Academic literature on the topic 'Transverse compression-extension'

AbstractAn experimental study of ice deformation at the confluence area of Unteraargletscher, Bernese Alps, Switzerland, has been carried out. Surface velocities were measured by repeatedly surveying stakes and with the use of remote-sensing methods. The variation of the vertical strain rates with depth was measured in boreholes. The confluence center line is subjected to longitudinal horizontal extension, which is exceeded in magnitude by a concomitant transverse compression. Vertical strain rates change from positive (extension) at the surface to negative (compression) in the lowest layers of the glacier.

AbstractAn experimental study of ice deformation at the confluence area of Unteraargletscher, Bernese Alps, Switzerland, has been carried out. Surface velocities were measured by repeatedly surveying stakes and with the use of remote-sensing methods. The variation of the vertical strain rates with depth was measured in boreholes. The confluence center line is subjected to longitudinal horizontal extension, which is exceeded in magnitude by a concomitant transverse compression. Vertical strain rates change from positive (extension) at the surface to negative (compression) in the lowest layers of the glacier.

Aluminum foams with a functionally graded density have exhibited better impact resistance and a better energy absorbing performance than aluminum foams with a uniform density. Nevertheless, the anisotropic compression behavior caused by the graded density has scarcely been studied. In this paper, a density graded aluminum foam (FG) was prepared by a controlled foaming process. The effect of density anisotropy on the mechanical behavior of FGs was investigated under quasi-static compression and a low-velocity impact. Digital image correlation (DIC) and numerical simulation techniques were used to identify deformation mechanisms at both macro and cell levels. Results show that transverse compression on FGs lead to a higher collapse strength but also to a lower energy absorption, due to the significant decrease in densification strain and plateau stress. The deformation behavior of FGs under longitudinal compression was dominated by the progressive extension of the deformation bands. For FGs under transverse compression, the failure mode of specimens was characterized by multiple randomly distributed deformation bands. Moreover, the transverse compression caused more deformation on cells, through tearing and lateral stretching, because of the high lateral strain level in the specimens. It was concluded that the transverse compression of FGs lead to a lower plateau stress and a lower cell usage, thus resulting in a poorer energy absorption efficient; this constitutes a key factor which should be taken into consideration in structural design.

The paper discusses the problem of longitudinal bending of a compound two-branch rod, with two symmetrical tightening, stressed with longitudinal compressive and transverse loads, which branches are affected by pre-plastic deformation as extension and compression. Calculations were carried out on the basis of equations of longitudinal bending process, taking into account the influence of the efforts of prior rod compression and plastic training of rod branches elements.

The results of an experimental programme aimed at studying the undrained behaviour of Hostun sand are presented in this paper. Specific conditions concerning the initial relative density (medium loose arrangements) and the loading paths (compression and extension under monotonic and cyclic loadings) were considered in the test programme. Monotonic tests carried out in both drained and undrained conditions show a significant difference in behaviour between compression and extension. It is observed that, in undrained conditions, Hostun sand is weaker in extension than in compression. In compression, the material is stable (dilatant) and the phase-transformation state controls the mechanical behaviour. In extension, the experimental results show an unstable behaviour (contractant), with monotonic, liquefaction-induced instability in undrained conditions. The results of cyclic tests, carried out with one- and two-way stress reversals, show a good correlation with the results of monotonic tests. The loading path strongly influences the undrained mechanical behaviour of the sand, mainly by inducing liquefaction in extension. This situation suggests that differences in soil fabric, caused by the sample preparation technique (air pluviation), can influence the sand behaviour by inducing a significant contraction in extension. By further analysing the cyclic results, it is shown that, during unloading, the stress paths reflect the transverse isotropy (orthotropy) of the sand, with stiffer elastic characteristics in the vertical direction than in the horizontal direction.Key words: liquefaction, cyclic mobility, sands, triaxial test, anisotropy, loading path.

AbstractA combination of uniaxial compression tests and Strip Model and Finite Element analyses of laminates artificially delaminated to create circular (±θ) sublaminates is used to assess the influence of fibre angle on the compressive strength of composite laminates.Sublaminates with 0° < θ < 40° are found to fail by sublaminate-buckling-driven delamination propagation and provide poor tolerance of delamination. This is a consequence of their relatively high axial stiffnesses, low sublaminate buckling strains, Poisson’s ratio induced compressive transverse strains and extension-twist coupling which produces unexpected sublaminate buckling mode shapes. Sublaminates with 40° < θ < 60° are most tolerant to delamination; axial and transverse stiffnesses are minimal, formation of sublaminate buckles is resisted, high laminate buckling strains reduce interaction between laminate and sublaminate buckling mode shapes and extension-twist coupling is minimal. Sublaminates with 60° < θ < 90° are shown to produce varied tolerance of delamination. Sublaminate buckling is generally prevented owing to transverse tensile strains induced by mismatches between laminate and sublaminate Poisson’s ratios but may occur in laminates with low Poisson’s ratios.

Diameters of anterior and posterior atlantodental intervals (AADI and PADI) are diagnostically conclusive regarding ongoing neurological disorders in rheumatoid arthritis. MRI and X-ray are mostly used for patients’ follow-up. This investigation aimed at analyzing these intervals during motion of cervical spine, when transverse and alar ligaments are damaged. AADI and PADI of 10 native, human cervical spines were measured using lateral fluoroscopy, while the spines were assessed in neutral position first, in maximal inclination second, and in maximal extension at last. First, specimens were evaluated under intact conditions, followed by analysis after transverse and alar ligaments were destroyed. Damage of the transverse ligament leads to an increase of the AADI’s diameter about 0.65 mm in flexion and damage of alar ligaments results in significant enhancement of 3.59 mm at mean. In extension, the AADI rises 0.60 mm after the transverse ligament was cut and 0.90 mm when the alar ligaments are damaged. After all ligaments are destroyed, AADI assessed in extension closely resembles AADI at neutral position. Ligamentous damage showed an average significant decrease of the PADI of 1.37 mm in the first step and of 3.57 mm in the second step in flexion, while it is reduced about 1.61 mm and 0.41 mm in the extended and similarly in the neutrally positioned spine. Alar and transverse ligaments are both of obvious importance in order to prevent AAS and movement-related spinal cord compression. Functional imaging is necessary at follow-up in order to identify patients having an advanced risk of neurological disorders.

AbstractUsing analytical and numerical techniques, a two-dimensional (2-D) map-plane model and a 2-D flowline model are utilized to elucidate the horizontal and vertical ice deformation at the confluence of two glaciers. For a perfectly symmetrical confluence, the junction point of the two tributaries can be modeled as a no-slip/free-slip transition. A strongly localized surface depression develops around the junction point, accompanied by two broadly elevated zones positioned close to the margins of the tributaries facing the junction point. The confluence center line is subjected to horizontal longitudinal extension and a transverse compression. The compression generally exceeds the concomitant longitudinal extension in magnitude. Depth-integrated vertical strain rates along the center line are positive (extension), but the strain-rate variation with depth depends critically on the type of basal boundary conditions at the glacier bed. For a no-slip boundary condition, vertical strain rates change from positive at the surface to negative close to the base, whereas for a free-slip boundary condition (perfect sliding) vertical strain rates are positive throughout the depth. These theoretical results are compared with field measurements from Unteraargletscher, Bernese Alps, Switzerland.

AbstractUsing analytical and numerical techniques, a two-dimensional (2-D) map-plane model and a 2-D flowline model are utilized to elucidate the horizontal and vertical ice deformation at the confluence of two glaciers. For a perfectly symmetrical confluence, the junction point of the two tributaries can be modeled as a no-slip/free-slip transition. A strongly localized surface depression develops around the junction point, accompanied by two broadly elevated zones positioned close to the margins of the tributaries facing the junction point. The confluence center line is subjected to horizontal longitudinal extension and a transverse compression. The compression generally exceeds the concomitant longitudinal extension in magnitude. Depth-integrated vertical strain rates along the center line are positive (extension), but the strain-rate variation with depth depends critically on the type of basal boundary conditions at the glacier bed. For a no-slip boundary condition, vertical strain rates change from positive at the surface to negative close to the base, whereas for a free-slip boundary condition (perfect sliding) vertical strain rates are positive throughout the depth. These theoretical results are compared with field measurements from Unteraargletscher, Bernese Alps, Switzerland.

Hundreds of YouTube videos show people running on cornstarch suspensions demonstrating that dense shear thickening suspensions solidify under impact. Such processes are mimicked by impacting and pulling out a plate from the surface of a thickening cornstarch suspension. Here, using both experiments and simulations, we show that applying fast oscillatory shear transverse to the primary impact or extension directions tunes the degree of solidification. The forces acting on the impacting surface are modified by varying the dimensionless ratio of the orthogonal shear to the compression and extension flow rate. Simulations show varying this parameter changes the number of particle contacts governing solidification. To demonstrate this strategy in an untethered context, we show the sinking speed of a cylinder dropped onto the suspension varies markedly by changing this dimensionless ratio. These results suggest applying orthogonal shear while people are running on cornstarch would de-solidify the suspension and cause them to sink.

This paper is concerned with the mechanics of woven fabrics under tensile loading. The yarns are treated as elastica. The yarns bent into shape for both warp and weft are assumed to be elastic, homogenous, and weightless. During deformation the yarns are subjected to bending, extension and transverse compression. The initial geometry of the yarns in the fabric, under no external loading, is first obtained using a force-equilibrium method based on Love’s ordinary approximate theory, a generalisation of the Bernoulli-Euler theory of elastic rods. A non-linear boundary-value problem with a system of five differential equations has been formulated and solved. Application of load will further change the shape of the bent yarns due to bending and stretching. For a yarn with given initial geometry, as obtained by the force-equilibrium method, the solution of the deformed configuration is obtained from the solution of two nonlinear differential equations using appropriate boundary conditions. The formulation of the latter problem is based on the energy method. The sum of the energy terms due to bending, stretching together with the potential energy due to the applied load provides an expression for the total energy of the system. The variation of the total energy in terms of the variations of two parameters is then obtained, using the techniques from calculus of variations. One parameter described the deviation of the bent yarn from a straight line while the other is the length as measured along the yarn axis. This leads to a set of differential equations that fully describe the deformed yarns. The models, initially developed for plain weave, are being currently extended to non-plain weaves and 3D woven fabrics.

Abstract Low-frequency distributed acoustic strain-rate sensors (LF-DAS) experience strain changes due to far-field fracture propagation. To better understand the LF-DAS response to fracture propagation, we performed laboratory-scale hydraulic fracture experiments with embedded optical strain sensors. The objectives of this research are to generate hydraulic fractures of known geometry, measure the strain response along the embedded fiber optic cable comparable to LF-DAS measurements, and use the results to inform interpretation of field-derived LF-DAS data. The experiments were conducted in unconfined transparent cubic blocks with a dimension of 8-inches on each side. The block was made of transparent epoxy in order to visualize the fracture propagation. Fiber optic sensing cables were embedded in the block with different distances to the source of injection. We injected dyed water through an injection tubing to generate a transverse, radial fracture along an initial flaw. An optical interrogator recorded the response of offset fiber Bragg grating strain sensors normal to the plane of the fracture. The strain data was visualized on a waterfall plot, akin to visualizations of field-derived LF-DAS data. Dimensional analysis was used to scale the lab results to field conditions. We compared the evolution of the strain response at the fiber optic cable, injection pressure, and rate with known fracture geometry. The measured strains were compared to Sneddon's (1946) linear elastic solution for a penny-shaped crack and found to follow this behavior. The generated radial fractures in transparent media can be modeled with Sneddon's linear elastic radial fracture model and a mode I critical stress intensity factor. The LF-DAS characteristic response of a narrowing region of extension surrounded by compression was exhibited as a fracture approached and intersected the fiber optic cable. The experimentally derived strain and strain-rate waterfall plots with known fracture geometry, injection rate and pressure response provide insight in understanding LF-DAS responses in the field. Furthermore, we developed a method to estimate fracture geometry evolution from the fiber optic strain data and validated the method against the experimental data.

Advanced woven fabrics can provide a wide range of mechanical properties since the yarns can be arranged in different architectural patterns thus allowing the fabric structure to be tuned based on the specific needs. This adjustable nature makes them an attractive material choice for applications where versatility is highly desired. Hence, there is an increasing interest in woven fabrics in the recent years. They have been used in various applications such as deployable structures, protective garments, medical scaffolds and composites. With the increased interest, there is a need for efficient and accurate computational tools to investigate the mechanical behavior and deformation of woven fabrics for specific applications. Although there are several computational models in the literature that can model uniaxial and biaxial behavior of woven fabrics, there are not any commonly accepted material models for woven fabrics due to the complex interaction of trellising and deformation. Here, we propose an easy to implement constitutive material model based on a mesoscale unit cell of the woven fabrics. The proposed model utilizes the two prominent deformation mechanisms affecting the mechanical response at the mesoscale level: (1) Yarn stretching, and (2) shearing. These mesoscale mechanisms are mechanistically implemented within an unit cell by using truss and rotational springs to generate the mechanical response of the woven fabric. The yarns’ nonlinear mechanical behavior is modeled with non-linear trusses and assumed to be pin-jointed at the center of the unit cell. The truss elements are allowed to rotate at the pin-joint reproducing the yarns’ relative rotational motion during shearing. The fabric’s shear resistance involves two components: yarn-to-yarn relative rotation/sliding and yarn locking due to the yarn transverse compression. These components of the fabric shear resistance are modeled as a non-linear rotational spring located at the pin-joint which generates a moment resisting the shear deformation. The developed forces and moments from the trusses and rotational spring within the unit cell structure are then used to determine the continuum stress state of the material point. The material properties and parameters defined in the proposed model are easy to obtain from uniaxial tensile and shear tests on fabrics. To validate the material model, plain weave Kevlar KM2 fabric is modeled by replicating the standard uniaxial tensile and bias extension tests. The results obtained show that the material model provides a good description of the in-plane deformation and mechanical response.

One of the more formidable problems in composite research is the study of delamination and other failure modes in the vicinity of a circular hole in a laminate, e.g., a circular cut-out in a structure. In this problem, the singularity varies around the periphery of the hole as well as through the thickness of the laminate. Under tensile loading, the early failure modes in this problem consist of transverse cracks in various layers, so that delamination occurs only after other damage is precipitated, followed by fiber breakage leading to failure. A literature review of past work clearly shows that mechanical testing with simultaneous AE monitoring is a fruitful technique to study damage accumulation in composite systems. The acoustic-ultrasonic (AU) testing combines the high sensitivity of ultrasonics to internal damage and the method of acoustic emission technique to characterize elastic waves. As damage accumulates in the specimen along the wave path, the net internal damping increases and changes the wave parameters such as peak amplitude, duration, etc. accordingly. Additionally, a range of experimental results over the last decade has further shown that the mechanical deformation and electric resistance of carbon fiber reinforced polymers are coupled, so that the material is inherently a sensor of its own damage state. The monitoring of electric resistance and capacitance changes, linked to the modifications of the conduction paths in the composite, allows the detection of damage growth. It seems logical that a natural extension of these different approaches is the determination of damage mode, e.g., fiber breakage, matrix cracking or delamination, and damage size and position, based on combined measurements from these techniques. These multiple techniques will serve a two-fold purpose, namely, enable comparison as well as complement each other in case of incomplete damage mapping from one set of sensors For this study, we will consider carbon fiber-reinforced toughened bismaleimide, (IM7/5250-4) quasi-isotropic laminate coupons 12” long, 4” wide with hole at the center under tension. Figure 1 shows the damage which occurs around a 0.75” hole in a [45/0/-45/90]s graphite epoxy laminate obtained by radiography after unloading the test specimen from an applied stress of 50 Ksi. The failure stress for this laminate was 56.4 Ksi. Damage in the form of ply cracks in the 90, 45, and −45 plies and delamination around hole edges is clearly evident. The radiograph taken after unloading from a 50 Ksi stress level clearly shows the location and extent of damage, but contains no specific information about the sequence and the timing of damage events. Figure 2 shows stress-strain curves obtained from strain gages mounted at various distances away from the hole edge along with the far-field value. The stress-strain curves provide useful information regarding the initiation as well as the growth of the damage, as evidenced by jump in strain levels and onset of nonlinearity. Damage initiation is first picked up by the strain gage which is mounted closest to the hole edge at a stress level of 21 Ksi. Subsequently, other strain gages begin to sense damage growth as the applied stress level increases. The strain gage data provides useful information regarding initiation, growth and severity of damage, but it is difficult to assign specific damage modes and their location to the measurements. This example clearly demonstrates the needs, with the associated benefits, of the multiple sensor approach. In this work, three different hole sizes (0.25”, 0.5” and 0.75”) will be investigated. This example problem will enable us to examine the combined effects of cut-outs, matrix cracking, delamination and fiber breakage on the ability of various NDE techniques to assess damage. The development and growth of damage in the composite laminate with a hole under compression will be markedly different than in tension. Under compression, the major damage modes are fiber buckling and delamination, and will also be investigated.