Instantaneous Stiffness Research Articles

Thermomechanical analysis of SiC-based duplex claddings with varying thickness ratio for accident-tolerant nuclear fuel systems

SiC-based duplex claddings, consisting of monolithic SiC and SiC/SiC fiber composite, are emerging as a promising candidate for accident-tolerant fuel (ATF) systems in nuclear reactors. To analyze the performance of ATFs with SiC-based duplex claddings, a comprehensive computational analysis framework is presented that captures the essential properties and behaviors of the UO2-SiC fuel system. Utilizing a previously developed continuum damage model, the pseudo-ductile behavior of SiC/SiC fiber composites is accurately modelled, connecting damage evolution parameters to instantaneous stiffness matrix degradation. This framework is used to investigate the performance of UO2-SiC fuel rods under normal operating conditions and a typical Loss of Coolant Accident (LOCA) scenario. We assess the effects of the thickness ratio of the monolithic SiC and SiC-based composite layers, as well as pellet-clad cold gap thickness on the failure and leakage probabilities of the cladding. These claddings, with a thickness ratio ranging from 0.25 to 0.75, demonstrated minimal failure and leakage probabilities for both the original and reduced pellet-clad gap thickness (82.5/70 µm). When the gap thickness was further reduced to 57.5 µm, pellet-cladding mechanical interaction was observed and this greatly elevated the failure probability of the MSiC layer, thus giving rise to a loss of hermeticity. This research underscores the significant role of varying individual layer thicknesses in shaping fuel rod safety and offers potential for optimization across diverse operational conditions.

Efficient semi-analytic method for single tooth contact analysis of loaded spiral bevel gears

Accurately and fast calculation of single tooth load contact state of a gear pair is the basis for accurate calculation of multi-tooth load contact analysis. Therefore, this study proposed a semi-analytical quick single tooth load tooth contact analysis (Q-SLTCA) method. First, the ease-off tooth contact analysis (ease-off TCA) method was established, and a numerically stable initial contact stress distribution and contact ellipse analytical model was derived. Then, considering the influence of edge contact, the real-time division method of gear tooth slice was derived. Based on this, the equivalent principle of contact elliptical node and the load correction strategy were innovatively proposed. Then, the calculation method of the meshing characteristics of the tooth slice was established by coupling the boundary element method (BEM) with the equivalent cylindrical Hertz contact theory. The bending deformation, tooth root stress distribution, contact stress, contact deformation and meshing stiffness of the tooth slice were analyzed and calculated, and the instantaneous meshing stiffness of the single tooth was determined by combining the parallel method of the gear tooth stiffness. Finally, a single-tooth finite element method (FEM) meshing model was created for comparison with the method in this study, which verified the calculation accuracy and efficiency of the proposed method. This method can be easily developed into a quick multi-tooth load contact analysis algorithm, which can provide a new method for gear tooth crack and failure analysis.

Experimental study on the strain energy evolution mechanism of thick and hard sandstone roof in Xinjiang Mining Area

For understanding the mechanical performance and strain energy evolution mechanism of thick hard roof sandstone samples, a sequence of uniaxial compression trials with acoustic emission (AE) monitoring were carried out. The results indicate: (1) The stress-strain curve of the thick hard roof sandstone specimens exhibits distinct stage characteristics. Based on the evolvement of instantaneous axial stiffness, it is separated into Fracture Closure Phase, Elastic Deformation Phase, Steady Fracture Expansion Phase, Unsteady Fracture Expansion Phase, and Post-Peak Phase. (2) The AE energy and cumulative count curves of the thick hard roof sandstone specimens also exhibit significant stage characteristics and can be mutually corroborated with the stage division of the stress-strain curve. (3) Based on the energy conservation principle, the evolution of strain energy density in the thick hard roof sandstone specimens under uniaxial compression loading was analyzed, and plastic strain energy increment was employed to study the stage characteristics of strain energy dissipation. (4) A damage constitutive model for the thick hard roof sandstone specimens was constructed, considering the characteristics of strain energy dissipation. This model effectively describes the stress-strain relationship among the samples, which undergo strain hardening, strain softening, and sudden destruction.

Subregional analysis of joint stiffness facilitates insight into ligamentous laxity after ACL injury.

Purpose: Increased incidence of anterior cruciate ligament injuries has amplified the need for quantitative research in clinical and academic settings. We used a novel digital arthrometer to measure knee laxity in healthy people and patients with anterior cruciate ligament injuries. Changes in stiffness were also assessed to develop new indicators for detecting anterior cruciate ligament injury. The purpose of this study was to use arthrometer to measure the quantitative indicator of knee laxity, bringing clinicians a new perspective on how to identify injury to the ACL. Methods: In this cross-sectional study, anterior tibial displacement under continuous loading was measured using a novel digital arthrometer in 30 patients with unilateral anterior cruciate ligament injury and 30 healthy controls. Load-displacement curves were plotted, using real-time load and displacement changes. Stiffness was defined by the slope of the applied load to tibial displacement. Anterior tibial displacement and instantaneous stiffness values under different loads were compared. The restricting contribution of the anterior cruciate ligament transformed the displacement-stiffness curve from a sharp decrease to a stable increase, resulting in a minimum stiffness value. Using the minimum stiffness as the turning point, the load-displacement curve was divided into regions 1 and 2. The two regions' stiffness changes were compared. Based on the findings, receiver operating characteristic curves were plotted and the area under the curve was calculated to estimate the diagnostic accuracy. Results: Anterior tibial displacement was significantly greater in the anterior cruciate ligament injury group than in the controls under each 10-N increase load (p < 0.05). In the anterior cruciate ligament injury group, instantaneous stiffness was significantly lower on the injured side than on the healthy side (p < 0.05). In the two regions of the load-displacement curve, stiffness was significantly lower in the anterior cruciate ligament injury group than in the control group (all, p < 0.05). Receiver operating characteristic curves were plotted, using changes in stiffness under the two regions in both groups. Stiffness in region 2 had the largest area under the curve (0.94; 95% CI, 0.88-0.99). Using the cut-off value of 9.62N/mm to detect ACL injury, the sensitivity and specificity were 93% and 82%, respectively. Conclusion: Our investigation of ligament stiffness provides novel insights into the properties of knee laxity. Stiffness in the later stages of increased loading <9.62N/mm could be a valid indicator for identifying knee laxity.

Effects of chemically induced ovarian failure on single muscle fiber contractility in a mouse model of menopause

ObjectiveMenopause is associated with impaired skeletal muscle contractile function. The temporal and mechanistic bases of this dysfunction are unknown. Using a mouse model of menopause, we identified how gradual ovarian failure affects single muscle fiber contractility. Study designOvarian failure was chemically induced over 120 days, representing the perimenopausal transition. Mice were sacrificed and soleus and extensor digitorum longus muscles were dissected and chemically permeabilized for single fiber mechanical testing. Main outcome measuresMuscle fiber contractility was assessed via force, rate of force redevelopment, instantaneous stiffness, and calcium sensitivity. ResultsPeak force and cross-sectional area of the soleus were, respectively, ~33 % and ~24 % greater following ovarian failure compared with controls (p < 0.05) with no differences in force produced by the extensor digitorum longus across groups (p > 0.05). Upon normalizing force to cross-sectional area there were no differences across groups (p > 0.05). Following ovarian failure, rate of force redevelopment of single fibers from the soleus was ~33 % faster compared with controls. There was no shift in the midpoint of the force‑calcium curve between groups or muscles (p > 0.05). However, following ovarian failure, Type I fibers from the soleus had a higher calcium sensitivity between pCa values of 4.5 and 6.2 compared with controls (p < 0.05), with no differences for Type II fibers or the extensor digitorum longus (p > 0.05). ConclusionsIn our model of menopause, alterations to muscle contractility were less evident than in ovariectomized models. This divergence across models highlights the importance of better approximating the natural trajectory of menopause during and after the transitional phase of ovarian failure on neuromuscular function.

Evaluation of cracking and deflection of GFRP bar reinforced recycled concrete beams with seawater and sea sand

In this paper, the feasibility of glass fiber reinforced polymer (GFRP) bar reinforced recycled concrete beams with seawater sea sand was investigated. A four-point flexural test was carried out, and the Digital Image Correlation (DIC) technique was applied to measure strain and deflection of beam at the same time. The cracking load was calculated and compared with the test data, and the deformability and instantaneous stiffness were also calculated as a further supplement to the evaluation of the service performance of the beams. The test results showed that the crack development and failure pattern of the GFRP bar reinforced recycled concrete beams with seawater and sea sand (SSRAC beams) did not change significantly compared with the steel reinforced concrete beams, but became more ductile due to sea sand. The overall deflection of the beam reinforced with GFRP bars increased but was still within the allowable range of the current code (ACI 318–05 and GB 50010-2010), but the cracking load decreased significantly. There was no significant difference in the performance of beams using various fine aggregates in most cases. However, the excessive amount of shell particles had the potential to change the failure patterns and deformability factors of the beams. Overall, there was no significant degradation in the serviceability of SSRAC beams reinforced by GFRP bars.

A novel method for simulating ex vivo tooth extractions under varying applied loads

BackgroundTooth extraction is a common surgical procedure where the invasiveness of the surgery can affect the nature of the dentoalveolar remodelling which follows. However, there is very little biomechanical data relating the loading applied during tooth extraction to the outcomes of the procedure. The purpose of this pilot study is to present a novel ex vivo experimental method for measuring tooth extraction mechanics and to explore preliminary metrics for predicting extraction success. MethodsA custom experimental apparatus was developed in-house to extract central incisors from ex vivo swine mandible samples. Twenty-five (n = 25) incisors were extracted at different rates in displacement- and force-control, along with an intermittent ramp-hold scheme for a total of five schemes. Peak forces and extraction success were recorded for each test. Video analysis assisted in determining the instantaneous stiffnesses of the dental complex during continuous extractions, which were compared using the K-means clustering algorithm. FindingsTooth extraction forces ranged from 102 N to 309 N, with higher-rate tests tending towards higher peak forces (141 N – 308 N) than the lower-rate tests (102 N–204 N) for displacement- and force-controlled schemes. The K-means algorithm clearly identified load rates among tests, indicating that higher-rate loading increased system stiffness relative to the lower-rate tests. InterpretationThe developed experimental method demonstrated a desirable degree of control. The preliminary results suggest the influence of load rate on the mechanical response of the dental complex and extraction outcome. Future work will further investigate the biomechanics of tooth extraction and relate them to tissue damage to improve future tooth extraction procedures.

Comparison of Loading-Displacement Relationships and Energy-Storing Properties of the Jaipur Foot Against Low-, Mid-, and High-Activity Prosthetic Feet Using Static Proof Testing

ABSTRACT Introduction The Jaipur foot is a low-cost prosthetic foot developed in Jaipur, India. Despite its worldwide use, few data are available on its mechanical properties. In general, there is a lack of objective data on the mechanical performance of prosthetic feet, hindering the objectivity of the prosthetic foot prescription process. The aim of this project was to compare the properties of the Jaipur foot with three prosthetic feet of differing activity levels (a SACH foot and two ESPFs) used commonly in the UK National Health Service (NHS), specifically evaluating loading-displacement relationships and energy-storing properties. Materials and Methods Static proof testing was performed on the four prosthetic feet (BMVSS Jaipur foot, 1D10 Dynamic, 1C30 Trias, and 1C60 Triton) using ISO:10328 methods. Loading-displacement graphs for the forefoot and heel were produced, from which instantaneous stiffness at forces typical of walking and running was produced and energy-storing properties were calculated. Results The Jaipur foot demonstrated the highest heel stiffness at both walking and running forces, the highest forefoot stiffness at walking forces, and the lowest energy return of the four feet overall. The ESPFs demonstrated the lowest forefoot stiffness, along with the highest energy returns. Conclusions Although low cost and cultural requirements should be taken into account, these data have demonstrated the inferior energy-storing properties of the Jaipur foot compared with Western prosthetic feet, using ISO methods to allow future cross-study comparison. Clinical Relevance The mechanical and energy-storing data from this study can be compared with other research using ISO methods to make the prosthetic prescription process more objective, allowing the most appropriate choices to be made for patients.

Load-induced fluid pressurisation in hydrogel systems before and after reinforcement by melt-electrowritten fibrous meshes

Fluid pressure develops transiently within mechanically-loaded, cell-embedding hydrogels, but its magnitude depends on the intrinsic material properties of the hydrogel and cannot be easily altered. The recently developed melt-electrowriting (MEW) technique enables three-dimensional printing of structured fibrous mesh with small fibre diameter (20 μm). The MEW mesh with 20 μm fibre diameter can synergistically increase the instantaneous mechanical stiffness of soft hydrogels. However, the reinforcing mechanism of the MEW meshes is not well understood, and may involve load-induced fluid pressurisation. Here, we examined the reinforcing effect of MEW meshes in three hydrogels: gelatin methacryloyl (GelMA), agarose and alginate, and the role of load-induced fluid pressurisation in the MEW reinforcement. We tested the hydrogels with and without MEW mesh (i.e., hydrogel alone, and MEW-hydrogel composite) using micro-indentation and unconfined compression, and analysed the mechanical data using biphasic Hertz and mixture models. We found that the MEW mesh altered the tension-to-compression modulus ratio differently for hydrogels that are cross-linked differently, which led to a variable change to their load-induced fluid pressurisation. MEW meshes only enhanced the fluid pressurisation for GelMA, but not for agarose or alginate. We speculate that only covalently cross-linked hydrogels (GelMA) can effectively tense the MEW meshes, thereby enhancing the fluid pressure developed during compressive loading. In conclusion, load-induced fluid pressurisation in selected hydrogels was enhanced by MEW fibrous mesh, and may be controlled by MEW mesh of different designs in the future, thereby making fluid pressure a tunable cell growth stimulus for tissue engineering involving mechanical stimulation.

Effect of edge riveting on the failure mechanism and mechanical properties of self-piercing riveted aluminium joints

In order to improve the use of aluminium alloys in lightweight automotive body panels, the failure mechanism and mechanical properties of AA5052 aluminium alloy sheets under different conditions were investigated by means of self-piercing riveting (SPR). The impact of riveting position on the structural strength, absorbed energy and instantaneous stiffness of self-piercing riveted connections was analyzed using the edge riveting method. Four edge distances of 1.65 mm, 2.65 mm, 3.65 mm and 4.65 mm were considered for the experimental study, and the riveted structure was analyzed and tensile shear tests were carried out by comparing the mechanical properties. The results indicated that this riveting method changed the failure mode of the joint, with the rivet pulling out from the lower sheet to a co-existence of rivet pull-out and riveted mouth sheet breakage; the maximum shear load, absorbed energy and deformation resistance decreased as the distance from the riveting point to the strip edge decreased; and the strength of the riveted joint based on the upper plate was significantly greater than that based on the bottom plate at the same edge pitch, and the stability of the joint is superior. This study provides a theoretical basis for the damage suppression of aluminium alloy edge riveted joints and the lightweight production of vehicles.

Distribution and Prediction of Incremental Cutter Flank Wear in High-Efficiency Milling

In the milling of titanium alloy workpieces, tool wear seriously affects the surface quality of a workpiece and its tool life. It is of great significance to study the influence of instantaneous contact stiffness on instantaneous friction variables and incremental wear, which is of great significance for the realization of control over the degree of flank wear and improving the service life of cutter teeth. In this paper, an experiment to monitor cutting with a Ti6Al4V workpiece with a high-feed milling cutter was carried out; according to the experimental results, the wear area of the flank face of the cutter tooth was determined. The feature points of the flank were selected, and an instantaneous contact stiffness calculation method for the flank was proposed. The infinitesimal method was used to characterize the distribution of the contact stiffness of the flank, and the evolution characteristics of instantaneous contact stiffness distribution under the influence of vibration were obtained. According to the calculation results, the instantaneous distribution of flank wear depth was calculated. A grey correlation degree was used to reveal the correlation between the instantaneous contact stiffness of the flank face and wear depth, and a positionable wear-prediction model based on the instantaneous contact stiffness of the flank was proposed. Based on a BPNN (back propagation neural network), a prediction model for flank wear was established. The results showed that the above model and method could accurately predict the instantaneous wear of the tool flank.

Modal Identification on Walking Leg Using EKF Method

The identification on the mechanical characteristic of walking leg has faced challenge due to the inconvenience installation on sensor with leg and expensive cost. This paper proposes a convenience method on identifying the leg parameters including its stiffness and damping ratio under walking state by Extend Kalman Filter (EKF) method, which only need to deal with the measured ground reaction force. Firstly, a mechanical oscillate system is used to describe the walking leg, and its corresponding dynamic governing equation is established. Then, a state-space equation is applied the governing equation and it is further inserted on the EKF method so as to set up a system update equation and measurement update equation. In addition, a solving algorithm is designed to acquire the instantaneous stiffness and damping ratio of the walking leg. Finally, a sample comprised of 760 curves of walking ground reaction force from 36 participants is employed to the identification method and the practice results demonstrate that it can efficiently discern the stiffness and damping ratio of walking leg. This study provides a novel perspective for seeking the dynamic parameters of walking leg and efficiently reduces experimental expenditure than those direct measurement of sensors installed on the surface of leg.

Estimation of Knee Assistive Moment in a Gait Cycle Using Knee Angle and Knee Angular Velocity through Machine Learning and Artificial Stiffness Control Strategy (MLASCS)

Nowadays, many people around the world cannot walk perfectly because of their knee problems. A knee-assistive device is one option to support walking for those with low or not enough knee muscle forces. Many research studies have created knee devices with control systems implementing different techniques and sensors. This study proposes an alternative version of the knee device control system without using too many actuators and sensors. It applies the machine learning and artificial stiffness control strategy (MLASCS) that uses one actuator combined with an encoder for estimating the amount of assistive support in a walking gait from the recorded gait data. The study recorded several gait data and analyzed knee moments, and then trained a k-nearest neighbor model using the knee angle and the angular velocity to classify a state in a gait cycle. This control strategy also implements instantaneous artificial stiffness (IAS), a control system that requires only knee angle in each state to determine the amount of supporting moment. After validating the model via simulation, the accuracy of the machine learning model is around 99.9% with the speed of 165 observers/s, and the walking effort is reduced by up to 60% in a single gait cycle.

Seismic Reduction Performance of Wrap Rope Connection Devices for Continuous Girder Bridges

In this article, wrap rope connection device (WRCD), which considers the relative acceleration of piers and beam as a control variable, is proposed for improving the current situation of continuous girder bridges whose bearing force of a single pier is along the longitudinal direction and based on the synergy principle. The WRCD device, which meets the slow displacement requirements of temperature and vehicle load under normal operation, is implemented and used to improve the performance of the sliding bearing pier. During earthquakes, because of the amplification effect of the wrap rope, the instantaneous large stiffness state in the longitudinal force can be achieved. Based on the shaking table test of a typical continuous girder bridge for examining the performance of the WRCD during earthquakes, the dynamic characteristics, structural acceleration, displacement, and strain responses of the structure under different frequency spectra, and seismic input intensities are analyzed and the seismic reduction performance of the WRCD is demonstrated. This analysis demonstrated that, by activating WRCD, the ratio of the acceleration response of the fixed bearing pier to the sliding bearing pier increased from 10% to 57%; moreover, the force on each pier appeared more uniform. Furthermore, with an increase in the input intensity of the earthquake, the displacement of the primary beam and the seismic response of the fixed pier bottom considerably decreased and the synergy effect of each pier was more prominent. Under certain site conditions, the WRCD can effectively improve the synergy effect between the sliding bearing piers and fixed bearing pier; however, the improvement in the obtained result is directly associated with the seismic input characteristics. The design parameters of the WRCD should be determined as per different site conditions and the optimum application range of the WRCD.

Multi-criteria decision-making analysis and numerical simulation of the low-velocity impact response of inter-ply S2-glass/aramid woven fabric hybrid laminates

Hybrid composites have gained a lot of attention due to their superior mechanical performance and energy absorption capacity compared to single-fibre counterparts, but studies on the hybridization of aramid and S2-glass fabrics are still scarce. This paper presents a multi-criteria decision-making analysis and numerical simulation applied to the study of the performance of asymmetric inter-ply hybrids of plain-weave aramid and satin-weave S2-glass fabrics/epoxy laminates subjected to low-velocity impact. Different aramid/glass fibre ratios, impact sides and impact energies (19 J, 37 J and 72 J) were investigated. A multi-criteria decision-making analysis was performed to identify the best laminate design based on the technique for order of preference by similarity to the ideal solution which considered areal density, deformation and absorbed energy as design criteria. A novel numerical FE model based on continuum damage mechanics was developed considering non-linear material constitutive behaviour and different interlaminar and intralaminar failure modes. The material model was implemented in Abaqus/Explicit solver using a user-defined material model, and the non-linear material behaviour in the normal direction is considered by defining instantaneous stiffnesses using third-degree polynomials. The results identified single fibre laminates as the worst designs and hybrid laminates with aramid on the impact side as the best design. Besides, for similar fibre ratios, the total delamination area was larger for the impact on aramid layers.

Selection of the Optimal Tire for an FSAE Vehicle based on Evaluation of Key Performance Parameters

Tires are the components which physically connect the vehicle body to the ground, thus choosing the correct set of tires is important, not only to achieve the most out of the car but also to provide the platform, based on which the suspension and steering geometry of the vehicle are designed. This selection has to be based on the comparison of various available sets of tires and evaluating them based on key performance parameters, such as peak lateral force (Fy), peak self-aligning torque (Mz), instantaneous cornering stiffness and instantaneous camber stiffness. The tire which gives the best possible combination of all these parameters would help achieve sufficiently good acceleration and speed, and also have a sufficiently large window of operation, where it is robust and less sensitive to changes. Thus, the tire, which achieves the best balance of properties between performance, driveability, cost and robustness would be the chosen tire for the car, which forms the basis of the next steps of the chassis design.

An accurate and numerically efficient time-varying mesh stiffness model for modified straight bevel gear under load

Gear time-varying mesh stiffness (TVMS) plays an important role in the analysis accuracy of a gear transmission mechanism. In previous research, the TVMS of a modified straight bevel gear (SBG) was mainly obtained by the finite element method (FEM), whose computation time is usually long to ensure computational accuracy. By contrast, this work proposes a fast calculation method with high accuracy for the TVMS of a modified SBG. First, B-spline surfaces are introduced to reconstruct a modified SBG using discrete tooth surface points. Next, based on the tooth contact analysis and loaded tooth contact analysis, combined with energy conservation principle and infinitesimal method, a semi-analytical instantaneous single mesh stiffness (SMS) model for the modified SBG is derived. Then, using the additional deformation compatibility condition and principle of force balance, the calculation method of the TVMS of the modified SBG is obtained. Finally, a comparison of the mesh stiffness calculation results between the method of this study and that of FEM is completed. The results show that the semi-analytical TVMS model used in this study can be accurately and quickly solved.

Influence of 4 weeks of downhill running on calcium sensitivity of rat single muscle fibers

Improved Ca2+ sensitivity has been suggested as a mechanism behind enhancements in muscle mechanical function following eccentric training. However, little is known regarding the effects of eccentric training on single muscle fiber Ca2+ sensitivity. Adult male Sprague–Dawley rats (sacrificial age ~18 weeks; mass = 400.1 ± 34.8 g) were assigned to an eccentric training (n = 5) or sedentary control group (n = 6). Eccentric training consisted of 4 weeks of weighted downhill running 3×/week at a 15° decline and 16 m/min for 35 min per day in 5‐min bouts. After sacrifice, vastus intermedius single muscle fibers were dissected, chemically permeabilized, and stored until testing. Fibers (n = 63) were isolated, and standard Ca2+ sensitivity, force, rate of force redevelopment (k tr), and active instantaneous stiffness tests were performed using [Ca2+] ranging from 7.0 to 4.5. Following all mechanical testing, fiber type was determined using SDS‐PAGE. There was no difference in pCa50 (i.e., [Ca2+] needed to elicit half of maximal force) between groups or between fiber types. However, when comparing normalized force across pCa values, fibers from the control group produced greater forces than fibers from the trained group at lower Ca2+ concentrations (p < 0.05), and this was most evident for Type I fibers (p = 0.002). Type II fibers produced faster (p < 0.001) k tr than Type I fibers, but there were no differences in absolute force, normalized force, or other measures of mechanical function between fibers from the trained and control groups. These findings indicate that eccentric training does not appear to improve single muscle fiber Ca2+ sensitivity.

Network dynamics of the nonlinear power-law relaxation of cell cortex

Living cells are known to exhibit universal power-law rheological behaviors, but their underlying biomechanical principles are still not fully understood. Here, we present a network dynamics picture to decipher the nonlinear power-law relaxation of cortical cytoskeleton. Under step strains, we present a scaling relation between instantaneous differential stiffness and external stress as a result of chain reorientation. Then, during the relaxation, we show how the scaling law theoretically originates from an exponential form of cortical disorder, with the scaling exponent decreased by the imposed strain or crosslinker density in the nonlinear regime. We attribute this exponent variation to the molecular realignment along the stretch direction or the transition of network structure from in-series to in-parallel modes, both solidifying the network toward our one-dimensional theoretical limit. In addition, the rebinding of crosslinkers is found to be crucial for moderating the relaxation speed under small strains. Together with the disorder nature, we demonstrate that the structural effects of networks provide a unified interpretation for the nonlinear power-law relaxation of cell cortex, and may help to understand cell mechanics from the molecular scale.

An Experimental Method to Determine Rock Joint Stiffness under Constant Normal Load Conditions

Being physical mechanical parameters of joints, normal and shear stiffnesses are indispensable components of the numerical simulation and theoretical analysis of the behavior of joints. The objective of this work is to put forward an experimental method to determine joint stiffness under constant normal load (CNL) conditions. For this purpose, joint closure and direct shear tests under CNL conditions were conducted. Normal stiffness was determined by the ratio of normal stress increment and the corresponding normal displacement; the shear stiffness was calculated by the ratio of shear stress increment to the relative shear displacement. The average and instantaneous shear stiffness were distinguished. Experimental results showed that joint normal and shear stiffness are time and spatially varying parameters during direct shearing. With increasing normal stress, average shear stiffness, maximum instantaneous shear stiffness, and normal stiffness increases. Normal stiffness was about 26–28 times higher than the average shear stiffness under one normal stress level. Average shear stiffness was little influenced by shear velocity. Instantaneous shear stiffness shows the velocity-dependent behavior. Maximum instantaneous shear stiffness decreases rapidly with increasing shear rate. At lower shear velocity, maximum instantaneous shear stiffness is higher than normal stiffness; minimum instantaneous shear stiffness can be negative and the absolute value also decreases with faster shear velocity. These findings provide a reference for selecting the appropriate value of normal and shear stiffness for evaluation of the mechanical response of interface.