both thin and thick walled cross-sections taking into account the warping along the thickness of the walls, while the displacements as well as the stress resultants are computed at any cross-section of the beam using the respective integral representations as mathematical formulae. All basic equations are formulated with respect to the principal shear axes coordinate system, which does not coincide with the principal bending one in a nonsymmetric cross-section. To account for shear deformations, the concept of shear deformation coefficients is used. Six coupled boundary value problems are formulated with respect to the transverse displacements, to the angle of twist, to the primary warping function and to two stress functions and solved using the analog equation method, a BEM based method. Several beams are analysed to illustrate the method and demonstrate its efficiency. The significant influence of the boundary conditions and the shear deformation effect on the buckling load are investigated through examples with great practical interest.

Pure shear axes and elastic strain energy

It is well known that a state of pure shear has distinct sets of basis vectors or coordinate systems: the principal axes, in which the stress is diagonal, and pure shear bases, in which diag(stress)=0. The latter is commonly taken as the definition of pure shear, although a state of pure shear is more generally defined by tr(stress)=0. New results are presented that characterize all possible pure shear bases. A pair of vector functions are derived which generate a set of pure shear basis vectors from any one member of the triad. The vector functions follow from compatibility condition for the pure shear basis vectors, and are independent of the principal stress values. The complementary types of vector basis have implications for the strain energy of linearly elastic solids with cubic material symmetry: for a given state of stress or strain, the strain energy achieves its extreme values when the material cube axes are aligned with principal axes of stress or with a pure shear basis. This implies that the optimal orientation for a given state of stress is with one or the other vector basis, depending as the stress is to be minimized or maximized, which involves the sign of one material parameter.