Displacement Gradient Research Articles

IOP-induced regional displacements in the optic nerve head and correlation with peripapillary sclera thickness

Mechanical insult induced by intraocular pressure (IOP) is likely a driving force in the disease process of glaucoma. This study aimed to evaluate regional displacements in human optic nerve head (ONH) and peripapillary tissue (PPT) in response to acute IOP elevations, and their correlations with morphological characteristics of the posterior eye. Cross-sectional (2D) images of the ONH and PPT in 14 globes of 14 human donors were acquired with high-frequency ultrasound during whole globe inflation from 5 to 30 mm Hg. High-frequency ultrasound has a spatial resolution of tens of micrometers and is capable of imaging through the ONH and PPT thickness. Tissue displacements were calculated using a correlation-based speckle tracking algorithm for a dense matrix of kernels covering the 2D imaging plane. The ONH was manually segmented in the ultrasound B-mode images acquired at 5 mmHg based on echogenicity. The lamina cribrosa (LC) boundaries were visible in eight of the fourteen eyes and the LC region was segmented using a semi-automated superpixel-based method. The ONH had larger radial displacement than the PPT in all tested eyes and the difference increased with increasing IOP. A significant negative correlation was found between ONH-PPT displacement difference and PPT thickness (p < 0.05), while no significant correlations were found between ONH-PPT displacement difference and other morphological parameters including PPT radius of curvature, scleral canal size, LC thickness and anterior LC surface depth. Within the ONH, the radial displacement decreased in the region anterior to and across LC but not in the region posterior to LC. Finite element models using simplified geometry and material properties confirmed the role of LC in reducing the overall ONH radial displacements, but did not predict the displacement gradient change observed experimentally. These results suggested that a thinner PPT may be associated with a larger relative posterior motion of the ONH with respect to the surrounding PPT and the LC may play a major role in preventing excessive posterior displacement of ONH during acute IOP elevations.

On Some Non-existence Results in a Semilinear Theory of the Dipolar Thermoelastic Bodies

We consider a thermoelastic theory in which the equations that govern the evolution are linear with respect to the thermal displacement and nonlinear with regards to gradients of displacements and temperature. Our results refer to the non-existence of solutions for some mixed problems, considered in this context. We also address the instability of solutions of the considered problems. We will treat separately the case where the mechanical effects are neglected, taking into account only the thermal effect. In this case our problem has a nonlinear structure.

On Green and Naghdi Thermoelasticity Model without Energy Dissipation with Higher Order Time Differential and Phase-Lags

In the present work, a modified model of heat conduction including higher order of time derivative is derived by extending Green and Naghdi theory without energy dissipation. We introduce two phase lag times to include the thermal displacement gradient and the heat flux in the heat conduction and depict microscopic responses more precisely. The constructed model is applied to study thermoelastic waves in a homogeneous and isotropic perfect conducting unbounded solid body containing a spherical cavity. We use the Laplace transform method to analyze the problem. The solutions for the field functions are obtained numerically using the numerical Laplace inversion technique. The results are analyzed in different tables and graphs and compared with those obtained earlier in the contexts of some other theories of thermoelasticity.

On a multi-phase-lag model of coupled thermoelasticity

Various qualitative properties of the dual/three-phase-lag heat equations are discussed. A refined model of coupled thermoelasticity is formulated to consider three delay times: a phase-lag of heat flux, a phase-lag of temperature gradient, and a phase-lag of thermal displacement gradient. Three special cases are considered to deal with all the considered models in the literature. In the first case one can obtain the simple and Tzou's dual-phase-lag, Lord–Shulman and the classical models. The Green–Naghdi type II model of generalized thermoelasticity without energy dissipation is obtained in the second case. Case 3 is devoted to considering the Green–Naghdi type III model. As an application, a unified form to a multi-phase-lag model is presented to yield all the preceding models as well as the Green–Lindsay generalized thermoelasticity model. A validation example is provided to discuss the coupled solution for photothermal semiconducting isotropic beam. Some illustrative flowcharts and plots are added and concluding remarks are presented.

Surface Displacement Distributions for the July 2019 Ridgecrest, California, Earthquake Ruptures

ABSTRACTSurface rupture in the 2019 Ridgecrest, California, earthquake sequence occurred along two orthogonal cross faults and includes dominantly left-lateral and northeast-striking rupture in the Mw 6.4 foreshock and dominantly right-lateral and northwest-striking rupture in the Mw 7.1 mainshock. We present &amp;gt;650 field-based, surface-displacement observations for these ruptures and synthesize our results into cumulative along-strike displacement distributions. Using these data, we calculate displacement gradients and compare our results with historical strike-slip ruptures in the eastern California shear zone. For the Mw 6.4 rupture, we report 96 displacements measured along 18 km of northeast-striking rupture. Cumulative displacement curves for the rupture yield a mean left-lateral displacement of 0.3–0.5 m and maximum of 0.7–1.6 m. Net mean vertical displacement based on the difference of down-to-the-west (DTW) and down-to-the-east (DTE) displacement curves is close to zero (0.02 m DTW). The Mw 6.4 displacement distribution shows that the majority of displacement occurred southwest of the intersection with the Mw 7.1 rupture. The Mw 7.1 rupture is northwest-striking and 50 km long based on 576 field measurements. Displacement curves indicate a mean right-lateral displacement of 1.2–1.7 m and a maximum of 4.3–7.0 m. Net vertical displacement in the rupture averages 0.3 m DTW. The Mw 7.1 displacement distributions demonstrate that maximum displacement occurred along a 12-km-long portion of the fault near the Mw 7.1 epicenter, releasing 66% of the geologically based seismic moment along 24% of the total rupture length. Using our displacement distributions, we calculate kilometer-scale displacement gradients for the Mw 7.1 rupture. The steepest gradients (∼1–3 m/km) flank the 12-km-long region of maximum displacement. In contrast, gradients for the 1992 Mw 7.3 Landers and 1999 Mw 7.1 Hector Mine earthquakes are &amp;lt;0.6 m/km. Our displacement distributions are important for understanding the influence of cross-fault rupture on Mw 6.4 and 7.1 rupture length and displacement and will facilitate comparisons with distributions generated remotely and at broader scales.

Three-phase-lag bioheat transfer model and its validation with experimental data

In this study, we introduce a three-phase-lag (TPL) bioheat transfer model for living biological tissue by considering the heat conduction law that includes heat flux, temperature gradient and thermal displacement gradient, among the constitutive relation. The formulated TPL bioheat model is an extension of bioheat transfer models proposed by Pennes, Cattaneo-Vernotte and Tzou. The semi-analytical method has been used for the solution of TPL bioheat transfer model and this model is validated with experimental data [Stolwijk, J. A. J., and J. D. Hardy. 1966. Temperature regulation in man: a theoretical study. Pflugers Archiv Fur Die Gesamte Physiologie Des Menschen Und Der Tiere 291(2):129–62]. The phase lag times due to heat flux, temperature gradient and thermal displacement gradient is semi analytically investigated and it is found that phase-lag due to thermal displacement gradient affects significantly on temperature distribution in tissue. The semi-analytical solution has been verified with a numerical solution. The effect of parameters, such as lagging times, blood perfusion rate, metabolic heat source term and TPL parameter on tissue temperature is also discussed in detail. Highlights Three-phase-lag bioheat transfer model has been introduced for the study of heat transfer in living biological tissue. The semi analytical method has been used for the solution of the TPL model. Proposed model is validated with experimental data. The formulated TPL model is more accurate than other existing models.

On dissipative gradient effect in higher-order strain gradient plasticity: the modelling of surface passivation

The phenomenological flow theory of higher-order strain gradient plasticity proposed by Fleck and Hutchinson (J. Mech. Phys. Solids, 2001) and then improved by Fleck and Willis (J. Mech. Phys. Solids, 2009) is used to investigate the surface-passivation problem and micro-scale plasticity. An extremum principle is stated for the theory involving one material length scale. To solve the initial boundary value problem, a numerical scheme based on the framework of variational constitutive updates is developed for the strain gradient plasticity theory. The main idea is that, in each incremental time step, the value of the effective plastic strain is obtained through the variation of a functional in regard to effective plastic strain, provided the displacement or deformation gradient. Numerical results for elasto-plastic foils under tension and bending, thin wires under torsion, are given by using the minimum principle and the numerical scheme. Implications for the role of dissipative gradient effect are explored for three non-proportional loading conditions: (1) stretch-passivation problem, (2) bending-passivation problem, and (3) torsion-passivation problem. The results indicate that, within the Fleck–Hutchinson–Willis theory, the dissipative length scale controls the strengthening size effect, i.e. the increase of initial yielding strength, while the surface passivation gives rise to an increase of strain hardening rate.

IN SITU MEASUREMENT OF TIRE PLY STEER BASED ON AN INTELLIGENT TIRE SYSTEM

ABSTRACT Ply steer is an inherent property of a belted tire, manifesting as the nonzero side force at a slip angle of zero, and it is thus an important design factor relevant to a vehicle's straight running, safety, and comfort. Although ply steer is a rolling contact phenomenon, there is a lack of approaches for direct measurement and modeling of tire ply steer force in motion. Thus, we developed an in situ measurement method for tire ply steer based on a recently proposed accelerometer-based intelligent tire system. This new measurement method is significant for three main reasons: it facilitates understanding of the inherent mechanism of ply steer for radial tires, it improves the intelligent tire's accuracy based on the accelerometer, and it provides an in situ measurement approach for tire ply steer. An accelerometer-based intelligent tire was developed to obtain acceleration measurements at different conditions in which the lateral behavior is of particular interest. Two unusual phenomena that have never been reported are observed: (1) lateral accelerations demonstrate asymmetrical behavior with respect to positive/negative slip angles and (2) lateral accelerations at zero slip angle still exist. It is hypothesized that the underlying reason for these two unusual phenomena is the ply steer–dependent kinematics, which can conversely be used to measure tire ply steer in situ. To this end, the mixed Lagrange–Euler approach for rolling contact kinematics is used to formulate tire lateral acceleration, which links both rigid motion and elastic displacement. It is clearly found that the lateral acceleration is proportional to the square of the rotating velocity and the second-order gradient of displacement. Based on this kinematic model, the features of lateral acceleration can be easily explained by tire ply steer, which manifests as the sinusoidal lateral deformation modes due to the coupling of the bending-twist deformation of the cord–rubber composites of the tire belt. The proposed hypothesis has been verified by finite element method simulations, and the experimental results prove that tire ply steer leads to the observed unusual lateral acceleration pattern. Thus, the quantitative value of ply steer could be measured in situ by integrating the obtained lateral acceleration and thus the apparent elastic slip angle, even under zero external wheel slip angle. In this manner, the intelligent tire system provides a direct measurement approach for tire ply in motion. In addition, the accuracy of the intelligent tire's algorithm might be improved by suitable modeling of the asymmetrical acceleration with respect to left/right slip based on the proposed hypothesis of ply steer–dependent kinematics.

Temperature dependence of differential capacitance in the electric double layer.Symmetric valency 1:1 electrolytes.

The differential capacitance of an electric double layer formed by an aqueous solution of KNO3 on a glassy carbon electrode is measured by impedance analysis at constant frequency. Results are obtained at electrolyte concentrations of 0.1 mol/dm3, 0.5 mol/dm3, and 1.0 mol/dm3, and at a series of temperatures, viz., 288 K, 298 K, 308 K, 318 K, and 328 K. The differential capacitance envelopes reveal a rich, complex pattern of maxima, minima, and local minima, whose magnitude and position change with a change in solution concentration. At the two lower concentrations, the temperature dependence of the capacitance, for example, at zero electrode potential, shows an alternating positive-negative behavior, while at the highest concentration of 1.0 mol/dm3, the slope of the differential capacitance-electrode potential curve is always positive. The experimental results are supplemented by a numerical grand canonical Monte Carlo simulation study of a restricted primitive model double layer but with an off-center cationic charge achieved by displacing the charge center from the ion sphere center toward its surface. The simulations, performed at the electrolyte concentration of 1.0 mol/dm3 and constant cation charge center displacement, and at varying electrode potentials and temperatures, show, in general, a negative temperature dependence of the differential capacitance. However, this temperature dependence can also be positive for a negative electrode charge and for a sufficiently large gradient of the cation charge center displacement with temperature. This feature is seen to be associated with an increase in the entropy of formation of the double layer.

Loose and Broken Distribution of Soft Coal-rock in Deep Coal Roadway Sidewall

A FLAC3D numerical model was established on the basis of the coal occurrence conditions of the pedestrian preparatory workings in the central mining block (Area 11–2) of Kouzidong Mine, Huainan, Anhui province, China. The distribution of displacement fields of coal roadway sidewalls was analyzed. The displacement gradient between the line connecting a location of the coal rock at the deep coal roadway wall to the roadway center was used to characterize the bulking conditions of the sidewall and the loose and broken distribution of soft coal rock in the sidewall was obtained. When the depth of a typical roadway ranged from 750 to 880 m, loose and broken coal rocks were distributed widely along the deep coal roadway sidewall, especially in the middle and upper part, with a scope of about 5.0 to 6.0 m. Bulking occurred largely in the middle and lower part of the roadway sidewall. This study will provide a basis for the selection of appropriate support materials to maintain the stability of deformation of coal roadway sidewalls.

Two-channel all-elastic solid-solid phononic switch

We have investigated the elastic wave switching based on nonlinear phononic crystals. The phononic crystal structure contains of an input waveguide and two output waveguides that acts as elastic 1 × 2 switch. The input wave with low intensity propagates through bar waveguide; in this case the performance of structure is linear. By increasing the intensity of input wave, nonlinear behavior is appeared and the applied wave propagates through cross waveguide. Increment of the gradient of displacement results in the nonlinear behavior in phononic structure and changing the mass density of the propagation medium. Changing the mass density of constituent materials shifts the frequency of defect modes. By these feature, designing of elastic 1 × 2 switch is realized.

Pixel Offset Fusion of SAR and Optical Images for 3-D Coseismic Surface Deformation

This letter presents a 3-D fusion method combining with the pixel offset results of synthetic aperture radar (SAR) and optical images for measuring 3-D coseismic deformation, which suffered the limitations of huge displacement gradient, low coherence, and large temporal interval. This method takes the advantages of the pixel offset results of the two different types of satellites. We use the hanging wall deformation of the 1999 Chi-Chi earthquake as an example and generate two sets of 3-D coseismic displacements from the fusion method and radar images only. We compare the two sets of results to GPS and field survey data, and the 3-D fusion result shows more consistent 3-D displacements than one derived from radar images with decreased root mean square (rms) values of 20%-50%. The results of this letter provide a detailed information of displacement distribution in the hanging wall of the Chelungpu fault (CLPF) during the Chi-Chi earthquake. Along the fault, the vertical displacement increases from south to north gradually and the vertical pattern follows the topography. The area where uplift starts to be higher than the average of vertical displacements is consistent with the turning point of CLPF. The 3-D fusion method appears not only the potentials to describe the uplift behavior of active fault, but also the abilities to constrain the subsurface fault geometry.

An Indirect Experimental Measurement Method for Contact Length Identification in Non-conforming Frictionless Contact

Background: The non-conforming contact usually induce stress concentration as the interaction only occurs at a small interface. Theoretical and numerical investigations have shown that the contact stress distribution and maximum pressure are closely related to the length of the contact interface. Objective: Therefore, the characterization of the contact length is a key issue in studying the contact behavior and the corresponding structural safety. Methods: In this paper, we propose an indirect experimental identification approach that can reliably characterize the contact length between non-conforming frictionless surfaces. The relationship between the contact length and the local displacement is established based on the contact theory, and a modified digital image correlation method is implemented to acquire the displacement field near the contact area. The contact length is then identified with the established model and the measured displacement gradient through an identification algorithm, which can be easily calculated and does not require an optimization process. Results: Both simulations and experiments are performed to evaluate the precision and applicability of the proposed approach. The identification error maintains within a very low level during different load steps. Conclusions: The results indicate that the proposed method can accurately identify the contact length and has the ability to against the inevitable measurement inaccuracy of the displacement field.

Effect of single and multiple parts manufacturing on temperature-induced residual stress problems in SLM

In this study, the effects of the single and multiple productions of samples by additive manufacturing on residual stress and displacement (distortions) were investigated. The samples were manufactured by Selective Laser Melting (SLM) machine using Ti6Al4V powders. Each time a different number (1, 5 and 13 samples) of cubic shaped samples were produced on the building platform. During the process, samples were observed with a thermal camera first, in order to understand the relationship amongst the residual stress, displacement and temperature gradients. Then, displacement values were measured experimentally with Coordinate Measurement Machine (CMM) device. Next, both displacement and residual stresses were calculated via Finite Element Analysis (FEA) method. Finally, residual stresses and displacement equations were determined by genetic expressional programming (GEP) using the results and data obtained from the tests and FEA. According to the results, the regression values of residual stress and displacement equation were found to be 0.96% and 0.88%, respectively. As the number of manufactured samples on the same platform increased, temperatures and irregular temperature distribution were increased.

Non-local modeling with asymptotic expansion homogenization of random materials

The aim of this study is to build a non-local homogenized model for three-dimensional composites with inclusions randomly embedded within a matrix according to a stochastic point process w=(wi)i∈N in a bounded open set of R3 associated with a suitable probability space (⅁,A,P) as defined in Nait-ali (2017) and Michaille et al. (2011). Both phases were linear elastic. Asymptotic expansion homogenization (AEH) was revisited by taking into account the stochastic parameter (w) representing the inclusion centers distribution. The macroscopic behavior was then studied by combining the variational approach with the mean-ergodicity. At the end, the advanced approach makes naturally emerge non-local terms (involving the second displacement gradient) as well as a strong microstructural content through the presence of the characteristic tensors in the expression of the homogenized elastic energy. Microstructures with a high contrast between constituents Young′s modulus leading to non-local effects were considered to test the model. Virtual microstructures were first generated with a fixed, simple, pattern before considering real microstructures of Ethylene Propylene Dien Monomer (EPDM) containing cavities in order to envision morphological situations with increasing complexity.

Normal fault networks and their spatial relationships in Plio-Quaternary sedimentary series: A case study in the Zanjan Depression, NW Iran

Well-exposed normal fault networks in the Plio-Quaternary sedimentary series of the Zanjan Depression, Iran, were studied in order to analyse the spatial relationships and evolution of fault and damage zone structures in low-burial (~200 m) conditions. Despite the poorly-consolidated, geologically young nature of sediment, fault networks show several characteristics more typical of faulting in lithified strata. Key controls on the evolution of fault networks are found to be fault interactions, segment linkage, and the mechanical stratigraphy resulting in dip refraction, fault segmentation, the development of fault bends and steps, vertical fault overlap zone breaching, and bed-parallel slip. The data show a decrease of fracture frequency away from the fault cores. The obtained data show that damage zones width increases with fault displacement in a non-linear manner. Furthermore, damage zones appear more deformed and wider in the hanging-wall than in the footwall. A plot of damage zone width versus total fault throw reveals a positive but non-linear correlation, and the best-fit function corresponds better to a power-law relationship. The relationship between displacement and length shows a sub-vertical growth path with large displacement gradients typical of faulting in partially-lithified strata, due to shale ductility accommodating fault tip-related strains. A model for the evolution of the normal fault system is proposed based on spatial distribution of deformation, particularly fault segmentation, segment linkage, and damage zone development, as influenced by initial fault spacing, mechanical stratigraphy and the low burial conditions.

A Re-Examination of Wave Dispersion and on Equivalent Spatial Gradient of the Integral in Bond-Based Peridynamics

In this paper, wave dispersion properties in bond-based peridynamics (BBPD) are re-examined. By BBPD formulation, wave dispersion (frequency (ω) - wavenumber (k)) relation is known to be transcendental in nature. In fact, for uniform micromodulus function (C), there exists a frequency bandwidth with multiple k. Further, there is a ω within this bandwidth at which propagating k are infinite in number. Question that needs an answer is can all k propagate in the BBPD? In literature, an agreement between certain continuum gradient models (CM) and BBPD has been reported. This agreement is established in the sense that, for a judicious choice of C, wave dispersion properties are the same between BBPD and CM. This equivalence between a finite-ordered (CM) and an infinite-ordered (BBPD) displacement gradient model motivates to an associated converse question: given a C, does BBPD integral represent an effective displacement gradient of a finite order? In this paper, an attempt has been made to fix an order to the BBPD integral with the help of a Fourier frequency-based spectral study, under a one-dimensional rod setting. Both kinetically local and nonlocal formulations of BBPD are considered. It is argued that only one wave mode may propagate in a BBPD rod. This implies, Neumann force condition at a boundary should read as a spatial gradient of order one. This further implies, the BBPD spatial integral effectively represents a second-order displacement gradient in space. The wave motion study of this paper corroborates with the literature that applies local boundary conditions to nonlocal boundary value problems.

A remeshing strategy for large deformations in the finite cell method

The simulation of large structural deformations with the finite element method poses several challenges. The severe distortion of elements may deteriorate the accuracy and robustness of the method and restrict it to smaller deformations than desired. This issue is especially present in the finite cell method (FCM), where complex geometries are discretized with a non-conforming Cartesian grid introducing a fictitious material with very low stiffness. The remeshing strategy presented here improves the robustness at the cost of generating a new Cartesian grid of the deformed geometry at load steps where the element distortion becomes critical. This allows us to use larger load steps and to further deform the structure under consideration. We use radial basis functions to transfer the displacements and the displacement gradients from one mesh to the next one. The method is investigated in combination with a hyperelastic material and exemplary applied to simulate a pore of a foam.

Crack path tracking from full field measurements: A novel empirical methodology

AbstractThe identification of crack growth models requires the knowledge of the crack path geometry and, in particular, of the crack tip position. The objective of the present paper is to provide a criterion for the detection of the crack tip position regardless of the loading conditions or the material behavior. The novelty of the proposed approach is its ability to provide a good estimation of the crack tip even when large plastic deformations occur. The proposed empirical criterion uses the evolution of the displacement gradient standard deviation along a potential crack path to locate the crack tip. It thus relies on full field measures that are relatively smooth while providing accurate displacement vectors even close to the lips. We successfully apply the proposed criterion in two cases of fatigue crack growth: A straight crack at high temperature and a curved crack at room temperature involving large plastic deformations.

Theoretical development of continuum dislocation dynamics for finite-deformation crystal plasticity at the mesoscale

The equations of dislocation transport at finite crystal deformation were developed, with a special emphasis on a vector density representation of dislocations. A companion thermodynamic analysis yielded a generalized expression for the driving force of dislocations that depend on Mandel (Cauchy) stress in the reference (spatial) configurations and the contribution of the dislocation core energy to the free energy of the crystal. Our formulation relied on several dislocation density tensor measures linked to the incompatibility of the plastic distortion in the crystal. While previous works develop such tensors starting from the multiplicative decomposition of the deformation gradient, we developed the tensor measures of the dislocation density and the dislocation flux from the additive decomposition of the displacement gradient and the crystal velocity fields. The two-point dislocation density measures defined by the referential curl of the plastic distortion and the spatial curl of the inverse elastic distortion and the associate dislocation currents were found to be more useful in deriving the referential and spatial forms of the transport equations for the vector density of dislocations. A few test problems showing the effect of finite deformation on the static dislocation fields are presented, with a particular attention to lattice rotation. The framework developed provides the theoretical basis for investigating crystal plasticity and dislocation patterning at the mesoscale, and it bears the potential for realistic comparison with experiments upon numerical solution.