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Nonlinear Constitutive Model of High-Temperature Viscoelastic Deformation of Gussasphalt Concrete

To accurately evaluate the high-temperature stability of cast asphalt concrete, based on the traditional viscoelastic mechanical model, this paper innovatively improves the traditional viscoelastic mechanical model considering the conditions of temperature and dynamic load and deduces the viscoelastic constitutive model of high-temperature deformation performance of cast asphalt concrete, using a dynamic penetration test (DPT) to regress improved the Burgers model parameters and verify the model’s applicability and reliability. The results show that for the modified Burgers model parameters, E1, E2, A, and η2 decrease with increasing temperature, while parameter B increases with the increase of temperature. The high-temperature deformation of cast asphalt concrete is mainly related to η1, and η1 decreases, and deformation increases with the increase in temperature. With the increase in loading times, the dynamic penetration of cast asphalt concrete (AC) gradually increases, that is, when the greater the permanent deformation is. When the specimen is loaded 3000 times, the dynamic penetration value at 60°C is about 1.237 mm, and the dynamic penetration value at 50°C is about 0.819 mm. Under other loading times, the permanent deformation of the specimen at 60°C is much greater than that at 50°C. There is a good fit between the mechanical model derived from the viscoelastic theory and the measured test data, and the correlation coefficient is greater than 0.98, indicating that the model can accurately describe the permanent deformation law of GA under periodic semivector sinusoidal pulse load at high temperatures. The research results of this paper provide a solid theoretical basis for the promotion and application of cast asphalt concrete, and the method has wide applicability in practical engineering.

Trends in COVID-19 hospital outcomes in England before and after vaccine introduction, a cohort study

Widespread vaccination campaigns have changed the landscape for COVID-19, vastly altering symptoms and reducing morbidity and mortality. We estimate trends in mortality by month of admission and vaccination status among those hospitalised with COVID-19 in England between March 2020 to September 2021, controlling for demographic factors and hospital load. Among 259,727 hospitalised COVID-19 cases, 51,948 (20.0%) experienced mortality in hospital. Hospitalised fatality risk ranged from 40.3% (95% confidence interval 39.4–41.3%) in March 2020 to 8.1% (7.2–9.0%) in June 2021. Older individuals and those with multiple co-morbidities were more likely to die or else experienced longer stays prior to discharge. Compared to unvaccinated people, the hazard of hospitalised mortality was 0.71 (0.67–0.77) with a first vaccine dose, and 0.56 (0.52–0.61) with a second vaccine dose. Compared to hospital load at 0–20% of the busiest week, the hazard of hospitalised mortality during periods of peak load (90–100%), was 1.23 (1.12–1.34). The prognosis for people hospitalised with COVID-19 in England has varied substantially throughout the pandemic and according to case-mix, vaccination, and hospital load. Our estimates provide an indication for demands on hospital resources, and the relationship between hospital burden and outcomes.

Sustained-release calcium alginate/diatomite capsules for sustainable self-healing asphalt concrete

Calcium alginate capsule can gradually release the encapsulated rejuvenator after compressive loading, thus realize self-repairment of micro cracks and in-situ regeneration of aged asphalt in pavement. Nevertheless, plain calcium alginate capsules show weak mechanical strength and over-quick oil release speed and thus long-term self-healing potenial cannot be achieved. Calcium alginate/diatomite composite capsules with varying manufacturing parameters were synthesized through using orifice-coagulation method, which aims to improve mechanical strength and retard the rejuvenator release of the capsules. A series of performance tests were carried out to characterize the interior structure, thermal property, compression strength, relative rejuvenator content and rejuvenator incorporation rate of the prepared capsules. Meanwhile, the spatial location and premature rejuvenator release of capsules within asphalt concrete after manufacturing process were investigated. The rejuvenator release ratios of capsules in asphalt mixture beams after compressive loading were explored. Furthermore, the healing levels of test beams after the compressive loading and healing period were also evaluated. The calcium alginate/diatomite capsules had obvious multi-cavity structure and the diatomite with multi-pore structure offered extra rejuvenator storage units for the capsules. Meanwhile, the incorporation of diatomite could improve the thermal resistance and compressive strength and made the rejuvenator release speed of calcium alginate capsules decelerate obviously. The test beams containing diatomite modified capsules obtained acceptable healing level after long-term compression loading, which indicated that the addition of modified capsules into asphalt mixtures could realize the long-term healing of the pavement.

Acute Effects of Different Overspeed Loads with Motorized Towing System in Young Athletes: A Pilot Study.

Simple SummaryThe towing system is a widely used method to increase running speed since it allows the athletes to run at a speed higher than the speed that they would achieve with their own methods. Currently, we dispose of motorized towing systems that provide overspeed conditions. In this study, we have analyzed the acute effects of using one of these devices with different loads in eight young athletes and thus determine the possible optimal load for their use during training. These effects have been analyzed on different variables of the sprint running technique, and it has been observed that the increase in speed is mainly due to the increase in stride length, flight time and horizontal distance of the vertical projection of the center of gravity to the first contact of the foot with the ground, as well as to reductions in contact time. However, it cannot be determined whether these results are produced by the muscular action of the athlete or by the action of the device. Following up the investigation of the effects of the motorized towing system and the individualization of loads may allow for the development of these training methods, giving them greater scientific evidence.Overspeed is a training method used to improve running speed, although its effects are not supported by consensual scientific evidence. The overspeed stimulus can be boosted by several methods, including motorized towing devices. Our objectives were to analyze the acute effects of three overspeed loads in young athletes and to select optimal loads for training periods. Eight young athletes (16.73 ± 1.69 years) performed one unassisted sprint and three assisted sprints, and kinematic and biomechanical data were compared. Significant increases (p < 0.05) in step velocity and step length were found with 2, 4, and 5.25 kg in maximum running speed, flight time and horizontal distance from the first contact to the vertical projection of the center of mass with 4 and 5.25 kg. Significant time decreases were found in 5 m flying sprint and contact time with 4 and 5.25 kg, and no significant changes were observed in step rate. The individually recommended loads would be between 3.47 ± 0.68% and 6.94 ± 1.35% body weight. Even having limitations, we can understand this work and its results as a pilot study to replicate the methodology and the use of new devices to more broadly investigate the effects of overspeed.

Dofetilide Dose Reductions and Discontinuation in Obese Compared with Nonobese Patients.

Dofetilide is an antiarrhythmic agent and primarily eliminated renally. Initial dosing is determined by creatinine clearance, calculated by total body weight in the Cockcroft-Gault equation. To date, there is no evidence comparing the dosing of dofetilide in obese versus nonobese patients. We conducted a retrospective review of 217 adults admitted for dofetilide loading to evaluate the tolerability of dofetilide in obese versus nonobese patients. The rate of dose adjustments, including dose reductions and discontinuations, was compared between obese versus nonobese patients in unadjusted and adjusted analyses. Electrocardiograms were collected throughout the loading period, and calculation of QT intervals was performed. Obese patients did not have a significantly higher frequency of dose adjustments compared with nonobese patients (51.5% vs. 44.8%, P = 0.33). Using total body weight to determine starting doses was associated with great odds of dose adjustments compared with ideal body weight (OR 3.69, P = 0.002) and adjusted body weight (OR 4.46, P = 0.02). Men required significantly fewer dose adjustments compared with women on multivariate analysis (OR 0.53, P = 0.03). Obesity is not associated with an increase in the rate of dose adjustments. Total body weight should be used with caution to calculate initial doses of dofetilide in women because it may lead to a higher rate of dose adjustments compared with ideal body weight. Additional studies are needed to confirm the optimal method for selecting starting doses of dofetilide in women, particularly those with a body mass index of ≥30.

The optimal design of a piezoelectric energy harvester for smart pavements

The traffic environment contains tremendous mechanical energy due to the dynamic loads of moving vehicles which can be converted into electricity by using piezoelectric materials. Considering the road environmental characteristics, we propose here a piezoelectric energy harvester (PEH) consisting of piezoelectric ceramics that are encapsulated in epoxy resin filler between the MC nylon protective plates. As an illustration, periodic traffic loading is considered and is simulated by a controlled MTS loading, using which the effects of various system parameters on the efficiency of energy harvesting are examined. A theoretical electromechanical model is also developed to predict the energy harvesting behavior of the PEH device. The theoretical predictions agree very well with the experimental measurements, and they both suggest that various load, material, and circuit factors will have diverse effects on output power. To figure out the best collection of all factors and their simultaneous effect on the output performance, we also establish a simple and universal scaling law to reveal the underlying mechanism of the correlation between various systematic parameters. The normalized output power depends only on the normalized intrinsic impedance that consists of all material properties, geometrical, electrical circuit, and loading condition parameters. The optimization strategy may provide a useful tool to guide the design of the PEH device for enhancing the efficiency of energy harvesting by properly selecting the system parameters.

Self-sealing MEMS spray-nozzles to prevent bacterial contamination of portable inhalers for aqueous drug delivery

Pulmonary drug delivery by portable inhalers is the gold standard in lung disease therapy. An increasing focus on environmentally friendly inhalation currently spurs the development of propellant-free devices. However, the absence of propellants in the drug creates a need for suitable sealing systems that can ensure the pathogenic safety of devices. Traditionally, liquid drug inhalers incorporate a spray nozzle and a separate check valve. Here we show a fully integrated MEMS-based spray system for aqueous drug solutions and demonstrate its bacterial safety. The device comprises a thin silicon membrane with spray orifices, which self-seal against a compliant parylene valve seat underneath. This sealing system prevents bacterial ingrowth in its default closed state, while actuation lifts the membrane from the valve seat upon pressurization and sprays an inhalable aerosol from the nozzles. To seal against bacterial contamination effectively, we found that a contact force between the valve seat and the membrane (featuring the spray nozzles) is needed. In our testing, both self-sealing and an otherwise identical unvalved version of the spray chip can be bacterially safe in continued use when thoroughly cleaned of excess fluids and subjected to low bacterial loads for brief periods. However, when directly exposed to 10^{7} CFU/ml of our test organism Citrobacter rodentium for 24 h, unvalved systems become contaminated in nearly 90% of cases. In contrast, self-sealing spray chips reduced contamination probability by 70%. This development may enable preservative-free drug formulations in portable inhalers that use propellant-free aqueous drug solutions.

An Improved Informer Model for Short-Term Load Forecasting by Considering Periodic Property of Load Profiles

Short-term load forecasting (STLF) is an important but a difficult task due to the uncertainty and complexity of electric power systems. In recent times, an attention-based model, Informer, has been proposed for efficient feature learning of lone sequences. To solve the quadratic complexity of traditional method, this model designs what is called ProbSparse self-attention mechanism. However, this mechanism may neglect daily-cycle property of load profiles, affecting its performance of STLF. To solve this problem, this study proposes an improved Informer model for STLF by considering the periodic property of load profiles. The improved model concatenates the output of Informer, the periodic load values of input sequences, and outputs forecasting results through a fully connected layer. This makes the improved model could not only inherit the superior ability of the traditional model for the feature learning of long sequences, but also extract periodic features of load profiles. The experimental results on three public data sets showed its superior performance than the traditional Informer model and others for STLF.

Innovative X-ray diffraction and micromagnetic approaches for reliable residual stress assessment in deep rolled and microfinished AISI 4140 components

The residual stress state in the subsurface is a key element of surface integrity. It is well known to have a significant impact on a component's properties in terms of fatigue behavior and resistance to wear and corrosion. For this reason, adjusting residual stresses during manufacturing is a major challenge in modern production engineering, to improve and ensure a component's fatigue strength. In this context, hydrostatic deep rolling of the workpiece surface using adapted parameters enables the targeted induction of compressive residual stresses into subsurface layers. Due to specific properties regarding subsurface and topography for functional components in tribological applications, a further machining operation by microfinishing following deep rolling seems to be purposeful. In particular with regard to the production of components exposed to periodic load changes when used, the process combination can enable a substitution of the typically required conventional subsurface zone hardening. With the aim of economical process design, the corresponding parts can be manufactured with significantly reduced time and costs. Efficient and well-founded methods for monitoring the resulting influence on the subsurface zone properties are essential for a reproducible and target-oriented process design. The prevailing method for the non-destructive assessment of residual stresses in both academia and industry is X-ray diffractometry using the sin2 ψ-method. However, this method is time-intensive and requires complex instrumentation. Thus, efforts have been undertaken in past decades to develop alternative methods for the efficient and reliable characterization of residual stresses. In this research, the applicability of the cos α-method in X-ray diffractometry and a micromagnetic approach for residual stress assessment was investigated, analyzing deep rolled and microfinished AISI 4140 specimen conditions. In addition to the diffractometric and micromagnetic measurements, metallographic and topographic analyses of machined surfaces were carried out. Deep rolling was found to induce significant compressive residual stresses of up to −1100 MPa. After microfinishing of the deep rolled surfaces, favorable compressive residual stresses remain in the subsurface, reaching approximately up to −750 MPa. Based on this, the production of tailored surfaces with respect to a suitable combination of topography and subsurface is possible. For all surface states investigated, a good agreement between the two approaches in X-ray diffraction was found. Magnetic Barkhausen noise (MBN) measurements prove to be well applicable for an efficient and holistic assessment of surface integrity in the subsurface of deep rolled and microfinished AISI 4140 specimens.

Solar Wind Energy Input: The Primary Control Factor of Magnetotail Reconnection Site

AbstractIn this paper, we examine the solar wind energy input (expressed by −Vx × Bs, where Vx is the x component of the solar wind velocity and Bs is the southward component of the interplanetary magnetic field IMF Bz) for an onset of magnetic reconnection in the near‐Earth magnetotail. There are 41 events in which in situ observations of magnetic reconnection were made by Geotail. Magnetic reconnection in the postmidnight (premidnight) sector of the plasma sheet occurred under strong (weak) solar wind energy input conditions. Furthermore, we study temporal variations in the solar wind energy input with two different approaches using ground magnetic field observations and proton injections at geosynchronous altitude. These two analyses confirmed the preference of the postmidnight sector for the onset of magnetic reconnection under the strong solar wind energy input conditions. It is also found that the medium and weak solar wind energy input may move the onset location to earlier magnetic local times. The onset location of magnetic reconnection in the near‐Earth magnetotail is controlled by the solar wind energy input through the global magnetospheric dynamics during the loading period.

Extended state observer-based model predictive temperature control of mechanically pumped two-phase loop: An experimental study

Mechanically pumped two-phase loop (MPTL), as an emerging two-phase heat dissipation transformational technique, has made booming progress in some critical but tough cases such as space stations and high-performance chips. However, accurate temperature regulation of MPTL is intractable due to periodic heat load disturbance, measurement noise, and micro-channel boiling nonlinearity. To address these issues, an extended state observer-based model predictive control (ESOMPC) strategy is developed in this paper. To describe the process model, this paper builds an MPTL platform equipped with a micro-channel evaporator, based on which a series of sinusoidal heat load variation is carried out to show the effects on the wall temperature. Open-loop step experiments are then conducted in terms of flow rate of the working fluid so that the process model can be identified and the nonlinearity can be analyzed. Then, the ESOMPC is developed by incorporating the disturbance information in the optimization framework of the MPC. The ESO part is utilized to estimate the unknown disturbances and compensate the nonlinearity of MPTL, and thus enhance the disturbance mitigation property of the MPC algorithm. Finally, the closed-loop experiments verifies the efficacy of the proposed solution, showing smaller temperature fluctuation and shorter settling time than the conventional controller. The results indicate the great potential of the proposed ESOMPC in enhancing the temperature control accuracy of MPTL in terms of thermal management performance.

Numerical study on triaxial compressive behavior of engineered cementitious composites confined by circular steel tubes

The mechanism of engineered cementitious composites (ECC) in triaxial compression is still unclear, and the existing method cannot accurately predict its compressive capacity due to the lower elastic modulus and the effect of fiber bridging. In this paper, the compressive behavior of ECC confined by circular steel tubes was studied by performing a series of nonlinear finite element (FE) analysis. The non-linear material properties of ECC and steel and composite actions were considered in developing the FE models. The accuracy of the models was verified by comparison with the test results, such as load–displacement histories, failure modes and ultimate strengths. The verified model was utilized to explore contact pressure, the contribution of ECC to compressive capacity, ductility, energy absorption, and the influence of important parameters. Additionally, the effective confining stress (fr) was modified by average contact pressure, and a constitutive model of ECC under triaxial compression was developed by stress–strain relationships. It is shown that the effect of boundary confinement effect coefficient on the post-peak period of load–displacement history is classified and discussed. Meanwhile, the results of Richart’s model achieve a good accuracy by modifying the effective confining stress. Finally, a constitutive model of ECC under triaxial compression is proposed, of which the prediction results can describe the variation law of stress–strain relationship.

Experimental and Numerical Investigation of Rotor–Stator Interaction in a Large Prototype Pump–Turbine in Turbine Mode

In recent years, large-capacity, high-head pump–turbine units have been developed for pumped storage power plants to effectively utilise water energy and store large amounts of electricity. Compared with the traditional Francis turbine unit, the radial distance between the trailing edge of the guide vanes and the leading edge of runner blades of high-head pump–turbine unit is smaller, so the rotor–stator interaction and the corresponding pressure fluctuations in the vaneless space of pumped storage units are more intense. The pressure fluctuations with high amplitudes and high frequencies induced by rotor–stator interaction (RSI) become the main hydraulic excitation source for the structures of the unit and may cause violent vibration and fatigue damage to structural components, and seriously affect the safe operation of the units. In this paper, the RSI of a high-head pump–turbine in turbine mode of operation is studied in detail by means of site measurement and full three-dimensional unsteady simulations. The results of RSI-induced pressure fluctuations in turbine mode are analysed experimentally and numerically. The accuracy of the numerical calculations is verified by comparing with the measured results, and the variation law of RSI is deeply analysed. The results show that the pressure fluctuations in the vaneless space are affected by the wake of the guide vane, the rotating excitation of the runner, the low-frequency excitation of the draft tube, and the asymmetric characteristics of the incoming flow of the spiral case, and shows significant differences in spatial position. The findings of the investigation are an important and valuable reference for the design and safe operation of the pumped storage power station. It is recommended to design the runner with inclined inlets to reduce the amplitudes of RSI-induced pressure fluctuations and to avoid operating the pump–turbine units under partial load for long periods of time to reduce the risk of pressure fluctuation induced severe vibration on the structures.

Modestly protective cytomegalovirus vaccination of young children effectively prevents congenital infection at the population level

A vaccine to prevent congenital cytomegalovirus infection (cCMV) is a public health priority. cCMV results from maternal primary or non-primary CMV infection (reinfection, or reactivation of chronic infection) during pregnancy. Young children are a major source of transmission to pregnant women because they shed CMV at high viral loads for prolonged periods. CMV vaccines evaluated in clinical trials so far have demonstrated only approximately 50% efficacy against maternal primary infection. None of these have been approved, as higher levels of vaccine efficacy are assumed to be required to substantially reduce cCMV prevalence. Here, we designed a mathematical model to capture the relationship between viral shedding by young children and maternal CMV infections during pregnancy. Using this model, we were able to quantify the impact of CMV post-infection immunity on protecting against reinfection and viral shedding. There was a 36% reduction in the risk of infection to a seropositive person with post-infection immunity (reinfection) versus a seronegative person without this immunity (primary infection), given the same exposure. Viral shedding following reinfection was only 34% the quantity of that following primary infection. Our model also predicted that a vaccine that confers the equivalent of post-infection immunity, when given to young children, would markedly reduce both CMV transmission to pregnant women and the prevalence of cCMV. Thus, we predict that existing vaccine candidates that have been shown to be only modestly protective may in fact be highly effective at preventing cCMV by interrupting child-to-mother transmission.

Fully nonlinear interfacial periodic waves in a two-layer fluid with a rigid upper boundary and their loads on a cylindrical pile

Based on the fully nonlinear potential flow theory, interfacial periodic gravity waves in a two-layer fluid with a rigid upper boundary are investigated quasi-analytically using the homotopy analysis method (HAM), and the corresponding wave loads on a cylindrical pile are estimated by Morison’s empirical formula. Because of the great freedom in the choices of auxiliary linear operators, initial guesses, and convergence-control parameter, convergent series solutions are obtained in the framework of the HAM. For Boussinesq wave loads on the cylinder in one wave period, there exists a phenomenon of peak–valley mismatch between the upper and lower layer inertial loads; the total drag, total inertial and global loads reach their own peaks almost at the same time when the upper layer load equals the lower layer load. As the wave height increases, the dominant load changes from inertial load to drag load. Previous theoretical studies about internal or interfacial periodic wave loads on a cylinder were mainly based on linear or weakly nonlinear wave models, which causes the lack of corresponding theoretical research in the frame of fully nonlinear wave theory. Compared with linear and weakly nonlinear wave models, the fully nonlinear wave model considered in this paper provides more accurate results for the maximal loads on a slender cylindrical pile exerted by Boussinesq interfacial periodic waves, especially for strongly nonlinear cases. All of these should enhance our understanding of internal periodic waves and their loads on a marine riser.

Sosialization of Chitosan as Natural Preservation for Palm Tree’s (Arenga pinnata Merr.) Sap in Akelamo, Central Oba

Palm tree’s (Arenga pinnata Merr.) sap is the main ingredient for palm sugar. Palm tree’s sap is obtained by tapping the male flowers of palm tree. The sap is rich in sugar thus it is easy to be fermented. Palm farmers in Akelamo Village use soap as a preservation agent to prevent fermentation during the taping and loading period before the sap is cooked. Soap is a non-food product which is unsafe to be used in food product. Based on this fact, the community service program was designed to educate and share information about the danger of non-food preservation agent in food product, and also introduce chitosan as potential natural preservation to prevent fermentation process on palm tree’s sap among the palm farmers in Akelamo Village. There were four activities that had been done, such as discourse about food preservation and chitosan as natural preservation agent, workshop about how to apply chitosan to prevent fermentation during palm tree tapping, workshop about how to make palm sugar, and interactive dialogue with palm farmers. All the activities were done succesfully. The farmers were actively participated in every activity during the program.

Evaluation of Resilience Parameters of Soybean Oil-Modified and Unmodified Warm-Mix Asphalts—A Way Forward towards Sustainable Pavements

The sustainable design and construction of highways is indispensable for the economic growth and progress of any region. Highway pavements are one of the core transportation infrastructures that require energy efficient materials with durability and an optimized lifecycle. Recent research has proven that warm-mix asphalt pavements prepared with renewable bio-binders are less susceptible to distresses. This study aims to investigate the resilience characteristics (load time, deformation time) of soybean oil modified and unmodified warm-mix asphalts. Aggregates, asphalt binders and asphalt mixes were characterized in accordance with the Superpave Mix Design Criteria. The resilient modulus tests were performed as per ASTM D7369. The test results indicated that the soybean-modified warm asphalt mix samples showed a 20% to 32% reduction in load-carrying capacity than unmodified warm asphalt mixes. The values of the horizontal and vertical recoverable deformations observed in the soybean-modified mixes were found to be 3% to 7% more than in the unmodified mixes. A slight variability (up to 7%) was also observed in the time-response spectra, i.e., peak load, unload and rest periods, in the soybean-modified mixes compared with the unmodified mixes. The Pearson correlation coefficient showed a significant trend between the resilient modulus test parameters for the soybean-modified warm asphalt mixes, i.e., load deformation, load time and deformation time. Soybean oil showed sustainable behavior as a bio-binder, particularly in the deformation-time response for the warm asphalt mixes. However, the effect of soybean in terms of the reduction of the load-carrying capacity from a sustainability perspective needs to be investigated.

Theoretical and experimental study of motion suppression and friction reduction of rotor systems with active hybrid fluid-film bearings

Active bearings (including fluid film bearing) are efficient in reducing vibration and improving dynamic performances of rotary machinery. The control systems have significant influence in the working processes of rotor-bearing systems, including hydrodynamic and tribological performance. The aim of the study is to investigate the feasibility of the joint controlling of the rotor vibration and simultaneously minimizing friction losses in active hybrid bearing (AHB) – rotor systems. The theoretical and experimental results show the rotor vibrations are reduced at the energy-efficient operating modes under complex loads. The theoretical study is performed by the verified simulation models of rigid rotors with thrust and journal AHB. The artificial neural networks are proposed to calculate the bearing forces to provide a balance of accuracy and computational costs. The controller for the thrust AHB is based on the PI law, while the journal AHB controller implements an adaptive nonlinear proportional law with integrating properties. Both controllers perform well in reducing the vibration magnitudes for the systems under the periodic and constant load forces. Such rotor motion control is also able to reduce power losses caused by the viscous friction in AHB. The theoretical study shows the relations between the position of the rotor with AHBs and the magnitude of the viscou forces of the lubricant film. The minimum friction areas could be used to choose the setpoints for AHBs’ controllers for joint rotor motion and friction control.

Reprint of: Viscoelastic dissipation in repeated normal indentation of an Hertzian profile

Simple exact solutions are known for the indentation problem of a viscoelastic halfspace by a rigid sphere only as long as the contact area is growing. We consider instead a more general cyclic repeated indentation with a pulsating load with a period of zero load. We show that a combination of exact with empirical relaxation solutions coming from simple uniaxial cases is sufficiently accurate to estimate the energy dissipated per cycle, which we report for the standard ”3-elements” solid and periodic half-sine loading for various parameters. The theoretical predictions favourably compare with boundary element numerical simulations. We find more energy is dissipated during the first indentation cycle with respect to the subsequent ones, due to the residual indentation left in the viscoelastic half-space. In load controlled systems, the maximum dissipation is reached at an angular frequency that is close to the reciprocal of the relaxation time of the material both for the first and subsequent cycles, but this is in general not true when displacement controlled systems are considered, when dissipation is much lower for subsequent cycles.

Insight into the hierarchical control governing leg stiffness during the stance phase of running

Leg stiffness plays a key role in the storage and release of elastic energy during stance. However, the extent to which a runner is able to reuse stored energy remains a limiting factor in determining their running effectiveness. In this study, ten habitual rearfoot strikers and ten habitual forefoot strikers were asked to run on a treadmill in three footwear conditions: traditional, neutral, and minimal running shoes. We examined the effect of habitual foot strike pattern and footwear on leg stiffness control within three task-relevant phases of stance (i.e. touch-down, loading, unloading). Control was quantified using stride-to-stride leg stiffness time-series and the coefficient of variability and detrended fluctuation analysis (DFA). The results are interpreted within a theoretical framework that blends dynamic systems theory and optimal feedback control. Results indicate that leg stiffness control is tightly regulated by an active control process during the loading period of stance. In contrast, the touch-down and unloading phases are driven mostly by passive allometric control mechanisms. The effect of footwear on leg stiffness control was inconclusive due to inconsistent trends across three shoe types. However, stiffness control was affected by landing technique. Habitual rearfoot strike runners have reduced DFA values during the touch-down and unloading phases. These sub-phases are associated with an allometric control process and suggests that rearfoot strike runners express a reduction in system complexity for leg stiffness control and hence, a less adaptable system.