Oblique Effect Research Articles

Effect of eccentricity and obliquity on the ballistic performance and energy dissipation of hemispherical shell subjected to ogive nosed

A numerical study was undertaken to investigate the effect of projectile eccentricity and obliquity impact on the ballistic performance of the Aluminium 1100-H12 1 mm thick hemispherical shell against ogive nose projectile. The projectile eccentric distance was taken with respect to the radius of the shell such as 0th, R/4th, 2R/4th and 3R/4th whereas, the incidence angle of the projectile as 0°, 15°, 30°, 45°, and 60° for each shell (68, 100, 150 and 200 mm diameter). The projectile was impacted at different velocities for each incidence angle and eccentric distance and ballistic limit obtained. Three-dimensional finite element simulations were carried out by using the Abaqus/explicit solver. Johnson cook material model was used to simulate the behaviour of a hemispherical shell. The results of the numerical study were elucidated through the experimental result conducted for normal impact. Moreover, user-defined coding written in python was used to obtain the energy dissipation in different stretching mode. The result showed that the ballistic performance of the target was influenced by both the eccentricity and obliquity. Also, the target was failed in ductile hole enlargement with petals formation however, the number of petals form was depended upon the eccentricity and obliquity.

Undercorrection: the undesired effect of compression on the osteotomy gap of the medial opening wedge high tibial osteotomy and its clinical significance.

Undercorrection is a common problem in opening wedge high tibial osteotomy (OWHTO). We investigated the compression effect of cortex screw on the osteotomy gap and its clinical significance. A standard OWHTO using the TomoFix plate was conducted on 20 bone models in two groups to get a 10-mm medial osteotomy gap. A cortex screw was used temporarily in a neutral (at the center) and an eccentric position (near the inclined plane) of the dynamic hole in group 1 and group 2, respectively. The mean of undercorrection observed in the two groups was compared using an independent t test. Also, the effect of compression on the gap between the plate and medial tibial cortex, and the osteotomy gap was evaluated using a Sine rule. Besides, the mean undercorrection observed was assessed for clinical significance based on the effect on the weight-bearing axis (WBA) using a Cosine Rule. The mean undercorrection was 1.3 ± 0.6mm and 2.6 ± 0.6mm in group 1 and group 2, respectively. A significantly greater undercorrection was observed in group 2 (p < 0.001). The correction loss in group 2 has resulted from combinations of the sliding effect of the dynamic hole and oblique compression effect over the gap between the plate and medial tibial cortex whereas in group 1 it has only resulted from the oblique compression effect. The observed undercorrection in group 2 has resulted in clinically significant WBA shift (10%) over the width of the tibial plateau. In OWHTO, compression is important for the stability and healing of osteotomy, but it can also cause loss of correction. In patients requiring large correction, the surgeon should control the amount of compression required and consider making extra osteotomy gap to avoid undercorrection. Furthermore, the placement of cortex screws in neutral is essential to lower the risk of undercorrection.

Perceptual Redundancy Estimation of Screen Images via Multi-Domain Sensitivities

Visual redundancy detection is essential for image and video communication. Human visual system (HVS) is difficult to perceive the pixel magnitude change below a certain visibility threshold which is also known as just-noticeable-difference (JND). In this letter, we present an efficient JND estimation approach for screen content images by considering high-frequency sensitivity and orientation sensitivity correction. Specifically, to better quantify the visual redundancy, we investigate the visibility threshold based on the high-frequency distortion sensitivity. To obtain the orientation sensitivity correction, we divide the screen image pixels into three levels based on the oblique effect that considers the sensitive integrity of edges. Compared with several state-of-the-art JNDs, experimental results show that our method tolerates more perceptual redundancy, and delivers better visual quality under the same injected-noise energy. The implementation of the proposed method is publicly available at https://sites.google.com/site/wangmiaohui/.

Centroid migration on an impacted granular slope due to asymmetric ejecta deposition and landsliding

ABSTRACT For a fundamental understanding of terrain relaxation occurring on sloped surfaces of terrestrial bodies, we analyse the crater shape produced by an impact on an inclined granular (dry-sand) layer. Owing to asymmetric ejecta deposition followed by landsliding, the slope of the impacted inclined surface can be relaxed. Using the experimental results of a solid projectile impact on an inclined dry-sand layer, we measure the distance of centroid migration induced by asymmetric cratering. We find that the centroid migration distance xmig normalized to the crater minor-axis diameter Dcy can be expressed as a function of the initial inclination of the target tan θ, the effective friction coefficient μ, and two parameters K and c that characterize the asymmetric ejecta deposition and oblique impact effect: xmig/Dcy = K tan θ/[1 − (tan θ/μ)2] + c, where K = 0.6, μ = 0.8, and c = −0.1 to 0.3. This result is consistent with a previous study that considered the effect of asymmetric ejecta deposition. The obtained results provide fundamental information for analysing the degradation of sloped terrain on planetary surfaces, such as crater-shape degradation due to the accumulation of micro-impacts.

Selective age-related changes in orientation perception.

Orientation perception is a fundamental property of the visual system and an important basic processing stage for visual scene perception. Neurophysiological studies have found broader tuning curves and increased noise in orientation-selective neurons of senescent monkeys and cats, results that suggest an age-related decline in orientation perception. However, behavioral studies in humans have found no evidence for such decline, with performance being comparable for younger and older participants in orientation detection and discrimination tasks. Crucially, previous behavioral studies assessed performance for cardinal orientation only, and it is well known that the human visual system prefers cardinal over oblique orientations, a phenomenon called the oblique effect. We hypothesized that age-related changes depend on the orientation tested. In two experiments, we investigated orientation discrimination and reproduction for a large range of cardinal and oblique orientations in younger and older adults. We found substantial age-related decline for oblique but not for cardinal orientations, thus demonstrating that orientation perception selectively declines for oblique orientations. Taken together, our results serve as the missing link between previous neurophysiological and human behavioral studies on orientation perception in healthy aging.

Effect of Oblique Tendon Laceration on Core Suture Strength: A Biomechanical Evaluation.

The effect of obliquity of tendon laceration on repair strength is not well studied. The overwhelming majority of biomechanical studies assess repair strength following a laceration that is perpendicular to the long axis of the tendon. The aim of this study was to investigate whether the angle of tendon laceration affects the core suture strength. In all, 110 fresh human cadaveric flexor tendons were cut at varying angles of 15°, 30°, 45°, and 60° and the control group at 90°. All tendons were repaired with 6-strand modified Tang technique. The repair strength was tested using a custom-made tensioning machine, and the initial static gap force and the ultimate breaking force were measured. The mean gap force and 95% confidence interval (CI) for the 15°, 30°, 45°, 60°, and 90° groups were 15.2 N (11.4-19.0 N), 15.8 N (13.6-18.1 N), 15.6 N (13.1-18.4 N), 16.6 N (13.7-19.5 N), and 22.3 N (16.6-27.9 N), respectively. In the same respective order, the break force and 95% CI were 25.9 N (21.9-29.8 N), 26.5 N (23.2-29.7 N), 31.1 N (26.1-36.1 N), 35.6 N (28.2-43.1 N), and 51.8 N (62.5-41.0), respectively. The Fisher least significant difference demonstrated significant differences between the control group and all experimental groups for both gap force and break force. Obliquity of tendon laceration affects the core suture strength when compared with a transverse cut. Flexor tendons cut at 90° demonstrated a higher overall gap force and breaking strength that were statistically significant when compared with all obliquely cut groups. These findings should be considered when repairing and starting postoperative therapy for obliquely cut tendons.

Optical solutions to the Kundu-Mukherjee-Naskar equation: mathematical and graphical analysis with oblique wave propagation

This paper retrieves some new optical solutions to the Kundu–Mukherjee–Naskar (KMN) equation in the context of nonlinear optical fiber communication systems. In this regard, a complex transformation is applied to the integer-order KMN equation for converting it to an ordinary differential equation (ODE). Then, the generalized Kudryashov method (gKM) and the new auxiliary equation method (NAEM) are employed to the ODE. As consequence, dark, bright, periodic -shaped, and singular soliton solutions are explored to the ODE. The discrepancies between the results obtained in the present study and the previously obtained solutions through different methods are discussed. Furthermore, the time-fractional derivative and an oblique wave transformation in conjunction with the mentioned methods are executed to the fractional-order KMN equation. All obtained wave solutions are found to be new in terms of fractionality, wave obliqueness, and applied methods sense. The effects of obliqueness and fractionality on the attained solutions are demonstrated graphically along with its physical descriptions. It is found that the optical wave phenomena are changed with the increase of obliqueness as well as fractionality. It is also found that both the applied methods are suitable for acquiring new optical soliton features to the KMN equation with or without fractional and obliqueness conditions. However, the NAEM is capable of exploring more solutions of the considered equation over the gKM. Precisely, it can be assured that the utilized methods and the relevant transformation are powerful over the other methods. Therefore, the methods can be applied for further studies to explain the various physical phenomena arising in optical fiber communication systems.

Orientation Tuning and End-stopping in Macaque V1 Studied with Two-photon Calcium Imaging.

Orientation tuning is a fundamental response property of V1 neurons and has been extensively studied with single-/multiunit recording and intrinsic signal optical imaging. Long-term 2-photon calcium imaging allows simultaneous recording of hundreds of neurons at single neuron resolution over an extended time in awake macaques, which may help elucidate V1 orientation tuning properties in greater detail. We used this new technology to study the microstructures of orientation functional maps, as well as population tuning properties, in V1 superficial layers of 5 awake macaques. Cellular orientation maps displayed horizontal and vertical clustering of neurons according to orientation preferences, but not tuning bandwidths, as well as less frequent pinwheels than previous estimates. The orientation tuning bandwidths were narrower than previous layer-specific single-unit estimates, suggesting more precise orientation selectivity. Moreover, neurons tuned to cardinal and oblique orientations did not differ in quantities and bandwidths, likely indicating minimal V1 representation of the oblique effect. Our experimental design also permitted rough estimates of length tuning. The results revealed significantly more end-stopped cells at a more superficial 150μm depth (vs. 300μm), but unchanged orientation tuning bandwidth with different length tuning. These results will help construct more precise models of V1 orientation processing.

Fracture Risk Through Oblique External Fixator Pin Tracks

A known complication following removal of an external fixator is fracture through a pin track. Certain advantages are granted by inserting external fixator half-pins at oblique (not orthogonal) angles, such as increased pull-out strength and increased stability against torsional strain with divergent half-pins. We sought to determine if oblique pin tracks also had protective properties against secondary fracture through the pin track after half-pin removal. Acrylic plastic tubing was used to evaluate the effects of pin track obliquity on load to failure after drilling pin tracks. Tubing of 5/8″ outside diameter with 3/8″ inside diameter was chosen to simulate a clinical representation of an adult femur. Torsional, anterior-posterior (A-P) 4-point bending, and medial-lateral (M-L) 4-point bending loads were applied to 12″ specimens with a 6 mm hole drilled mid-shaft at either 0, 10, 20, or 30 degrees. In the A-P 4-point bending model, the drill hole was oriented in the direction of the applied force. In the M-L bending model, the drill hole was oriented perpendicular to the applied force. With increasing half-pin obliquity, less force was needed to produce a fracture through the drilled pin track with torsional stress (13.0 Nm for 0 degrees, 10.6 Nm for 30 degrees, P=0.004). There was no significant difference in the amount A-P and M-L force needed to cause failure. The M-L pin trajectory demonstrated higher load to failure compared with the A-P pin trajectory. Highest load to failure was demonstrated in the 0 degree M-L sample. A statistically significant reduction in force was required to cause fracture with increased pin obliquity. The M-L pin trajectory demonstrated higher load to failure than the A-P pin trajectory. Increased pin obliquity may lead to higher risk of fracture after half-pin removal. Placing a half-pin at 0 degree, orthogonal to the direction of highest physiological force, is likely to reduce the risk of fracture after half-pin removal.

On the propagation of alphabetic-shaped solitons to the (2 + 1)-dimensional fractional electrical transmission line model with wave obliqueness

This manuscript deals with the (2 + 1)-dimensional nonlinear electrical transmission line (NETL) equation of fractional-order to explain the dynamics of waves in the nonlinear network lines. The fractional transform with conformable derivative and wave obliqueness is applied to the model equation for converting it into an ordinary differential equation (ODE). To explore alphabetic-shaped solitons, an ansatz and the auxiliary equation methods are utilized to the ODE. The utilized transformation is then put back to the received solutions of the ODE. The solutions of the model equations representing alphabetic solitons are attained in terms of fractionality and wave obliqueness. It is seen that some of the beforehand generated solutions are the particular case of the newly derived solutions. The effects of fractionality, obliqueness, and free parameters on the attained solutions are tested and are demonstrated graphically with physical descriptions. Also, the behavior of the voltage wave propagation of the attained solutions are described. It is found that the alphabetic wave phenomena are changed with the change of obliqueness and fractionality, and the free parameters have substantial effects on the attained solutions. All the attained solitons propagate in the xy-plane as time (t) increases and the soliton propagation is found to be controlled by the free parameters, fractionality, and wave obliqueness. All the reported alphabetic-shaped solitons are found to be new in the sense of conformable derivative, wave obliqueness, and the applied methods.

How the known reference weakens the visual oblique effect: a Bayesian account of cognitive improvement by cue influence

This paper investigates the influence of a known cue on the oblique effect in orientation identification and explains how subjects integrate cue information to identify target orientations. We design the psychophysical task in which subjects estimate target orientations in the presence of a known oriented reference line. For comparison the control experiments without the reference are conducted. Under Bayesian inference framework, a cue integration model is proposed to explain the perceptual improvement in the presence of the reference. The maximum likelihood estimates of the parameters of our model are obtained. In the presence of the reference, the variability and biases of identification are significantly reduced and the oblique effect of orientation identification is obviously weakened. Moreover, the identification of orientation in the vicinity of the reference line is consistently biased away from the reference line (i.e., reference repulsion). Comparing the predictions of the model with the experimental results, the Bayesian Least Squares estimator under the Variable-Precision encoding (BLS_VP) provides a better description of the experimental outcomes and captures the trade-off relationship of bias and precision of identification. Our results provide a useful step toward a better understanding of human visual perception in context of the known cues.

Orientation-specific long-term neural adaptation of the visual system in keratoconus

Eyes with the corneal ectasia keratoconus have performed better than expected (e.g. visual acuity) given their elevated levels of higher-order aberrations that cause rotationally asymmetric retinal blur. Adapted neural processing has been suggested as an explanation but has not been measured across multiple meridional orientations. Using a custom Maxwellian-view laser interferometer to bypass ocular optics, sinusoidal grating neural contrast sensitivity was measured in six eyes (three subjects) with keratoconus and four typical eyes (two subjects) at six spatial frequencies and eight orientations using a two-interval forced-choice paradigm. Total measurement duration was 24 to 28 hours per subject. Neural contrast sensitivity functions of typical eyes agreed with literature and generally showed the oblique effect on a linear-scale and rotational symmetry on a log-scale (rotational symmetry was quantified as the ratio of the minor and major radii of an ellipse fit to all orientations within each spatial frequency; typical eye mean 0.93, median 0.93; where a circle = 1). Mean sensitivities of eyes with keratoconus were 20% to 60% lower (at lower and higher spatial frequencies respectively) than typical eyes. Orientation-specific neural contrast sensitivity functions in keratoconus showed substantial rotational asymmetry (ellipse radii ratio: mean 0.84; median 0.86) and large meridional reductions. The visual image quality metric VSX was used with a permutation test to combine the asymmetric optical aberrations of the eyes with keratoconus and their measured asymmetric neural functions, which illustrated how the neural sensitivities generally mitigated the detrimental effects of the optics.

Experimental investigation of a reinforced soil retaining wall with a flexible geogrid-wrapped ecological bag facing

This paper presented a field study of the reinforced soil wall (RSW) with a geogrid wrap-around facing. In addition to the conventional monitoring content, the strain of the face-wrapping geogrid, which was neglected in most previous studies, was monitored during the construction process. The positional relationship between the maximum vertical earth pressure and horizontally laid geogrid strain was revealed by using the proposed oblique dragging effect. It was found that the strain on the face-wrapping geogrid occurred mainly in the early stage of construction. The oblique dragging effect existing in the flexible RSWs increased the vertical earth pressure and changed its distribution law, resulting in the position of the maximum vertical soil pressure appearing behind the position of the maximum horizontally laid geogrid strain. The horizontal earth pressure at different positions behind the wall was obviously lower than the theoretical result by using Rankine's theory. Also, a modified 0.3H method (where H refers to the wall height) was presented to account for the slope of the wall face, which could be used to determine the potential sliding surfaces for single-stage RSWs and two-tier RSWs with small offset.

Mind-Craft: Exploring the Effect of Digital Visual Experience on Changes to Orientation Sensitivity in Visual Contour Perception.

Visual perception depends fundamentally on statistical regularities in the environment to make sense of the world. One such regularity is the orientation anisotropy typical of natural scenes; most natural scenes contain slightly more canonical (horizontal and vertical) information than oblique information. This property is likely a primary cause of the oblique effect in which subjects experience greater perceptual fluency with horizontally and vertically oriented content than oblique. Recent changes in the visual environment, including the "carpentered" content in urban scenes and the framed, caricatured content in digital screen media presentations, may have altered the typical (natural) level of orientation anisotropy. The current work evaluated whether digital visual experience, or visual experience with framed digital content, has the potential to alter the magnitude of the oblique effect in visual perception. Experiment 1 successfully established a novel eye-tracking method capable of indexing the visual oblique effect quickly and reliably and demonstrated the oblique effect. Experiment 2 used this method and found that one session of exposure to a specific video game altered visual orientation perception. Taken together, these results indicate that exposure to the realistic, but caricatured scene statistics of digital screen media, can alter visual contour perception in one session.

Spike root oblique jet effect on drag and heat load reduction performance for hypersonic vehicles

How to effectively reduce aeroheating load and drag is an important issue in the engineering application of the hypersonic vehicles. In this paper, a novel combined aerodisk-spike root oblique jet strategy has been proposed for drag and heat reduction. The Reynolds-averaged Navier Stokes equations are solved based on the finite volume method, and the shear stress transport turbulence model is used. The reliability of the developed in-house codes has been verified systematically. The results demonstrate that the introduction of aerodisk and oblique jet makes the flow field change obviously, and this novel strategy gets an excellent effect on drag and heat reduction. Then the laws of pressure and Stanton number distributions have been studied in deep. Furthermore, the influences of spike length, oblique jet pressure ratio, and aerodisk diameter on the flow field, drag and heat reduction performance are investigated. Increasing the spike length-to-diameter and jet pressure ratio can enhance the performance of drag and heat reduction. The drag coefficient decreases by about 26% when the spike length-to-diameter increases from 0.5 to 3.0, and the total heat load can be decreased by 38.6% as the jet pressure ratio increases from 0.4 to 0.7. The larger aerodisk diameter can also get a better heat reduction performance. However, the increasing of aerodisk diameter makes the total drag rise sharply. The total drag coefficient increases by about 43% as the aerodisk diameter ratio varies from 0.18 to 0.48.

A High-Efficiency Conformal Transmitarray Antenna Employing Dual-Layer Ultrathin Huygens Element

A high-efficiency conformal transmitarray with ultrathin dual-layer Huygens element is developed. The element consists of “I” shape patches for magnetic response and “T” shape stubs for electric response printed on two metal layers of a single substrate with only 0.5 mm thickness (λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> /60 at 10 GHz). By tuning the magnetic and electric responses, the transmitting phase of the element can be changed. Eight elements are designed to cover quantized 360° phase range with a maximal 1.67 dB loss. Then, the proposed elements are employed in a small conformal transmitarray design. To improve the antenna efficiency, the elements' dimensions are calculated by considering the oblique incidence effects. Finally, a cylindrically conformal transmitarray with a larger aperture size is simulated, fabricated, and measured. It can achieve a measured gain of 20.6 dBi with a 47% aperture efficiency.

Intrasubstance degeneration of medial meniscus horizontal cleavage tear in young patients is associated with increased joint line obliquity in the coronal plane of the knee.

To evaluate the effect of joint line obliquity of the knee on intrasubstance degeneration of isolated medial meniscus horizontal cleavage tear (HCT) in young patients. Sixty knees of 50 patients aged < 40years (mean age, 33.3 ± 5.5years old), who underwent arthroscopic partial meniscectomy (APM) for HCT, were retrospectively reviewed. The radiologic parameters of alignment, including mechanical hip-knee-ankle (mHKA) angle, posterior tibial slope, and joint line obliquity, were measured on preoperative long-standing whole-leg radiographs. The patients were classified into two groups, simple horizontal type (type 1) and complicated type (type 2), according to the presence of diffuse intrasubstance degeneration of the meniscus on preoperative magnetic resonance imaging. The risk factors for intrasubstance degeneration of HCT were analyzed using multiple logistic regression analysis. Medial joint space width (JSW) on weight-bearing 45° flexion posteroanterior radiographs and the mHKA were measured to evaluate the radiographic outcomes. The clinical outcomes were evaluated using the modified Lysholm score. Among patients followed-up for > 5years, the clinical and radiologic outcomes were compared between the two groups. The joint line obliquity was significantly greater in the type 2 group than in the type 1 group (2.9 ± 1.3 vs. 0.9 ± 1.4, P < 0.001), and a significant risk factor for diffuse intrasubstance degeneration (P < 0.001; odds ratio, 2.88; 95% confidence interval, 1.27-6.54). The relative changes in the JSW in the type 2 group were greater than those in the type 1 group during the mean follow-up period of 7.9 ± 2.5years (26% vs 10%, P = 0.045). The modified Lysholm score was not significantly different between the two groups (n.s). The diffuse intrasubstance degeneration of medial meniscus HCTs in young patients is associated with increased joint line obliquity of the knee joints. The radiologic outcomes after APM were inferior in the patients with diffuse intrasubstance degeneration. However, the clinical outcomes were not different during the mid-term follow-up. Level III.

Bifurcation analysis with chaotic motion of oblique plane wave for describing a discrete nonlinear electrical transmission line with conformable derivative

The present work discusses the basic features of bifurcation properties with chaotic motion of oblique plane wave in the discrete nonlinear electrical transmission lines having conformable derivative evolution. The planar dynamical systems are obtained to understand such physical issues for this model. In addition, the analytical plane wave solutions of nonlinear mathematical leading equation are determined by using two different mathematical methods. Both methods are supported only by the shock plane wave solutions. The conditions for other types of oscillatory plane wave solutions are also determined. The effect of obliqueness on the bifurcation properties, chaotic motion and shock plane waves structures are focused graphically with discussions by considering both of locality and non-locality in the system. It is found that the parameter of non-local operator is only affected on the nonlinear shock wave phenomena, whereas all basic features of discrete nonlinear electrical transmission line are changed with the changes of obliqueness.

Tungsten and Molybdenum Surfaces Exposed to Warm Deuterium Ion Plasma with Q-Nonextensive Distribution of Electrons

This work is concerned with the effect of non-Maxwellian electrons and obliqueness of magnetic field on magnetized plasma sheath characteristics, in which plasma interacts with tungsten (W) and molybdenum (Mo) surfaces via non-neutral plasma sheath using two fluids model. It is assumed that the singly charged positive ions are treated as warm fluid whereas the electrons obey q-nonextensive distribution. It is found that the q-nonextensive distributed electrons and the temperature of ions affect the entrance velocity of positive ions, which is a key parameter in the plasma sheath formation. Also, the nonextensive parameter q affects the distribution of ions and electrons in the sheath region and their distributions explicitly related with the electrostatic potential variation. The parallel and perpendicular components of ions velocity are affected by the obliqueness of magnetic field. As the nonextensivity of electrons increases, the gradient in electric potential increases towards the wall and hence the impact energy also increases. The obliqueness of magnetic field and impact energy of ions is a key factor that determines the physical sputtering rate, particle reflection and absorption from the target surface. Furthermore, the probability of particle reflection coefficient from the W-surface is higher than that of Mo-surface.

A modified rough interface model considering shear and normal elastic deformation couplings

This paper presents an analytical description of frictional contact hysteresis behavior between two flat rough surfaces in partial and gross slip. Couplings between shear and normal forces in the contact interface are included by considering spherical asperities in oblique contact. In the oblique contact, the relation between shear and normal interface forces is determined using asperities tangential friction forces and Hertzian normal contact forces. The Mindlin elastic spherical contact solution is modified in this study using the rod contact model leading to higher maximum tangential friction force and pre-slip limit compared to the classical solution. Based on the proposed modified Mindlin spherical contact solution, this paper develops a modified two rough interface (MTRI) model using the multi-asperity contact theory. The MTRI model provides accurate estimates of the contact interface behavior in an explicit form by including the oblique contact effects and the rod solution.In obtaining the hysteresis behavior of two flat rough interface contact, the contact regions associated with the pre-slip and sliding state at different tangential loading phases, i.e., virgin loading, unloading, and reloading, are determined. Then by the integration of pairs of asperities contact forces over the contacting regions at each state, restoring forces of contacting surfaces are obtained. The proposed MTRI model predictions are validated against experimental observations andfound to be in good agreement.