Contact with friction using the augmented Lagrangian Method: a conditional constrained minimization problem

This work presents a formulation of the contact with friction between elastic bodies. This is a non linear problem due to unilateral constraints (inter-penetration of bodies) and friction. The solution of this problem can be found using optimization concepts, modelling the problem as a constrained minimization problem. The Finite Element Method is used to construct approximation spaces. The minimization problem has the total potential energy of the elastic bodies as the objective function, the non-inter-penetration conditions are represented by inequality constraints, and equality constraints are used to deal with the friction. Due to the presence of two friction conditions (stick and slip), specific equality constraints are present or not according to the current condition. Since the Coulomb friction condition depends on the normal and tangential contact stresses related to the constraints of the problem, it is devised a conditional dependent constrained minimization problem. An Augmented Lagrangian Method for constrained minimization is employed to solve this problem. This method, when applied to a contact problem, presents Lagrange Multipliers which have the physical meaning of contact forces. This fact allows to check the friction condition at each iteration. These concepts make possible to devise a computational scheme which lead to good numerical results.

Ankle joint pressure in pes cavovarus after lateralizing calcaneal osteotomies

BACKGROUND: Tendon transfers and calcaneal osteotomies are commonly used to treat symptoms related to medial ankle arthrosis in fixed pes cavovarus. However, the relative effect of these osteotomies in terms of lateralizing the ground contact point of the hindfoot and redistributing ankle joint contact stresses are unknown. MATERIALS AND METHODS: Pes cavovarus with fixed hindfoot varus was simulated in eight cadaver specimens. The effect of three types of calcaneal osteotomies on the migration of the center of force and tibiotalar peak pressure at 300 N axial static load (half-body weight) were recorded using pressure sensors. RESULTS: A significant lateral shift of the center of force was observed: 4.9 mm for the laterally closing Z-shaped osteotomy with additional lateralization of the tuberosity, 3.4 mm for the lateral sliding osteotomy of the calcaneal tuberosity, and 2.7 mm for the laterally closing Z-shaped osteotomy (all p < 0.001). A significant peak pressure reduction was recorded: -0.53 MPa for the Z-shaped osteotomy with lateralization, -0.58 MPa for the lateral sliding osteotomy of the calcaneal tuberosity, and -0.41 MPa for the Z-shaped osteotomy (all p < 0.01). CONCLUSION: This cadaver study supports the hypothesis that lateralizing calcaneal osteotomies substantially help to normalize ankle contact stresses in pes cavovarus.

Investigation of Plastic Pipes for Highway Applications, HR-373A, Phase II, 1997

It is generally accepted that high density polyethylene pipe (HDPE) performs well under live loads with shallow cover, provided the backfill is well compacted. Although industry standards require carefully compacted backfill, poor inspection and/or faulty construction may result in soils that provide inadequate restraint at the springlines of the pipes thereby causing failure. The objectives of this study were: 1) to experimentally define a lower limit of compaction under which the pipes perform satisfactorily, 2) to quantify the increase in soil support as compaction effort increases, 3) to evaluate pipe response for loads applied near the ends of the buried pipes, 4) to determine minimum depths of cover for a variety of pipes and soil conditions by analytically expanding the experimental results through the use of the finite element program CANDE. The test procedures used here are conservative especially for low-density fills loaded to high contact stresses. The failures observed in these tests were the combined effect of soil bearing capacity at the soil surface and localized wall bending of the pipes. Under a pavement system, the pipes' performance would be expected to be considerably better. With those caveats, the following conclusions are drawn from this study. Glacial till compacted to 50% and 80% provides insufficient support; pipe failureoccurs at surface contact stresses lower than those induced by highway trucks. On the other hand, sand backfill compacted to more than 110 pcf (17.3 kN/m3) is satisfactory. The failure mode for all pipes with all backfills is localized wall bending. At moderate tire pressures, i.e. contact stresses, deflections are reduced significantly when backfill density is increased from about 50 pcf (7.9 kN/m^3) to 90 pcf (14.1 kN/m^3). Above that unit weight, little improvement in the soil-pipe system is observed. Although pipe stiffness may vary as much as 16%, analyses show that backfill density is more important than pipe stiffness in controlling both deflections at low pipe stresses and at the ultimate capacity of the soil-pipe system. The rate of increase in ultimate strength of the system increases nearly linearly with increasing backfill density. When loads equivalent to moderate tire pressures are applied near the ends of the pipes, pipe deflections are slighly higher than when loaded at the center. Except for low density glacial till, the deflections near the ends are not excessive and the pipes perform satisfactorily. For contact stresses near the upper limit of truck tire pressures and when loaded near the end, pipes fail with localized wall bending. For flowable fill backfill, the ultimate capacity of the pipes is nearly doubled and at the upper limit of highway truck tire pressures, deflections are negligible. All pipe specimens tested at ambient laboratory room temperatures satisfied AASHTO minimum pipe stiffness requirements at 5% deflection. However, nearly all specimens tested at elevated pipe surface temperatures, approximately 122°F (50°C), failed to meet these requirements. Some HDPE pipe installations may not meet AASHTO minimum pipe stiffness requirements when installed in the summer months (i.e. if pipe surface temperatures are allowed to attain temperatures similar to those tested here). Heating of any portion of the pipe circumference reduced the load carrying capacity of specimens. The minimum soil cover depths, determined from the CANOE analysis, are controlled by the 5% deflection criterion. The minimum soil cover height is 12 in. (305 mm). Pipes with the poor silt and clay backfills with less than 85% compaction require a minimum soil cover height of 24 in. (610 mm). For the sand at 80% compaction, the A36 HDPE pipe with the lowest moment of inertia requires a minimum of 24 in. (610 mm) soil cover. The C48 HDPE pipe with the largest moment of inertia and all other pipes require a 12 in. (305 mm) minimum soil cover.

The slippery slope - Critical perspectives on in vitro research methodologies

Objectives. This paper attempts to provide critical perspectives on common in vitro research methodologies, including shear bond testing, wear testing, and load-to-failure tests. Origins of interest in high-quality laboratory data is reviewed, in vitro data is categorized into property and simulation protocols, and two approaches are suggested for establishing clinical validity. It is hoped that these insights will encourage further progress toward development of in vitro tests that are validated against clinical performance and/or by producing clinically validated failure or damage mechanisms.Materials and methods. Published shear and tensile bond data (macro and micro) is examined in light of published finite element analyses (FEA). This data is subjected to a Weibull scaling analysis to ascertain whether scaling is consistent with failure from the bonded interface or not. Wear tests results are presented in light of the damage mechanism(s) operating. Quantitative wear data is re-examined as being dependent upon contact pressure. Load-to-failure test results are re-analyzed by calculating contact stresses at failure for 119 tests from 54 publications over more than 25 years.Results. FEA analyses and reported failure modes (adhesive, mixed, cohesive) are consistent with failure not involving interfacial "shear stresses" as calculated in published work. Weibull scaling clearly suggests failure involving external surfaces of specimens, not interfacial origins. Contact stresses (pressures) are clearly an important variable in wear testing and are not well-controlled in published work. Load-to-failure tests create damage not seen clinically due to excessively high contact stresses. Most contact stresses in the 119 tests examined were calculated to be between 1000 MPa and 5000 MPa, whereas clinical contact stresses at wear facets have been measured not to exceed 40 MPa.Conclusions. Our community can do a much better job of designing in vitro tests that more closely simulate clinical conditions, especially when contact is involved. Journals are encouraged to thoughtfully consider a ban on publishing papers using bond tests and load-to-failure methods that are seriously flawed and have no clinical relevance. (C) 2011 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Ankle joint pressure changes in a pes cavovarus model after lateralizing calcaneal osteotomies

Tendon transfers and calcaneal osteotomies are commonly used to treat symptoms related to medial ankle arthrosis in fixed pes cavovarus. However, the relative effect of these osteotomies in terms of lateralizing the ground contact point of the hindfoot and redistributing ankle joint contact stresses are unknown.

Ankle joint pressure changes in a pes cavovarus model: supramalleolar valgus osteotomy versus lateralizing calcaneal osteotomy

BACKGROUND: A fixed cavovarus foot deformity can be associated with anteromedial ankle arthrosis due to elevated medial joint contact stresses. Supramalleolar valgus osteotomies (SMOT) and lateralizing calcaneal osteotomies (LCOT) are commonly used to treat symptoms by redistributing joint contact forces. In a cavovarus model, the effects of SMOT and LCOT on the lateralization of the center of force (COF) and reduction of the peak pressure in the ankle joint were compared. METHODS: A previously published cavovarus model with fixed hindfoot varus was simulated in 10 cadaver specimens. Closing wedge supramalleolar valgus osteotomies 3 cm above the ankle joint level (6 and 11 degrees) and lateral sliding calcaneal osteotomies (5 and 10 mm displacement) were analyzed at 300 N axial static load (half body weight). The COF migration and peak pressure decrease in the ankle were recorded using high-resolution TekScan pressure sensors. RESULTS: A significant lateral COF shift was observed for each osteotomy: 2.1 mm for the 6 degrees (P = .014) and 2.3 mm for the 11 degrees SMOT (P = .010). The 5 mm LCOT led to a lateral shift of 2.0 mm (P = .042) and the 10 mm LCOT to a shift of 3.0 mm (P = .006). Comparing the different osteotomies among themselves no significant differences were recorded. No significant anteroposterior COF shift was seen. A significant peak pressure reduction was recorded for each osteotomy: The SMOT led to a reduction of 29% (P = .033) for the 6 degrees and 47% (P = .003) for the 11 degrees osteotomy, and the LCOT to a reduction of 41% (P = .003) for the 5 mm and 49% (P = .002) for the 10 mm osteotomy. Similar to the COF lateralization no significant differences between the osteotomies were seen. CONCLUSION: LCOT and SMOT significantly reduced anteromedial ankle joint contact stresses in this cavovarus model. The unloading effects of both osteotomies were equivalent. More correction did not lead to significantly more lateralization of the COF or more reduction of peak pressure but a trend was seen. CLINICAL RELEVANCE: In patients with fixed cavovarus feet, both SMOT and LCOT provided equally good redistribution of elevated ankle joint contact forces. Increasing the amount of displacement did not seem to equally improve the joint pressures. The site of osteotomy could therefore be chosen on the basis of surgeon's preference, simplicity, or local factors in case of more complex reconstructions.

Modelling comminution patterns within a pilot scale AG/SAG mill

The patterns of rock comminution within tumbling mills, as well as the nature of forces, are of significant practical importance. Discrete element modelling (DEM) has been used to analyse the pattern of specific energy applied to rock, in terms of spatial distribution within a pilot AG/SAG mill. We also analysed in some detail the nature of the forces, which may result in rock comminution. In order to examine the distribution of energy applied within the mill, the DEM models were compared with measured particle mass losses, in small scale AG and SAG mill experiments. The intensity of contact stresses was estimated using the Hertz theory of elastic contacts. The results indicate that in the case of the AG mill, the highest intensity stresses and strains are likely to occur deep within the charge, and close to the base. This effect is probably more pronounced for large AG mills. In the SAG mill case, the impacts of the steel balls on the surface of the charge are likely to be the most potent. In both cases, the spatial pattern of medium-to-high energy collisions is affected by the rotational speed of the mill. Based on an assumed damage threshold for rock, in terms of specific energy introduced per single collision, the spatial pattern of productive collisions within each charge was estimated and compared with rates of mass loss. We also investigated the nature of the comminution process within AG vs. SAG mill, in order to explain the observed differences in energy utilisation efficiency, between two types of milling. All experiments were performed using a laboratory scale mill of 1.19 m diameter and 0.31 m length, equipped with 14 square section lifters of height 40 mm. (C) 2006 Elsevier Ltd. All rights reserved.

Residual stresses in TiN, DLC and MoS(2) coated surfaces with regard to their tribological fracture behaviour

Thin hard coatings on components and tools are used increasingly due to the rapid development in deposition techniques, tribological performance and application skills. The residual stresses in a coated surface are crucial for its tribological performance. Compressive residual stresses in PVD deposited TiN and DLC coatings were measured to be in the range of 0.03-4 GPa on steel substrate and 0.1-1.3 GPa on silicon. MoS(2) coatings had tensional stresses in the range of 0.8-1.3 on steel and 0.16 GPa compressive stresses on silicon. The fracture pattern of coatings deposited on steel substrate were analysed both in bend testing and scratch testing. A micro-scale finite element method (FEM) modelling and stress simulation of a 2 mu m TiN-coated steel surface was carried out and showed a reduction of the generated tensile buckling stresses in front of the sliding tip when compressive residual stresses of 1 GPa were included in the model. However, this reduction is not similarly observed in the scratch groove behind the tip, possibly due to sliding contact-induced stress relaxation. Scratch and bending tests allowed calculation of the fracture toughness of the three coated surfaces, based on both empirical crack pattern observations and FEM stress calculation, which resulted in highest values for TiN coating followed by MoS(2) and DLC coatings, being K(C) = 4-11, about 2, and 1-2 MPa M(1/2), respectively. Higher compressive residual stresses in the coating and higher elastic modulus of the coating correlated to increased fracture toughness of the coated surface. (C) 2009 Elsevier B.V. All rights reserved.

Effect of pH, temperature and surface contact on the elaboration of fimbriae and flagella by Salmonella serotype Enteritidis

Survival of enteric pathogens exposed to various environmental stresses depends upon a number of protective responses, some of which are associated with induction of virulence determinants. Flagella and fimbriae are putative virulence determinants of Salmonella spp, and ELISAs specific for the detection of flagella and SEF21, SEF14 and SEF17 fimbriae were used to assess the effect of temperature and pH upon their elaboration by isolates of Salmonella serotype Enteritidis in planktonic growth and on the surface of two-dimensional gradient agar plates, For three phage type 4 isolates of Enteritidis of comparative clinical provenance, similar phenotypes for the elaboration of these surface antigens were observed. SEF14 fimbriae were elaborated in planktonic growth at 37 degrees C, but not 20 degrees C, at pH 4.77 and above but not at pH 4.04; whereas on agar gradient plates SEF14 fimbriae were elaborated poorly but with best yields at pH 4.04, SEF17 fimbriae were elaborated in planktonic growth at 20 degrees C, but not at 37 degrees C, at pH 6.18 and above but not at pH 5.09 or below; whereas on agar gradient plates SEF17 fimbriae were elaborated well even at pH 4.65, SEF21 fimbriae were expressed very poorly under all conditions tested, Planktonic growth at 37 degrees C induced least flagella whereas growth at 20 degrees C, and particularly surface growth at lower pH values, induced a 'hyper-flagellate' phenotype, Single colonies allowed to form on gradient agar plates were shown to generate different colonial morphologies which were dependent on initial pH. These results demonstrate that the physicochemical environment is an important determinant of bacterial response, especially the induction of putative virulence factors.

Influence of occlusal contact area on cusp defection and stress distribution

The purpose of this study was to evaluate the effect of occlusal contact area for loading on the cuspal defection and stress distribution in a first premolar restored with a high elastic modulus restorative material. The Rhinoceros 4.0 software was used for modeling the three-dimensional geometries of dental and periodontal structures and the inlay restoration. Thus, two different models, intact and restored teeth with three occlusal contact areas, 0.1, 0.5 and 0.75 mm(2), on enamel at the occlusal surface of buccal and lingual cusps. Finite element analysis (FEA) was performed with the program ANSYS (Workbench 13.0), which generated a mesh with tetrahedral elements with greater refinement in the regions of interest, and was constrained at the bases of cortical and trabecular bone in all axis and loaded with 100 N normal to each contact area. To analysis of maximum principal stress, the smaller occlusal contact area showed greater compressive stress in region of load application for both the intact and inlay restored tooth. However, tensile stresses at the occlusal isthmus were similar for all three tested occlusal contact areas (60 MPa). To displacement of the cusps was higher for teeth with inlay (0.46-0.48 mm). For intact teeth, the smaller contact area showed greater displacement (0.10 mm). For teeth with inlays, the displacement of the cusps were similar in all types of occlusal area. Cuspal displacement was higher in the restored tooth when compared to the intact tooth, but there were no significant variations even with changes in the occlusal contact area. RELEVANCE CLINICAL: Occlusal contacts have a great influence on the positioning of teeth being able to maintain the position and stability of the mandible. Axial loads would be able to generate more uniform stress at the root presenting a greater concentration of load application in the point and the occlusal surface. Thus, is necessary to analyze the relationship between these occlusal contacts as dental wear and subsequent occlusal interferences.

Zirconia-based dental crown to support a removable partial denture: a three-dimensional finite element analysis using contact elements and micro-CT data

Veneer fracture is the most common complication in zirconia-based restorations. The aim of this study was to evaluate the mechanical behavior of a zirconia-based crown in a lower canine tooth supporting removable partial denture (RPD) prosthesis, varying the bond quality of the veneer/coping interface. Microtomography (μCT) data of an extracted left lower canine were used to build the finite element model (M) varying the core material (gold core - MAu; zirconia core - MZi) and the quality of the veneer/core interface (complete bonded - MZi; incomplete bonded - MZi-NL). The incomplete bonding condition was only applied for zirconia coping by using contact elements (Target/Contact) with 0.3 frictional coefficients. Stress fields were obtained using Ansys Workbench 10.0. The loading condition (L = 1 N) was vertically applied at the base of the RPD prosthesis metallic support towards the dental apex. Maximum principal (σmax) and von Mises equivalent (σvM) stresses were obtained. The σmax (MPa) for the bonded condition was similar between gold and zirconia cores (MAu, 0.42; MZi, 0.40). The incomplete bonded condition (MZi-NL) raised σmax in the veneer up to 800% (3.23 MPa) in contrast to the bonded condition. The peak of σvM increased up to 270% in the MZi-NL. The incomplete bond condition increasing the stress in the veneer/zirconia interface.

Finite element based estimation of contact areas and pressures of the human scaphoid in various functional positions of the hand

The scaphoid is the most frequently fractured carpal bone. When investigating fixation stability, which may influence healing, knowledge of forces and moments acting on the scaphoid is essential. The aim of this study was to evaluate cartilage contact forces acting on the intact scaphoid in various functional wrist positions using finite element modeling. A novel methodology was utilized as an attempt to overcome some limitations of earlier studies, namely, relatively coarse imaging resolution to assess geometry, assumption of idealized cartilage thicknesses and neglected cartilage pre-stresses in the unloaded joint. Carpal bone positions and articular cartilage geometry were obtained independently by means of high resolution CT imaging and incorporated into finite element (FE) models of the human wrist in eight functional positions. Displacement driven FE analyses were used to resolve inter-penetration of cartilage layers, and provided contact areas, forces and pressure distribution for the scaphoid bone. The results were in the range reported by previous studies. Novel findings of this study were: (i) cartilage thickness was found to be heterogeneous for each bone and vary considerably between carpal bones; (ii) this heterogeneity largely influenced the FE results and (iii) the forces acting on the scaphoid in the unloaded wrist were found to be significant. As major limitations, accuracy of the method was found to be relatively low, and the results could not be compared to independent experiments. The obtained results will be used in a following study to evaluate existing and recently developed screws used to fix scaphoid fractures.

Impact of normal and shear stresses due to wheel slip on hydrological properties of an agricultural clay loam: Experimental and new computerized approach

The main purpose of this study was to evaluate the effect that mechanical stresses acting under the slipping driving wheels of agricultural equipment have on the soil’s pore system and water flow process (surface runoff generation during extreme event). The field experiment simulated low slip (1%) and high slip (27%) on a clay loam. The stress on the soil surface and changes in the amounts of water flowing from macropores were simulated using the Tires/tracks And Soil Compaction (TASC) tool and the MACRO model, respectively. Taking a 65 kW tractor on a clay loam as a reference, results showed that an increase in slip of the rear wheels from 1% to 27% caused normal stress to increase from 90.6 kPa to 104.4 kPa at the topsoil level, and the maximum shear contact stress to rise drastically from 6.0 kPa to 61.6 kPa. At 27% slip, topsoil was sheared and displaced over a distance of 0.35 m. Excessive normal and shear stress values with high slip caused severe reductions of the soil’s macroporosity, saturated hydraulic conductivity, and water quantities flowing from topsoil macropores. Assuming that, under conditions of intense rainfall on sloping land, a loss in vertical water flow would mean an increase in surface runoff, we calculated that a rainfall intensity of 100 mm h-1 and a rainfall duration of 1 h would increase the runoff coefficient to 0.79 at low slip and to 1.00 at high slip, indicating that 100% of rainwater would be transformed into surface runoff at high slip. We expect that these effects have a significant impact on soil erosion and floods in steeper terrain (slope > 15°) and across larger surface areas (> 16 m2) than those included in our study.

Dynamic analysis using finite elements to calculate the critical wear section of the contact wire in suburban railway overhead conductor rails

The purpose of this study is to determine the critical wear levels of the contact wire of the catenary on metropolitan lines. The study has focussed on the zones of contact wire where localised wear is produced, normally associated with the appearance of electric arcs. To this end, a finite element model has been developed to study the dynamics of pantograph-catenary interaction. The model includes a zone of localised wear and a singularity in the contact wire in order to simulate the worst case scenario from the point of view of stresses. In order to consider the different stages in the wire wear process, different depths and widths of the localised wear zone were defined. The results of the dynamic simulations performed for each stage of wear let the area of the minimum resistant section of the contact wire be determined for which stresses are greater than the allowable stress. The maximum tensile stress reached in the contact wire shows a clear sensitivity to the size of the local wear zone, defined by its width and depth. In this way, if the wear measurements taken with an overhead line recording vehicle are analysed, it will be possible to calculate the potential breakage risk of the wire. A strong dependence of the tensile forces of the contact wire has also been observed. These results will allow priorities to be set for replacing the most critical sections of wire, thereby making maintenance much more efficient. The results obtained show that the wire replacement criteria currently borne in mind have turned out to be appropriate, although in some wear scenarios these criteria could be adjusted even more, and so prolong the life cycle of the contact wire.

Die load and stresses in press forging

Several axi-symmetric EN3B steel components differing in shape and size were forged on a 100 ton joint knuckle press. A load cell fitted under the lower die inserts recorded the total deformation forces. Job parameters were measured off the billets and the forged parts. Slug temperatures were varied and two lubricants - aqueous colloidal graphite and oil - were used. An industrial study was also conducted to check the results of the laboratory experiments. Loads were measured (with calibrated extensometers attached to the press frames) when adequately heated mild steel slugs were being forged in finishing dies. Geometric parameters relating to the jobs and the dies were obtained from works drawings. All the variables considered in the laboratory study could not, however, be investigated without disrupting production. In spite of this obvious limitation, the study confirmed that parting area is the most significant geometric factor influencing the forging load. Multiple regression analyses of the laboratory and industrial results showed that die loads increase significantly with the weights and parting areas of press forged components, and with the width to thickness ratios of the flashes formed, but diminish with increasing slug temperatures and higher billet diameter to height ratios. The analyses also showed that more complicated parts require greater loads to forge them. Die stresses, due to applied axial loads, were investigated by the photoelastic method. The three dimensional frozen stress technique was employed. Model dies were machined from cast araldite cylinders, and the slug material was simulated with plasticene. Test samples were cut from the centres of the dies after the stress freezing. Examination of the samples, and subsequent calculations, showed that the highest stresses were developed in die outer corners. This observation partly explains why corner cracking occurs frequently in industrial forging dies. Investigation of die contact during the forging operation revealed the development of very high stresses.