Principal Strain Directions Research Articles

High-resolution CINE MRI allows estimation of 3D regional atrial strains

Abstract Introduction It is increasingly evident that atrial function is an important marker of cardiovascular health. Impaired global left atrial strain has been associated with risk of thromboembolic events, atrial fibrillation and heart failure. When performed at high spatial resolution, CINE MRI allows the estimation of regional atrial strains, which may facilitate earlier identification of atrial disease and improved (non-contrast) characterisation of atrial fibrosis. Nevertheless, to date, high resolution regional atrial strains has not been assessed using CINE MRI. Purpose We introduce a novel rapid 2.2-mm isotropic atrial CINE MRI protocol used to image healthy subjects and patients with cardiovascular disease (CVD). We additionally present a dedicated image analysis pipeline to estimate regional 3D atrial strains from these images. Methods We imaged 10 healthy subjects (5 female, 24–36 years old) and 6 patients referred for cardiac MRI due to known or suspected CVD (2 female, 25–80 years old). All subjects were scanned in a 1.5T Philips Ingenia MRI scanner in a single breath-hold (<25 s), using a short-axis 3D bSSFP protocol (flip angle: 60°, TE/TR: 1.6/3.3 ms) with retrospective cardiac gating, SENSE = 2.3 (along both phase encode directions), typical FOV: 400 x 270 x 70 mm3, isotropic acquisition resolution of 2.2 mm3. Images were reconstructed to 20 cardiac phases with 55% view sharing. The left atrium (LA) was manually segmented in atrial diastole. We tracked the position of evenly spaced points along the LA contour across all phases of the cardiac cycle using the Medical Image Tracking Toolbox. This was used to create a series of deforming smooth triangular meshes, from which Lagrange strain tensors were estimated. Results Figs a-c show 3 orthogonal views of the proposed high-resolution atrial CINE MRI scans for a representative CVD patient, with the LA segmentation overlaid in red. Representative LA principal strain directions (as arrows) with the colour indicating the amount of strain observed along this direction are shown in Fig d for active atrial contraction (posterior view). The calculated strain directions varied smoothly in space and time, as expected, and were largest in amplitude in the regions closest to the mitral valve. Overall, principal strains were larger in healthy subjects (AC strains: 0.12±0.06) than in the CVD cohort (AC strains: 0.04±0.01). This difference was statistically significant during AC (p-value: 0.02), but not during atrial diastole (p-value: 0.06). Conclusions We present a novel high-resolution CINE-MRI protocol for estimating regional atrial strains in 3D, with pilot data from 10 healthy subjects and 6 cardiovascular patients. Future studies will compare regions of abnormal atrial strain with fibrosis identified in late gadolinium enhanced MRI to assess whether regional strains can provide a better characterisation of atrial tissue and improved stratification of patients at risk. Figure 1 Funding Acknowledgement Type of funding source: Foundation. Main funding source(s): British Heart Foundation, EPSRC/Wellcome Trust Centre for Medical Engineering

Application of the exact regularized point particle method (ERPP) to bubble laden turbulent shear flows in the two-way coupling regime

Direct numerical simulations of a bubbly laden homogeneous shear flow have been carried out using the exact regularized point particle method as the inter-phase momentum coupling approach. The aim of this study consists in addressing the modulation of shear turbulence and the bubble clustering geometry in the presence of different inter-phase momentum coupling conditions. Suspensions with different combinations of the void fraction and Kolmogorov-based Stokes number, in the dilute regime, have been addressed. Bubbles suppress the turbulent kinetic energy and turbulent dissipation as well. Turbulent modulation occurs via the direct change of the Reynolds shear stress. In fact, the bubble energy source is proved to be negligible in the scale-by-scale turbulent energy budget. The bubble clustering, in agreement with the literature, occurs in the form of thin elongated structures. The clusters are aligned with the principal strain direction of the mean flow, as usual in shear flows. The bubble clustering and turbulent modification are strictly related: both increase with the Stokes number and are independent of the void fraction. The data show that the turbulent modification is disadvantaged when the bubble distribution is homogeneous (i.e., small Stokes number). Finally, the small-scale bubble clustering is slightly reduced by two-way coupling effects even though the clustering anisotropy still persists at small scales as it occurs for inertial particles.

The Effect of the Loading Rate on the Full-Field Strain Distribution on the Surface on the Intervertebral Discs.

Contrasting results are reported when the spine is tested at different strain rates. Tissue specimens from the ligaments or the intervertebral discs (IVD, including annulus fibrosus and nucleus pulposus) exhibit higher stiffness and lower dissipation at high strain rates. Counterintuitively, when spine segments are tested at high rates, the hysteresis area and loop width increase. It is unclear how the load is shared between the different structures at different loading rates. The hypotheses of this study were: (i) As the IVD stiffens at higher loading rates, the strain distribution around the disc would be different depending on the loading rate; (ii) Preconditioning attenuates the strain-rate dependency of the IVD, thus making differences in strain distribution smaller at the different rates. Six segments of three vertebrae (L4-L6) were extracted from porcine spines and tested in presso-flexion at different loading rates (reaching full load in 0.67, 6.7, and 67 s). The full-field strain maps were measured using digital image correlation on the surface of the IVDs from lateral. The posterior-to-anterior trends of the strain were computed in detail for each IVD, and compared between loading rates. The values and the direction of principal strain on the surface of the IVDs, vertebrae, and endplates remained unchanged at different rates. In the transition zone between IVD and vertebra, only slight differences due to the loading rate appeared but with no statistical significance. These findings will allow better understanding of the rate-dependent behavior and failure of the IVD.

Strain Field Evolution Characteristics of Free Surface during Crater Blasting in Sandstone under High Stress

Considering the problems related to hard rock blasting under high in-situ stresses at large depths, we conducted crater blasting tests on sandstone specimens under three static load conditions to investigate the strain field evolution of rock blasting under high stress. The digital image correlation (DIC) technique was used to monitor the evolution of the strain field on the free surface. Thus, the influence of the static stress on the blasting strain field was analyzed, and the formation mechanism of cracks on the free surface was elucidated. The results indicate that a circular tensile strain zone was formed without static loading. The direction of the maximum principal strain was perpendicular to the radius, which lead to the random emergence of multiple radial tensile cracks. Under a uniaxial static loading, an elliptical tensile strain zone was formed. The direction of the maximum principal strain was perpendicular to the static loading direction. This facilitated the initiation and propagation of tensile cracks preferentially in the direction parallel to the static loading. Under an equal biaxial static loading, the initial compressive strain in the specimen reduced the increment rate of the blasting strain, and restrained the formation of surface cracks. Besides, a determination method for dynamic tensile fracture strain of rock was proposed.

Visualization of principal strain direction by a mechanical device

Abstract Generally, the strains at a point must be measured at least in three directions simultaneously in order to find the principal strain. In this paper, a simple device is proposed to visualize the principal strain direction in structure in real-time. Different from the conventional methods, it is able to indicate the principal strain by detecting the largest deformation in the elliptical zone which is deformed from a circular zone. The mechanism and key structure of the device are introduced in detail. The main factors which influence the sensitivity and accuracy of the visualization are analyzed. The fundamental experiments including a uniaxial compression test and the simply supported beam experiment were conducted to verify the validity of the method. It is found that the device can work well to visualize the direction of principal strain.

Multi-technique damage monitoring of concrete beams: Acoustic Emission, Digital Image Correlation, Dynamic Identification

Acoustic Emission (AE), Digital Image Correlation (DIC) and Dynamic Identification (DI) techniques are used to analyse crack formation and propagation in plain concrete pre-notched beam specimens subject to three-point bending. Four dimensional scales are considered and scale effects on fracture energy, bending strength, and AE energy per unit area are investigated. The energy brittleness numbers are calculated for the different beam sizes to characterise the fragility of the specimens. For the larger sample, the principal strain directions obtained by DIC are put in relation with the crack path, while the analysis of resonant frequencies is used to correlate the bending stiffness reduction to the crack advancement.

A Hysteretic Constitutive Model for Reinforced Concrete Panel Elements

A simple yet effective constitutive model-referred to as the “Fixed Strut Angle Model” (FSAM)-is presented in this paper for simulating the nonlinear axial/shear behavior of reinforced concrete membrane (panel) elements subjected to generalized and reversed cyclic loading conditions. In the formulation of the FSAM, normal stresses in cracked concrete are calculated along fixed crack (strut) directions. Shear stresses developing along crack surfaces, which are calculated using a simple friction-based constitutive relationship, are superimposed with the concrete stresses along the struts, for obtaining the total stress field in concrete. Model predictions were compared with panel tests results available in the literature, at various global and local response levels. The model was demonstrated to reasonably capture the overall response characteristics of reinforced concrete panels, including hysteretic shear stress vs. strain behavior, shear stress capacity, hysteretic shear stiffness attributes, ductility, pinching behavior, governing failure mode, principal strain and stress directions, and local deformations.

Measurement of in vitro cardiac deformation by means of 3D digital image correlation and ultrasound 2D speckle-tracking echocardiography

Ultrasound-based 2D speckle-tracking echocardiography (US-2D-STE) is increasingly used to assess the functionality of the heart. In particular, the analysis of cardiac strain plays an important role in the identification of several cardiovascular diseases. However, this imaging technique presents some limitations associated with its operating principle that result in low accuracy and reproducibility of the measurement.In this study, an experimental framework for multimodal strain imaging in an in vitro porcine heart was developed. Specifically, the aim of this work was to analyse displacement and strain in the heart by means of 3D digital image correlation (3D-DIC) and US-2D-STE. Over a single cardiac cycle, displacement values obtained from the two techniques were in strong correlation, although systematically larger displacements were observed with 3D-DIC. Notwithstanding an absolute comparison of the strain measurements was not possible to achieve between the two methods, maximum principal strain directions computed with 3D-DIC were consistent with the longitudinal and circumferential strain distribution measured with US-2D-STE. 3D-DIC confirmed its high repeatability in quantifying displacement and strain over multiple cardiac cycles, unlike US-2D-STE which is affected by accumulated errors over time (i.e. drift).To conclude, this study demonstrates the potential of 3D-DIC to perform dynamic measurement of displacement and strain during heart deformations and supports future applications of this method in ex vivo beating heart platforms, which replicate more fully the complex contraction of the heart.

4941Machine learning based automated diagnosis of ischemic vs non-ischemic dilated cardiomyopathy using 3D myocardial deformation analysis

Abstract Background Late Gadolinium Enhancement (LGE) imaging is a reference standard technique for the differentiation of ischemic cardiomyopathy (ICM) from non-ischemic dilated cardiomyopathy (NIDCM) in patients with heart failure and reduced ejection fraction (HFrEF). 3D myocardial deformation analysis (3D-MDA) offers highly reproducible phenotypic assessments of regional architecture and function that may provide value for artificial-intelligence-assisted cardiomyopathy diagnosis without need for LGE imaging. Purpose In this study, we trained and validated a machine-learning-based model to enable automated diagnosis of ischemic versus non-ischemic dilated cardiomyopathy exclusively using regional patterns of deformation among patients otherwise matched by age, sex and global contractile dysfunction. Methods 100 ICM and 100 NIDCM patients matched for age, sex, and LVEF underwent standard cine SSFP and LGE imaging. Patient diagnoses were established using a combination of clinical and LGE-based criteria. 3D-MDA was performed using validated software (GIUSEPPE) to compute regional 3D strain measures at each cardiac phase in both conventional and principal strain directions. Principal Component Analysis (PCA) was performed on the composite 3D-MDA dataset. The first 20 components were chosen, accounting for approximately 65% of the population variance. Subsequently, a support-vector-machine-based algorithm was used with 10-fold cross-validation to discriminate ICM from NIDCM. Results Patients were 63±10 years (ICM: 63±10 years, NIDCM: 63±10 years, p=0.955), 74% male (ICM: 74%, NIDCM: 74%, p=1.000), and had a mean LVEF of 27±8% (ICM: 27±7%, NIDCM: 28±7%, p=0.688). Global time to peak strain was significantly shorter in ICM patients relative to NIDCM patients across all surfaces and in all directions (p<0.05). The highest single-variable Area Under the Curve (AUC) achieved for the classification of ICM versus NIDCM from global data was for minimum principal strain (ICM: 43.7±7.8, NIDCM: 48.3±7.5, p<0.001, AUC: 0.682) (Figure 1). However, a multi-feature machine-learning-based model exposed to all available regional 3D deformation data achieved an AUC of 0.903 (sensitivity 87.7%, specificity 75.5%). Conclusions Machine learning-based analyses of3D regionaldeformation patterns allows for robust discrimination of ICM versus NIDCM. Further expansion of the presented findings is planned on a wider, multi-centre cohort. Acknowledgement/Funding Dr. White was supported by an award from Heart and Stroke Foundation of Alberta. This study was funded in part by Calgary Health Trust.

INFLUENCE OF DISEASE PHENOTYPE ON THE ACCURACY OF EJECTION FRACTION TO ESTIMATE CONTRACTILE PERFORMANCE: ASSESSMENT BY MULTI-DIRECTIONAL 3D GLOBAL AXIS-DEPENDENT AND PRINCIPAL STRAIN ANALYSIS

Left Ventricular (LV) Ejection Fraction (EF) is a ubiquitously reported estimate of global contractile performance. While practical, the value of this marker across different geometric configurations has been challenged. With expanding availability of myocardial strain analysis techniques, opportunity exists to explore direct markers of tissue deformation. In this study we use 3-dimensional myocardial deformation analysis (3D-MDA) of cardiovascular magnetic resonance (CMR) cine images to calculate global circumferential, longitudinal, radial, and principal directions strain amplitude. This was performed across classified cohorts of ischemic cardiomyopathy (ICM), non-ischemic dilated cardiomyopathy (DCM), hypertrophic cardiomyopathy (HCM) and healthy volunteers. Respective associations of LVEF to each strain-based marker of contractile performance were evaluated. Three-hundred-ninety-seven subjects underwent standard CMR imaging (3T) inclusive of multi-axial cine imaging. The study population included 78 with ICM, 86 with DCM, 85 with HCM, and 148 healthy controls. All cardiomyopathy states were confirmed by published criteria. LV volumes and LVEF were blindly calculated using commercial software. Axis dependent (circumferential, longitudinal, and radial) as well as principal strain (minimum, secondary, and maximum) amplitudes were computed by means of validated in-house software (3D-MDA) leveraging on short-axis and long-axis cine images. For the current analysis, association of global estimates of strain were reported and compared to LVEF using linear regression analysis. Mean age was 55.6±10.8 years (DCM: 58.4±11.3, ICM: 61.3±9.8, HCM: 50.1±11.2, normals: 54.0±8.8 years) with 134 (34%) female (DCM: 13%, ICM: 34%, HCM: 35%, normals: 40%). Mean LVEF was 50.5±21.2% (DCM: 26.5±8.3, ICM: 26.9±6.8%, HCM: 70.0±7.4%, normals: 65.6±5.5%). All associations of strain amplitude markers and LVEF are reported in Table 1. Across the entire population, strong associations were found between LVEF and all measures of strain amplitude (r=0.75 to r=0.92, p < 0.0001 for all). Performance was good in normal controls (r=-0.20 to r=-0.40, p < 0.005), although poor correlation was seen subepicardially for both minimum principal and circumferential directions of strain. Among diseased cohorts, associations were strongest for DCM (r=0.42 to r=0.60, p < 0.0001 for all). ICM patients maintained strong associations, although were objectively weaker with loss of significance for radial strain (wall thickening). HCM patients showed poor associations for LVEF across all strain-based parameters, statistical significance only maintained for subendocardial-based estimates of strain. Versus validated reference standards of myocardial deformation, LVEF is a sub-optimal measure of global contractile performance in patients with HCM and is associated with variable performance in patients with ICM.

Effects of strain state and slip mode on the texture evolution of a near-α TA15 titanium alloy during hot deformation based on crystal plasticity method

A thorough understanding of the texture evolution of near-α titanium alloys during the hot metal forming can help obtain an optimal crystallographic texture and material performance. The strain state has an obvious effect on the texture evolution of near-α titanium alloys during the hot metal forming. In this paper, the texture evolution of a near-α TA15 titanium alloy during the hot metal forming under different strain states were discussed based on the crystal plasticity finite element method. It is found that the basal and prismatic slip systems are regarded as the dominant slip modes due to the similar low critical resolved shear stress during the hot metal forming of the TA15 sheet rotating the lattice around the [101¯0] and 〈0001〉 axis, respectively. Once both of them cannot be activated, the pyramidal-2 slipping occurs rotating the lattice around the [101¯0] axis. The relationship between the texture evolution and strain state is established. All the (0001) orientations form a band perpendicular to the direction of the first principal strain. The width of the band along the direction of the second principal strain depends on the ratio of the compressive effect to the tensile effect of the second principal strain. This relationship can help control the crystallographic texture and mechanical properties of the titanium alloys component during the hot metal forming.

Two-shape-tensor model for tumbling in nematic polymers and liquid crystals.

Most, but not all, liquid crystals tend to align when subject to shear flow, while most nematic polymeric liquid crystals undergo a tumbling instability, where the director rotates with the flow. The reasons of this instability remain elusive, as it is possible to find similar molecules exhibiting opposite behaviors. We propose a continuum theory suitable for describing a wide range of material behaviors, ranging form nematic elastomers to nematic polymers and nematic liquid crystals, where the material parameters have meaningful physical interpretations and the conditions for tumbling emerge clearly. There are two possible ways to relax the internal stress in a nematic material. The first is the reorganization of the polymer network, the second is the alignment of the network natural axis with respect to the principal direction of the effective strain. We show that tumbling occurs whenever the second mechanism is less efficient than the first. Furthermore, we provide a justification of the experimental fact that at high temperatures, in an isotropic phase, only flow alignment is observed and no tumbling is possible, even in polymers.

Shear Strength of Trapezoidal Corrugated Steel Webs for Horizontally Curved Girder Bridges

Curved composite girder bridges with corrugated steel webs (CSWs) have already been constructed around the world. However, limited work has been done on their shear behavior. In this paper, the corrugated steel web (CSW) in horizontally curved girders (HCGs) is treated as an orthotropic cylindrical shallow shell, and the analytical formula for the elastic global shear buckling stress is deduced by the Galerkin method. Calculation tables for the global shear buckling coefficient for a four-edge simple support, for a four-edge fixed support, and for the two edges constrained by flanges fixed and the other two edges simply supported are given. Then, a parametric study based on a linear buckling analysis is performed to analyze the effect of the curvature radius and girder span on the shear buckling stress. Analytical and numerical results show that the difference of shear buckling stress of CSWs between curved girders and straight girders is small, so the shear design formulas for straight girders can be applied for curved girders. Finally, a series of tests were performed on three curved box girders with CSWs. Similar to CSWs in straight girders, the shear strain distributions of CSWs in HCGs are almost uniform along the direction of the web height and the principal strain direction angles are close to 45°. For the three specimens, CSWs carry about 76% of the shear force. In the destructive test, shear buckling after yielding occurred in all specimens which is in good agreement with the theoretical prediction, which means that the analytical formulas provide good predictions for the shear buckling stress of CSWs in HCGs and can be recommended for design purposes.

Validation of three-dimensional echocardiographic principal strain analysis for assessing left ventricular contractility: An animal study.

The three-dimensional (3D) principal strain represents the major direction and magnitude of the deformation by its definition and can be measured using 3D echocardiography. We aimed to validate 3D echocardiographic left ventricular (LV) global principal strains as an assessment of LV contractility by comparison with gold standard invasive measurements. In 14 beagles, the LV pressure-volume loop was recorded to invasively measure the end-systolic pressure-volume relationship (ESPVR) and dP/dt as reference indicators representing LV contractility. The echocardiographic image was obtained simultaneously, and endocardial motions and volume changes were extracted in the form of speckle-tracking point grids to calculate strains. High or low inotropic states were induced pharmacologically by using an intravenous infusion of dobutamine and esmolol, respectively. The direction of 3D endocardial global principal strain (GP1S) appeared to be circumferential. The dP/dt showed the highest Pearson's correlation coefficients with GP1S (r = -0.845, P < 0.001), whereas ESPVR showed the best correlation with global secondary strain (GP2S; r = -0.819, P < 0.001). In comparison with GP1S and GP2S, global circumferential (GCS) and longitudinal strains (GLS) tended to correlate less with invasive measurements, respectively. LV ejection fraction showed excellent correlations with GP1S or GCS, but the correlation with GLS was relatively weak. The correlations between invasive measurements and GP2S or GLS were strengthened when strains were corrected by the LV residual volume ratio, whereas those of GP1S or GCS were weakened after correction. The principal direction of the LV endocardial contraction presents circumferential behavior reflecting LV volume change. The 3D principal strains derived from 3D echocardiography are reliable indicators for LV contractility and seem better than conventional strains.

Non-uniform strain distribution in anterolateral capsule of knee: Implications for surgical repair.

The existence of a ligamentous structure within the anterolateral capsule, which can be injured in combination with the anterior cruciate ligament, has been debated. Therefore, the purpose of this study was to determine the magnitude and direction of the strain in the anterolateral capsule in response to external loads applied to the knee. The anterolateral capsule was hypothesized to not function like a traditional ligament. A 6-degree-of-freedom robotic testing system was used to apply ten external loads to human cadaveric knees (n = 7) in the intact and anterior cruciate ligament (ACL) deficient states. The position of strain markers was recorded on the midsubstance of the anterolateral capsule during the resulting joint kinematics to determine the magnitude and direction of the maximum principal strain. The peak maximum principal strain ranged from 22% to 52% depending on the loading condition. When histograms of strain magnitude values were analyzed to determine strain uniformity, the mean kurtosis was 1.296 ± 0.955, lower than a typical ligament, and the mean variance was 0.015 ± 0.008, higher than a typical ligament. The mean angles of the strain direction vectors compared to the proposed ligament ranged between 38° and 130° (p < 0.05). The magnitude of the maximum principal strain in the anterolateral capsule is much larger than a typical ligament and does not demonstrate a uniform strain distribution. The direction of strain is also not aligned with the proposed ligament. Clinical Significance: Reconstruction methods using tendons will not produce normal joint function due to replacement of a multi-axial structure with a uni-axial structure. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res.

Contemporary crustal tectonic movement in the southern Sichuan-Yunnan block based on dense GPS observation data

We analyzed 360 permanent and campaign GPS data from 1999 to 2017 in the southern Sichuan-Yunan block, and obtained crustal horizontal deformation in this region. Then, we derived the strain rate using a multi-scale spherical wavelet method. Results reveal a complex pattern of tectonic movement in the southern Sichuan-Yunnan block. Compared to the stable Eurasian plate, the maximum rate of the horizontal deformation in the southern Sichuan-Yunnan block is approximately 22 mm/a. The Xiaojiang fault shows a significantly lower deformation—a left-lateral strike-slip movement of 9.5 mm/a. The Honghe fault clearly shows a complex segmental deformation from the north to south. The northern Honghe fault shows 4.3 mm/a right strike-slip with 6.7 mm/a extension; the southern Honghe fault shows 1.9 mm/a right strike-slip with 1.9 mm/a extension; the junction zone in the Honghe and Lijiang–Xiaojinhe faults shows an obvious clockwise-rotation deformation. The strain calculation results reveal that the maximum shear-strain rate in this region reaches 70 nstrain/a, concentrated around the Xiaojiang fault and at the junction of the Honghe and Lijiang–Xiaojinhe faults. We note that most of the earthquakes with magnitudes of 4 and above that occurred in this region were within the high shear strain-rate zones and the strain rate gradient boundary zone, which indicates that the magnitude of strain accumulation is closely related to the seismic activities. Comparison of the fast shear-wave polarization direction of the upper-crust with the upper-mantle anisotropy and the direction of the surface principal compressive strain rate obtained from the inversion of the GPS data reveals that the direction of the surface principal compressive strain is basically consistent with the fast shear-wave polarization direction of the upper crust anisotropy, but different from the polarization direction of the upper mantle. Our results support the hypothesis that the principal elements of the deformation mechanism in the southern Sichuan-Yunnan block are decoupling between the upper and lower crust and ductile flow in the lower crust.

Strain Field Associated With a Component of Divergent Motion Along the Southern Dead Sea Fault: Insights From Magnetic Fabrics

AbstractIn order to reconstruct the strain field along the southern segment of the Dead Sea Fault (DSF) plate boundary, we analyzed the magnetic fabrics of carbonate rocks, outcropping along it. The magnetic fabrics provide a microstructural indicator that help to approximate the principal strain directions in the rocks. Our analysis includes ~900 cores from 58 sampling localities, along ~400 km of the southern DSF. We measured the magnetic fabrics of (1) pure calcite‐bearing limestones that consist diamagnetic fabrics and (2) chalks with composite fabrics, which we further separated into diamagnetic and paramagnetic subfabrics, using measurements of Anisotropy of Magnetic Susceptibility at low temperatures. The results show that 87% of the diamagnetic fabrics and subfabrics are of tectonic origin. The orientations of the maximum Anisotropy of Magnetic Susceptibility axes (K3 axes) approximately align with the maximum horizontal shortening directions along the southern segment of the DSF, differ from the remote stress direction, and are largely parallel to the main trace of the DSF. This parallelism is not related to local variations in the geometry of the faults. We suggest that the deflection of the maximum horizontal shortening parallel to the transform plate boundary is a kinematic consequence of the Sinai‐Arabia relative plate motion, which expresses a component of divergence along the southern segment of the DSF. We conclude that magnetic fabrics of carbonate rocks are sensitive and reliable microstructural indicators for determination of the strain field along major fault systems.

Simple shear: eigenvectors of cauchy-green tensors rotate against each other

Simple shear represents a somewhat complex case of deformation although it is very good studied. In this paper, we discuss a new aspect of simple shear which has not been observed before. Rotations of the eigenvectors of the right and left Cauchy-Green tensors with increasing amount of shear under the kinematically defined simple shear are theoretically studied. An analysis has been done within a framework of the nonlinear theory of elasticity. Mathematical processor Maple is used for the calculations and animation of the results. Phenomena of mutually opposite rotations of the eigenvectors of the right and left Cauchy-Green tensors is fond that can be important for anisotropic and in particular fibre-reinforced materials. We studied rotations of principal strain directions under the kinematically defined simple shear. Accordingly, eigenvectors of the right and left Cauchy-Green tensors rotate against each other with the increasing amount of shear. Interestingly, the eigenvectors of b rotate in the same direction as line elements of the material while the eigenvectors of C in the opposite direction. For example, this can be important for anisotropic and in particular fiber reinforced materials. In this case, the direction of the maximal stretch will rotate with respect to reinforcement directions.

Determination of the block movements in the eastern section of the Gediz Graben (Turkey) from GNSS measurements

The source parameters of an earthquake should be determined in detail to calculate deformations caused by that earthquake and to identify faults that are likely to break. Today, the GNSS method is frequently used to determine these source parameters. However, to date, no detailed study has been conducted for this purpose in the eastern section of the Gediz Graben. Therefore, in this study, the GNSS technique was used to determine the tectonic movements in the area between Alaşehir and Sarıgöl in the Gediz Graben. For the implementation of the GNSS technique, 11 benchmark sites, which had been previously established for different purposes in the area, were used, and the measurements were performed in 2013, 2014, and 2015. The GNSS measurements obtained at these sites were evaluated by GAMIT/GLOBK software, and the annual velocity values of the sites were obtained (with respect to the Eurasian plate). The resulting annual horizontal velocity values obtained at the GNSS sites ranged from 12 mm/yr to 27 mm/yr. It was observed that the sites with the highest vertical movements were within the graben. The annual vertical velocity value at the TRAZ site located in the east of the graben was obtained to be approximately −90 mm/yr. This site was followed by BGCL (-33 mm/yr) and AKCL (−13 mm/yr) toward the west of the graben. Furthermore, significant strain accumulations were derived in the study area, and their compliance with the tectonic structure of the region was revealed. The maximum and minimum principal strain parameters and the direction of maximum principal strain that provided the average drift and compression directions for the region were obtained to be 0.604 μs/yr, -0.375 μs/yr, and 11.27 °, respectively. Block modeling in the study area revealed that the annual strike slip ranged from 4 ± 1.2 mm/yr to 19.3 ± 0.6 mm/yr, and the dip slip varied between -23.3 ± 0.5 mm/yr and -16.0 ± 0.5 mm/yr.

Analytical model for shear strength estimation of reinforced concrete beam-column joints

A model capable of predicting the shear response of beam-column joints subjected to seismic actions is presented. The analytical model, originally developed for walls and based on a simple physical formulation, is adapted. It considers mean stress and strain fields based on a reinforced concrete panel representing the joint, under the assumption that the principal concrete stress and principal strain directions coincide. Simple constitutive material laws are considered for concrete and steel. To estimate the shear capacity, the model satisfies the equilibrium in the longitudinal (vertical) direction. In order to analyze the accuracy of the model, a database integrated by 92 tests of exterior and interior beam-column joints is collected from the literature. Noting that the original model does not consider the effect of confinement product of adjacent elements to the connection, this effect is introduced through factors that reduce the values of the longitudinal and transverse strain used to calibrate the angle of the strut. In addition, the contribution of the transverse reinforcement in the capacity of the element is included. These modifications together with the influence of the boundary reinforcement, yields a good strength estimate for exterior and interior joints that fail in shear. When comparing with other models from the literature, it is observed that the proposed model provides one of the best correlations.