Inversion Force Research Articles

A controlled release antibiotic wound protectant gel formulated for use in austere environments.

Battlefield wounds are at high risk of infection due to gross contamination and delays in evacuation from forward-deployed locations. The aim of this study was to formulate an antibiotic wound gel for application by a field medic in austere environments to protect traumatic wounds from infection during transport. Formulation development was conducted over multiple phases to meet temperature, handling, in vitro elution, and in vivo tissue response requirements. Thermal properties were evaluated by vial inversion, DSC, and syringe expression force in a temperature range of 4-49°C. Handling was evaluated by spreading onto blood-contaminated tissue and irrigation resistance. Controlled antibiotic release was evaluated by a modified USP immersion cell dissolution method. Local tissue effects were evaluated in vivo by subcutaneous implantation in rats for 7 and 28 days. An oleogel composition of cholesterol, hydrogenated castor oil, soybean oil, and glyceryl monocaprylocaprate met the target performance criteria. Peak expression force from a 5 mL syringe at 4°C was 48.3 N, the dropping point temperature was 68°C, and the oleogel formulation could be spread onto blood-contaminated tissue and resisted aqueous irrigation. The formulation demonstrated sustained release of tobramycin in PBS at 32°C for 5 days. Implantation in a rat dorsal pocket demonstrated a slight tissue reaction after 7 days with minimal to no reaction after 28 days, comparable to a commercial hemostat control. Material resorption was evident after 28 days. The formulation met target characteristics and is appropriate for further evaluation in a large animal contaminated blast wound model.

Balance Control Deficits are Associated With Diminished Ankle Force Sense, Not Position Sense, in Athletes With Chronic Ankle Instability

ObjectivesTo compare balance control and ankle proprioception between athletes with and without chronic ankle instability (CAI). A further objective was to explore the relationship between balance control performance and ankle proprioception in athletes with CAI. DesignCross-sectional study. SettingsSports Rehabilitation Laboratory. ParticipantsEighty-eight recreational athletes (47 CAI and 41 healthy control) were recruited. InterventionsNo applicable. Main Outcome MeasuresBalance control performance was assessed using the sway velocity of the center of the pressure during the one-leg standing tasks. Ankle proprioception, including joint position sense and force sense, were tested using absolute error (AE) associated with joint position reproduction and force reproduction tasks in 4 directions, that is, plantarflexion, dorsiflexion, inversion, and eversion. ResultsAthletes with CAI performed significantly worse than those without CAI in balance control tasks. In addition, CAI athletes showed significantly worse joint position sense and force sense in all 3 movement directions tested (plantarflexion, inversion, and eversion). Correlation analysis showed that the AE of the plantarflexion force sense was significantly moderately correlated with medial-lateral sway velocity in the one-leg standing with eyes open and closed conditions (r=.372-.403, P=.006-.012), and the AE of inversion force sense was significantly moderately correlated with medial-lateral sway velocity in the one-leg standing with eyes open (r=.345, P=.018) in athletes with CAI, but the joint position sense measures were not (all P>0.05). ConclusionsAthletes with CAI showed significantly impaired balance control performance and diminished ankle proprioception. Deficit in force sense was deemed as a moderate predictor of one-leg standing balance control deficits in athletes with dominant-side injury CAI, whereas ankle position sense may be a small predictor.

Application of GA-BP in Displacement Force Inverse Analysis and Mechanical Parameter Inversion of Deep Foundation Pits

Aiming at the defects of various existing displacement inverse analysis methods, using the nonlinear mapping ability of neural network and the global random search ability of genetic algorithm, this paper proposes a displacement inverse analysis method based on optimized Genetic Algorithm- Back Propagation (GA-BP) for deep foundation pit support. The method changes the method that BP algorithm relies on the guidance of gradient information to adjust the network weights, but uses the characteristics of global search of genetic algorithm to find the most suitable network connection rights and network structure, etc. to achieve the purpose of optimization. Firstly, the deformation mechanism of deep foundation pit is analyzed, its failure mode is summarized, and the calculation method of lateral rock and soil pressure is sorted out according to the code. The theory and characteristics of BP neural network and genetic algorithm are discussed, and the method of using genetic algorithm to optimize BP neural network is proposed to improve the prediction accuracy. In view of the shortcomings of GA-BP neural network prediction model in training sample pretreatment and hidden layer structure design, the optimal normalization interval was determined by correlation coefficient regression analysis, and the analytical expression of the number of neurons in hidden layer was derived by statistical principle, and the value range of the optimal number of neurons in single hidden layer was proposed. Combined with the actual engineering, the mechanical parameters inversion and displacement force inverse analysis are performed using this method, and the results show that the optimized GA-BP has higher prediction accuracy compared with BP neural network and GA-BP, and the deviation of the displacement prediction value at each depth is kept within 0.2 mm, the absolute error interval width is 0.07 mm, and the maximum relative error is 1.35% at 4.0 m depth.

Simulating Polymerization by Boltzmann Inversion Force Field Approach and Dynamical Nonequilibrium Reactive Molecular Dynamics

The radical polymerization process of acrylate compounds is, nowadays, numerically investigated using classical force fields and reactive molecular dynamics, with the aim to probe the gel-point transition as a function of the initial radical concentration. In the present paper, the gel-point transition of the 1,6-hexanediol dimethacrylate (HDDMA) is investigated by a coarser force field which grants a reduction in the computational costs, thereby allowing the simulation of larger system sizes and smaller radical concentrations. Hence, the polymerization is investigated using reactive classical molecular dynamics combined with a dynamical approach of the nonequilibrium molecular dynamics (D-NEMD). The network structures in the polymerization process are probed by cluster analysis tools, and the results are critically compared with the similar all-atom system, showing a good agreement.

Validity of Using the Scratch Collapse Test in the Lower Extremities.

The scratch collapse test is a provocative test that has been successfully used for peripheral neuropathies. The elbow is the main testing site, but there may be times when use of the upper extremities is contraindicated. This study sought to determine the sensitivity of using the scratch collapse test on the lower extremity for upper extremity neuropathies. One hundred patients with an electromyographically confirmed diagnosis of carpal tunnel or cubital tunnel syndrome were prospectively enrolled. As a control, the scratch collapse test was conducted normally using the elbow as a testing site. After a baseline was established, the test was repeated using eversion of the foot and ankle against an inversion force. Of the 100 study patients, 89 had a positive scratch collapse test on the upper extremity and 84 had a positive test on the lower extremity. In the 51 patients with carpal tunnel syndrome, 45 had a positive test on the upper extremity (sensitivity, 88.2 percent; 95 percent CI, 76.13 to 95.56 percent), and 42 had a positive test of the lower extremity (sensitivity, 82.35 percent; 95 percent CI, 69.13 to 91.60 percent). In the 49 patients with cubital tunnel syndrome, 44 had a positive test on the upper extremity (sensitivity, 89.8 percent; 95 percent CI, 77.77 to 96.6 percent), and 42 had a positive test on the lower extremity (sensitivity, 85.7 percent; 95 percent CI, 72.76 to 94.06 percent). There were no statistically significant differences in the sensitivities of the scratch collapse test on the upper or lower extremities, suggesting that the lower extremity could serve as an alternative site for the scratch collapse test. Diagnostic, II.

Peroneus brevis tendon rupture in ankle fracture: a case report

This study shows the case of a patient with peroneus brevis tendon rupture in ankle fracture. The patient com-plained of swelling, pain and activity limitation in her right ankle caused by sprain. She was diagnosed with ankle fracture, supina-tion-adduction (Lauge-Hansen typing) by medical history, physical examination and imaging. The peroneus brevis tendon was not-ed complete ruptured when suturing the incision after ORIF, which was then repaired by 8 shaped suture. Based on literature re-view, the injury mechanism of the case may be because of overload inversion force toward to lateral inferior from the fracture of fib-ula on the peroneus brevis tendon. Additional attention should be paid to patients who suffered from an supination-adduction ankle fracture for whether peroneus brevis tendon tears before and during surgery.

Accuracy in the Air: Pollution and Analyst Forecasts

We investigate the causal impacts of air pollution on analyst forecast accuracy around earnings announcements. Using the air quality index in analyst workplaces, we provide direct evidence of the following. First, air pollution significantly reduces analysts’ earnings forecast accuracy in response to earnings announcements. Second, we introduce thermal inversion and wind force as instruments of air pollution to alleviate endogeneity, thereby establishing causality. Third, our findings are particularly pronounced in companies with more complications and for analysts who are younger, have lower levels of education, and are male. Furthermore, they are robust to alternative measures and different specifications. Overall, our findings contribute to the broader psychology and economics literature on the economic impacts of air pollution on analyst forecasts.

Peritalar fracture dislocation: A case report with review on its biomechanics

Peritalar dislocations are very rare injuries involving a simultaneous dislocation to both the subtalar and talonavicular joints. Mostly, they result from high-energy trauma such as road traffic accident and may also result from sports injuries. The most common type is medial dislocation. An inversion force in medial dislocation and an eversion force in lateral dislocation are applied to a plantar flexed foot. The treatment modalities for most peritalar dislocations include closed reduction and below-knee cast, although surgical intervention may be required in failed close reduction. We report a case of medial peritalar dislocation and comminuted fracture involving the posterior aspect of the talus with literature review on its biomechanics. A thorough knowledge of the biomechanics is essential for its better understanding and successful reduction maneuver.

Suture-button fixation and anterior inferior tibiofibular ligament augmentation with suture-tape for syndesmosis injury: A biomechanical cadaveric study

BackgroundSuture-button (SB) fixation has been widely performed for syndesmosis injuries, but it has been reported unstable in some biomechanical studies. The purpose of this study was to evaluate the stability of the syndesmosis using SB fixation with anterior inferior tibiofibular ligament augmentation using suture-tape (ST). MethodsEight normal fresh-frozen cadaveric legs were used. After initial tests of intact and injured models, SB fixation, SB fixation with ST augmentation, ST augmentation alone, and screw fixation were performed sequentially for each specimen. Loading tests stimulating dorsiflexion, inversion, and external rotation of the ankle joint were performed for each model. The tibiofibular diastasis (TFD) and the fibular rotational angle related to the tibia (FRA) were measured using a magnetic tracking system. FindingsIn the injured model, both TFD and FRA increased significantly compared with the intact model in all directions (P < .05). In the SB fixation model, TFD and FRA generally showed significant increases (P < .05, except for TFD in external rotation). In the SB fixation with ST augmentation model and ST augmentation alone, TFD and FRA were not significantly different compared with the intact model (P > .05). In the screw fixation model, FRA with inversion force at the ankle was significantly decreased compared with the intact model (P = .027). InterpretationSB fixation alone did not provide stability of the syndesmosis, and screw fixation became too rigid compared with the intact model. Using ST augmentation achieved dynamic stability similar to the intact model for syndesmotic injuries.

The Role of the Calcaneofibular Ligament in Chronic Ankle Pain Following Severe Ankle Sprains

Category: Sports Introduction/Purpose: Lateral ankle pain persists in 10%-20% of patients following severe ankle sprains treated non-operatively. The authors hypothesize that the peroneal tendons may become interposed between the ruptured ends of the calcaneofibular ligament (CFL). Though previously visualized and noted in the literature, no studies have evaluated this lesion biomechanically and anatomically. The purpose of this study is to demonstrate that following a severe lateral ankle sprain that the interposition of the peroneal tendons between the ruptured ends of the CFL can occur. Methods: Eight fresh-frozen cadaveric lower extremity specimens (defrosted) were secured by the foot to a wooden board in the method of Lauge-Hansen. A manual inversion force was then applied to the ankle, both with the ankle in plantar flexion and also in a neutral position to approximate a severe ankle sprain. Magnetic resonance imaging (MRI) was then performed on each ankle. Each specimen was then dissected to observe the integrity and relationship of the lateral ankle structures. Results: Four of the eight specimens sustained CFL tears as viewed by MRI and confirmed through anatomic dissection. One of the four specimens with a CFL tear had a mid substance ligament rupture with the proximal half of the ligament positioned superficial to the peroneal tendon complex. This relationship was observed using the MRI. Conclusion: Creating severe lateral ankle sprain produced ruptures of the CFL with interposition of the peroneal tendon complex between the torn ends of the ligament was seen and identified. This phenomenon may prevent primary ligament healing of the CFL and may be a contributing factor in the chronic ankle pain of non-surgically treated lateral ankle sprains. Perhaps surgical intervention should be considered if clinical suspicion exists, such as with a Stener lesion of the hand.

Experimental, numerical and analytical investigations into the internal inversion of mild steel tubes under high velocity axial impact using a die

This paper investigates the internal inversion process of mild steel tubes under axial impact analytically, numerically and experimentally using a die. The analytical model which is based on the energy method, is able to predict the shortening length of the tube and the required force for tube inversion considering tube thickness variation. In order to validate the analytical model, some experimental tests are performed on the steel tubes in a gas gun and the required force for tube inversion is obtained using an impact loading measurement system. The tube inversion process is also simulated using the finite element software Abaqus and finally the obtained results are compared with each other. In the present paper, the effect of impact parameters included the projectile mass and velocity, is investigated on deformation mechanism and energy absorption of the tubes in the internal inversion process. The effect of tube thickness and die radius are also studied in the mentioned process. It is observed that in the situation of constant projectile mass, increasing the impact velocity doesn’t have a tangible effect on the inversion force and just increases the tube displacement, but if the impact velocity remains constant, increasing the projectile mass causes increase in the inversion force as well as increased tube displacement. It is also concluded that increasing the tube wall thickness increases the inversion force which makes the tube not to be a good absorbent and decreases the tube displacement. Comparing the experimental, analytical and numerical results provides good agreements between them.

Single-limb landing biomechanics are altered and patellar tendinopathy related pain is reduced with acute infrapatellar strap application

BackgroundPatellar tendinopathy, a common condition of the knee, is often treated with patellar tendon straps to control pain during dynamic activity. Little is known regarding their effect on pain, landing kinematics and kinetics with their application. The purpose of this study was to determine if patellar tendon straps influenced pain, kinematics at landing and ground reaction forces in individuals with patellar tendinopathy versus healthy controls. MethodsThirty participants with patellar tendinopathy and 30 controls participated. They completed single-limb landings with and without patellar tendon straps while pain, three-dimensional kinematics and vertical ground reaction forces were measured. A multivariate analysis of variance was completed to determine the differences in strapping condition and group for the dependent variables. ResultsIndividuals with patellar tendinopathy demonstrated a significant decrease in pain (no strap=37.1±22.1mm (mean±SD), strap=28.0±18.5mm (mean±SD)). With the strap at landing all participants displayed less hip rotation (F=7.16, p=.01), knee adduction (F=10.20, p=.002), ankle inversion (F=4.60, p=.04), and peak vertical ground reaction force (F=7.30, p=.009). ConclusionsPatellar tendon straps reduced pain in those with patellar tendinopathy. Additionally, with the strap, individuals landed in a more neutral alignment and decreased landing forces which could provide a benefit to those with patellar tendinopathy.

Analytical solutions for elastic binary nanotubes of arbitrary chirality

Analytical solutions for the elastic properties of a variety of binary nanotubes with arbitrary chirality are obtained through the study of systematic molecular mechanics. This molecular mechanics model is first extended to chiral binary nanotubes by introducing an additional out-of-plane inversion term into the so-called stick-spiral model, which results from the polar bonds and the buckling of binary graphitic crystals. The closed-form expressions for the longitudinal and circumferential Young’s modulus and Poisson’s ratio of chiral binary nanotubes are derived as functions of the tube diameter. The obtained inversion force constants are negative for all types of binary nanotubes, and the predicted tube stiffness is lower than that by the former stick-spiral model without consideration of the inversion term, reflecting the softening effect of the buckling on the elastic properties of binary nanotubes. The obtained properties are shown to be comparable to available density functional theory calculated results and to be chirality and size sensitive. The developed model and explicit solutions provide a systematic understanding of the mechanical performance of binary nanotubes consisting of III–V and II–VI group elements.

Consequences of simulated car driving at constant high speed on the sensorimotor control of leg muscles and the braking response.

Due to the increase in time spent seated in cars, there is a risk of fatigue of the leg muscles which adjust the force exerted on the accelerator pedal. Any change in their sensorimotor control could lengthen the response to emergency braking. Fourteen healthy male subjects (mean age: 42±4 years) were explored. Before and after a 1-h driving trial at 120km h-1 , we measured the braking response, the maximal leg extension and foot inversion forces, the tonic vibratory response (TVR) in gastrocnemius medialis (GM) and tibialis anterior (TA) muscles to explore the myotaticreflex, and the Hoffmann reflex (H-reflex). During driving, surface electromyograms (EMGs) of GM and TA were recorded and the ratio between high (H) andlow (L) EMG energies allowed to evaluate the recruitment of high- and low-frequency motor unit discharges. During driving, the H/L ratio decreased in TA, whereas modest and often no significant H/L changes occurred in GM muscle. After driving, the maximal foot inversion force decreased (-19%), while the leg extension force did not vary. Reduced TVR amplitude (-29%) was measured in TA, but no H-reflex changes were noted. The braking reaction time was not modified after the driving trial. Driving at constant elevated speed reduced the myotatic reflex and the recruitment of motor units in TA muscle. The corresponding changes were rarely present in the GM muscle that plays a key role in the braking response, and this could explain the absence of a reduced braking reaction time.

Theoretical model of a metal tube under inversion over circular dies

The inversion of a metal tube over a circular die is an important energy absorption device. Taking into consideration the curvature change during inversion process, this study proposes a two-dimensional theoretical model. Using rigid-perfectly plastic (R-PP) material idealization, its steady inversion load, curling radius after the tube׳s separation from the die, and the optimization of the die radius are analytically obtained based on energy conservation.Compared with the FE simulations, the current model greatly improves the prediction accuracy of the steady inversion force, with the deviation smaller than 10%. The prediction of the tube radius after inversion agrees well with the FE simulation and experimental data. Out of our expectation, the optimized die radius is found to be different from that of free inversion radius of the same tube. In this study, a simple formula of the optimized die radius is given.

Ultrasound elasticity imaging for determining the mechanical properties of human posterior tibial tendon: a cadaveric study.

Posterior tibial tendon dysfunction (PTTD) is a common degenerative condition leading to a severe impairment of gait. There is currently no effective method to determine whether a patient with advanced PTTD would benefit from several months of bracing and physical therapy or ultimately require surgery. Tendon degeneration is closely associated with irreversible degradation of its collagen structure, leading to changes to its mechanical properties. If these properties could be monitored in vivo, they could be used to quantify the severity of tendonosis and help determine the appropriate treatment. The goal of this cadaveric study was, therefore, to develop and validate ultrasound elasticity imaging (UEI) as a potentially noninvasive technique for quantifying tendon mechanical properties. Five human cadaver feet were mounted in a materials testing system (MTS), while the posterior tibial tendon (PTT) was attached to a force actuator. A portable ultrasound scanner collected 2-D data during loading cycles. Young's modulus was calculated from the strain, loading force, and cross-sectional area of the PTT. Average Young's modulus for the five tendons was (0.45 ± 0.16 GPa) using UEI, which was consistent with simultaneous measurements made by the MTS across the whole tendon (0.52 ± 0.18 GPa). We also calculated the scaling factor (0.12 ± 0.01) between the load on the PTT and the inversion force at the forefoot, a measurable quantity in vivo. This study suggests that UEI could be a reliable in vivo technique for estimating the mechanical properties of the PTT, and as a clinical tool, help guide treatment decisions for advanced PTTD and other tendinopathies.

Intra-Tester Reliability of Hand-Held Dynamometry and Strap-Mounted Dynamometry for Assessment of Ankle Strength

Context:Measurement of ankle evertor and invertor strength is important for assessment of ankle sprain risk and assessment of restoration of normal function after an ankle sprain.Objective:To compare the intra-tester reliability of ankle evertor and invertor strength measurements derived from hand-held dynamometry (HHD) and strap-mounted dynamometry (SMD) for both make-test and break-test techniques.Participants:25 healthy individuals.Main Outcome Measure:Repeated measurements of isometric evertor and invertor strength derived from both HHD and SMD devices using both make-test and break-test techniques.Results:High make-test reliability values were found for both inversion and eversion force measured by both the HHD and SMD devices (ICC = 0.80 to ICC = 0.88). The correlation coeffcients between HHD and SMD measurements for the inversion make-test, the inversion break-test, and the eversion make-test ranged from r = 0.74 to r = 0.87, but the correlation between HHD and SMD measurements for the eversion break-test was poor.Conclusion:The fndings suggest that testers with limited experience can obtain reliable measurements of ankle evertor and invertor strength using either HHD or SMD.

Plantar Forces in Flexor Hallucis Longus Versus Flexor Digitorum Longus Transfer in Adult Acquired Flatfoot Deformity

Flexor hallucis longus (FHL) and flexor digitorum longus (FDL) tendon transfers are frequently used to restore the function of a deficient tibialis posterior tendon in stage II adult acquired flatfoot deformity (AAFD). Either transfer causes some loss in toe flexion force, although the decision to tenodese the cut tendon to restore associated function remains controversial. This study quantified changes in plantar force before and after tendon transfer and with or without distal tenodesis in a cadaveric model. The plantar force distribution of 10 matched pairs of statically loaded cadaveric lower extremities was investigated. Each foot was tested when it was intact, after FDL/FHL tendon transfer, and after tendon transfer + tenodesis. Transfer of either FHL or FDL showed a statistically significant decrease in flexion force of the great toe (P < .01) and lesser toes (P < .001), respectively. Subsequent tenodesis in either tendon demonstrated an ability to restore flexion force in the great (P < .05) and lesser (P < .01) toes, respectively, with the FHL transfer + tenodesis restoring great toe loading to near pretransfer levels. Following either transfer, plantar force increased in the medial forefoot; this was sustained with FDL transfer + tenodesis but reduced under FHL transfer + tenodesis. Lateral forefoot force increased modestly (8%) with FHL transfer (P < .05) but returned to near intact levels with tenodesis. FDL transfer + tenodesis resulted in increased medial midfoot and heel loading. FHL or FDL transfer notably reduces associated toe flexion force. This loss can be restored to near normal levels with tenodesis for FHL transfer. As increased lateral forefoot loading is commonly associated with AAFD corrective procedures, FHL tenodesis may mitigate the unintended increases caused by the tendon transfer. The medial midfoot and heel loading with FDL transfer + tenodesis underscores that tendon transfers alone do not reestablish the passive architecture of the foot but augment deficient subtalar inversion force. This cadaveric study shows that the FHL is more biomechanically suitable for tibialis posterior tendon insufficiency than the FDL, which may be a basis for a study to investigate whether it is superior in a clinical situation.

Decreased foot inversion force and increased plantar surface after maximal incremental running exercise

Formulating the hypothesis that a maximal running exercise could induce fatigue of some foot muscles, we searched for electromyographic (EMG) signs of fatigue in the tibialis anterior (TA), peroneus longus (PL), and gastrocnemius medialis (GM) muscles. We also searched for post-exercise alterations of the stationary upright standing in normal-arched feet subjects.Healthy subjects performed a maximal running exercise. Surface EMGs of the TA, PL, and GM muscles were analysed during maximal dynamic efforts. Before and after the running bout, we measured the evoked compound muscle potential (M-wave) in TA, the maximal force into inversion (MIF), and the repartition of the plantar and barycentre surfaces with a computerised stationary platform.During maximal running exercise, the median frequency of the EMG spectra declined in TA while it remained stable in the PL and GM muscles. After the exercise, MIF decreased, and both the rearfoot plantar surface and the barycentre surface increased.We concluded that a maximal running bout elicits EMG signs of fatigue, though only in the TA muscle. It also elicits post-exercise changes in the foot position during stationary upright standing which indicates a foot eversion. These data solely concern a maximal running test and they can not be extrapolated to walking or running at a low speed.

Theoretical and experimental studies of the external inversion process in the circular metal tubes

This article introduces a new theoretical model of deformation and based on the energy method derives a new theoretical relation to predict the axial load versus the axial displacement during the external inversion process in the circular metal tubes. Several deformation mechanisms are assumed in the theoretical model: bending around circular hinge line, bending in normal to meridian direction and circumferential expansion. A total inversion process in the tubes is divided to three different stages versus the inversion angle, θ: 0⩽θ⩽π, π⩽θ⩽2π and after θ=2π. In each stage, the total dissipated energy is calculated by different deformation modes. The different strain components are calculated and based on the principle of energy conservation; some theoretical relations are derived to predict the instantaneous inversion force. Then, some circular brazen tubes are used in the external inversion tests with die radiuses of R=2.85mm and 4mm and diagrams of axial load versus the axial displacement are sketched. Comparison of the theoretical predictions and the experimental results shows a reasonable correlation. The theoretical relations can predict variations of the axial load versus the axial displacement of three considered stages during the whole inversion process with a good agreement. Comparison of the theoretical and experimental curves shows a better correlation in the horizontal part and position of start point of the inversion process with the die radius of R=4mm, comparing with the inversion process with the die radius of R=2.85mm. Also, the theoretical analysis shows that the absorbed energy and the axial load during the inversion process in the circular tubes depend on the wall thickness and diameter of the tube, tube material type, and the die radius.