Tangent Modulus Values Research Articles

An analytical investigation on the crushing behavior of thin-walled tubes filled with a foam with strain hardening region

In this paper, the axial crushing behavior of a foam-filled thin-walled circular tube, assuming the strain hardening for the foam. The theoretical model is based on the super folding element and unlike the previous researches, the interaction effect between the wall of the tube and the foam which had a tangent modulus (Et) in the plateau region is considered. The governing equations of energy absorption consist of four types of consuming energy mechanisms: membrane deformation, bending deformation, the interaction between the tube and foam, and axial crushing of the foam. In order to validate the theoretical model, the results of the model are compared with numerical simulations presented in this paper and previous experimental results and reveal good agreement. Furthermore, the effects of different values of tangent modulus (Et) of the foam material on the folding length, crushing force, energy absorption, and specific energy absorption of the foam-filled circular tube are also investigated and the changes in the energy-consuming mechanisms are fully described. According to the results, as the value of the tangent modulus of the foam material increased, the value of mean crushing force, energy absorption, and specific energy absorption of the foam-filled circular tube increased, too, and the folding length decreased.

The effect of vertebral level on biomechanical properties of the lumbar paraspinal muscles in a rat model

IntroductionPassive mechanical properties of the paraspinal muscles are important to the biomechanical functioning of the spine. In most computational models, the same biomechanical properties are assumed for each paraspinal muscle group, while cross-sectional area or fatty infiltration in these muscles have been reported to differ between the vertebral levels. Two important properties for musculoskeletal modeling are the slack sarcomere length and the tangent modulus. This study aimed to investigate the effect of vertebral level on these biomechanical properties of paraspinal muscles in a rat model. MethodsThe left paraspinal muscles of 13 Sprague-Dawley rats were exposed under anesthesia. Six muscle biopsies were collected from each rat: three from multifidus (one per each of the L1, L3, and L5 levels) and similarly three from longissimus. Each biopsy was cut into two halves. From one half, two to three single muscle fibers and two to six muscle fiber bundles (14 ± 7 fibers surrounded in their connective tissue) were extracted and mechanically tested in a passive state. From the resulting stress-strain data, tangent modulus was calculated as the slope of the tangent at 30% strain and slack sarcomere length (beyond which passive force starts to develop) was recorded. The other half of each biopsy, which represented the muscle at the fascicle level, was snap frozen, sectioned, stained for Collagen I and its area fraction was measured. To evaluate the effect of spinal level on these biomechanical properties of multifidus and longissimus, one-way repeated measures ANOVA (p < 0.05) was performed for tangent modulus and slack sarcomere length, while for collagen I content linear mixed-models analysis was adopted. ResultsIn total, 192 fibers and 262 fiber bundles were mechanically tested. For both muscle groups, no significant difference in tangent modulus of the single fibers was detected between the three spinal levels (p = 0.9 for multifidus and p = 0.08 for longissimus). Similarly, the tangent modulus values for the fiber bundles were not significantly different between the three spinal levels (p = 0.13 for multifidus and p = 0.49 for longissimus). In both muscle groups, the slack sarcomere lengths were not different among the spinal levels except for multifidus fibers (p = 0.02). Collagen I area fraction in muscle fascicles averaged 6.8% for multifidus and 5.3% for longissimus and was not different between the spinal levels. DiscussionThe results of this study highlighted that the tangent modulus, slack sarcomere length, and collagen I content of the lumbar paraspinal muscles are independent of spinal level. This finding provides the basis for the assumption of similar mechanical properties along a paraspinal muscle group.

Development of electrically conductive porous silk fibroin/carbon nanofiber scaffolds

Tissue engineering applications typically require three-dimensional scaffolds which provide the requisite surface area for cellular functions, while allowing transport of nutrients, waste and oxygen to and from the surrounding tissues. Scaffolds need to ensure sufficient mechanical properties to provide mechanically stable frameworks under physiologically relevant stress levels. Meanwhile, electrically conductive platforms are also desirable for the regeneration of specific tissues, where electrical impulses are transmitted throughout the tissue for proper physiological functioning. Towards this goal, carbon nanofibers (CNFs) were incorporated into silk fibroin (SF) scaffolds whose pore size and porosity were controlled during a salt leaching process. In our methodology, CNFs were dispersed in SF due to the hydrogen bond-forming ability of hexafluoro-2-propanol, a fluoroalcohol used as a solvent for SF. Results showed enhanced electrical conductivity and mechanical properties upon the incorporation of CNFs into the SF scaffolds, while the metabolic activities of cells cultured on SF/CNF nanocomposite scaffolds were significantly improved by optimizing the CNF content, porosity and pore size range of the scaffolds. Specifically, SF/CNF nanocomposite scaffolds with electrical conductivities as high as 0.023 S cm−1, tangent modulus values of 260 ± 30 kPa, a porosity as high as 78% and a pore size of 376 ± 53 µm were fabricated for the first time in the literature. Furthermore, an increase of about 34% in the wettability of SF was achieved by the incorporation of 10% CNF, which provided enhanced fibroblast spreading on scaffold surfaces.

Elastic and plastic properties of epoxy resin syntactic foams filled with hollow glass microspheres and glass fibers

ABSTRACTRepresentative volume elements of syntactic foams with a random filling of short glass fibers and hollow glass microspheres in epoxy resin were established by a random sequential adsorption method. The fiber volume fraction was set at 4%, and the microsphere volume fraction range was from 5 to 30%. This numerical simulation was studied with ANSYS software. The influence on the elastic and plastic mechanical properties of syntactic foams of the microsphere volume fraction and relative wall thickness were investigated, and the plastic strain evolution process in the composites was analyzed. The results show that the compressive yield limit and Young's modulus values of the syntactic foams decreased with increasing microsphere volume fraction when the microsphere relative wall thickness was 0.02, but these properties were enhanced with increasing microsphere volume fraction when the relative wall thickness exceeded 0.04. The specific strength and tangent modulus values of the composites increased with increasing microsphere volume fraction. In addition, we observed that the yield stress, Young's modulus, and tangent modulus values of the syntactic foams were obviously enhanced by the addition of glass fibers. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 44188.

Mechanical properties vary for different regions of the finger extensor apparatus

The extensor apparatus, an aponeurosis that covers the dorsal side of each finger, transmits force from a number of musculotendons to the phalanges. Multiple tendons integrate directly into the structure at different sites and the extensor apparatus attaches to the phalanges at multiple points. Thus, prediction of the force distribution within the extensor apparatus, or hood, and the transmission to the phalanges is challenging, especially as knowledge of the underlying mechanical properties of the tissue is limited. We undertook quantification of some of these properties through material testing of cadaver specimens. We punched samples at specified locations from 19 extensor hood specimens. Material testing was performed to failure for each sample with a custom material testing device. Testing revealed significant differences in ultimate load, ultimate strain, thickness, and tangent modulus along the length of the extensor hood. Specifically, thickness, ultimate load, and ultimate strain were greater in the more proximal sections of the extensor hood, while the tangent modulus was greater in the more distal sections. The variations in mechanical properties within the hood may impact prediction of force transmission and, thus, should be considered when modeling the action of the extensor apparatus. Across the extensor hood, tangent modulus values were substantially smaller than values reported for other soft tissues, such as the Achilles tendon and knee ligaments, while ultimate strains were much greater. Thus, the tissue in the extensor apparatus seems to have greater elasticity, which should be modeled accordingly.

PFM.37 Cyclic tensile strain increases PGE2 release leading to weakening of the human term amniotic membrane

IntroductionUterine contractions, blood and infection may weaken the amniotic membrane (AM) leading to loss in biomechanical properties mediated by PGE2 release. We investigated AM mechanical properties and the effect of...

Finite-Element-Based Multiple Normal Loading-Unloading of an Elastic-Plastic Spherical Stick Contact

The repeated normal elastic plastic contact problem of a deformable sphere against a rigid flat under full stick contact condition is investigated with a commercial finite element software ANSYS. Emphasis is placed on the effect of strain hardening and hardening model with the maximum interference of load ranging from elastic to fully plastic, which has not yet been reported. Different values of tangent modulus coupled with isotropic and kinematic hardening models are considered to study their influence on contact parameters. Up to ten normal loading-unloading cycles are applied with a maximum interference of 200 times the interference required to initiate yielding. Results for the variation of mean contact pressure, contact load, residual interference, and contact area with the increasing number of loading unloading cycles at high hardening parameter as well as for low tangent modulus with two different hardening models are presented. Results are compared with available finite element simulations and in situ results reported in the literature. It is found that small variation of tangent modulus results in same shakedown behavior and similar interfacial parameters in repeated loading-unloading with both the hardening rules. However at high tangent modulus, the strain hardening and hardening rules have strong influence on contact parameters.

Contact analysis of spherical ball and a deformable flat model with the effect of tangent modulus

The paper is on contact analysis of a spherical ball with a deformable flat, considering the effect of tangent modulus on the contact parameters of a non-adhesive frictionless elastic-plastic contact. The contact analysis of this model has been carried out using analysis software Ansys and Abaqus. The contact parameters such as area of contact between two consecutive steps, volume of bulged material are evaluated from the formulated equations. The effect of the tangent modulus is considered for determining these parameters. The tangent modulus are accounted between 0.1E and 0.5E of materials E/Y value greater than 500 and less than 1750. Result shows that upto an optimal tangent modulus values the elastic core push up to the free surface in the flat. The simulation is also carried out in Abaqus and result provide evidence for the volume of bulged material in the contact region move up and flow into the free surface of the flat from the contact edge between the ball and flat. The strain energy of the whole model is varied between 20 to 40 percentage of the stipulated time for analysis.

The Effect of Temperature on the Tangent Modulus of Granular Composite Sport Surfaces

A series of tests were conducted to determine the tangent modulus (vertical stiffness) values for a wax-coated granular composite material. This material is commonly used as the surface for Thoroughbred horse racetracks. The tangent modulus is important in the vertical loading of the surface by the hoof for a highly nonlinear material. Test temperatures span a range from 0 to 64°C and include the thermal transition regions of the wax coating obtained from differential scanning calorimetry tests. These temperatures also include the range of temperatures that are encountered during use. Creep tests were conducted to obtain steady-state strain conditions at loads ranging from 0.89 to 4.45 kN, the latter load approximating the weight of a Thoroughbred racehorse. Through-transmission ultrasonic waves were utilized to determine the tangent modulus values. The tangent moduli ranged from 74 to 573 MPa for the conditions tested. For all loads tested, a large decrease in modulus and decrease in material nonlinearity occurred as temperatures increased from 20 to 32°C. This temperature range matches the first thermal transition temperature for the wax coating of the track material. The results of this work provide a basis for racetrack maintenance decisions that can eliminate potentially adverse temperature effects and may reduce equine injuries.

Analysis of Elastic-Plastic Contact Performance of Rigid Sphere Against a Deformable Flat-Effect of Strain Hardness

Problem statement: The present study considers an elastic-plastic contact analysis of a rigid sphere with a deformable flat (Rigid Sphere-model) using finite element analysis. The effect of tangent modulus on the contact behavior of a no adhesive frictionless elastic-plastic contact was analyzed using commercial finite element software ANSYS. Approach: Different materials, in terms of the ratio of Young's modulus to yield strength, had been considered to study the effect of tangent modulus. The Finite Element (FE) contact analysis was carried out by incorporating the various tangent modulus values of different materials. Results: The result clearly shows that for different tangent modulus the material hold different stress values. When this modulus increases the strain hardness value of material was also increased. Conclusion: With increase in tangent modulus, strain hardening resistance to deformation of a material is increased and the material becomes capable of carrying higher amount of load in a smaller contact area.

Effect of Strain Hardening on Elastic-Plastic Contact of a Deformable Sphere against a Rigid Flat under Full Stick Contact Condition

The present study considers the effect of strain hardening on elastic-plastic contact of a deformable sphere with a rigid flat under full stick contact condition using commercial finite element software ANSYS. Different values of tangent modulus are considered to study the effect of strain hardening. It is found that under a full stick contact condition, strain hardening greatly influences the contact parameters. Comparison has also been made between perfect slip and full stick contact conditions. It is observed that the contact conditions have negligible effect on contact parameters. Studies on isotropic and kinematic hardening models reveal that the material with isotropic hardening has the higher load carrying capacity than that of kinematic hardening particularly for higher strain hardening.

Effect of glucose on the stress–strain behavior of ex-vivo rabbit cornea

The biomechanical changes in rabbit cornea preserved in storage media with different glucose concentrations are experimentally assessed. Two groups of eight fresh rabbit corneas were preserved for 10 days in storage medium Optisol-GS with glucose concentrations of 14 and 28 mM, respectively. Eight additional corneas preserved, glucose-free, in the same medium served as the control group. All specimens were tested under inflation conditions up to 45 mmHg posterior pressure, and the pressure-deformation data obtained experimentally were analyzed using shell theory to derive the stress–strain behavior. Comparisons were held between the three specimen groups in order to determine the effect of glucose concentration on corneal biomechanical behavior and thickness. After storage, the mean central corneal thickness in the control, low-glucose and high-glucose groups underwent statistically significant increases of 38.7 ± 11.3%, 45.4 ± 7.6% and 50.6 ± 8.6%, respectively. The corneas also demonstrated consistent stiffness increases with higher glucose concentrations. The tangent modulus values determined at different pressure levels between 10 and 40 mmHg underwent statistically significant increases with glucose level (P < 0.05). Compared to the control group, other specimens had higher tangent modulus by 17–20% on average with low glucose and 30–37% with high-glucose concentration. The results of the study indicate that the influence of the high-glucose level commonly experienced in diabetes on the biomechanical stiffness of the cornea should be considered in clinical management and in understanding corneal ectasia, glaucoma and the response to refractive surgery.

Experimental investigation of the strength properties of sand–clay mixtures reinforced with randomly distributed discrete polypropylene fibers

ABSTRACT: This paper describes the findings of a series of laboratory unconfined compression tests and split tensile tests performed on specimens of varying fiber–sand–clay proportions. Sand was mixed with clay at six different proportions, namely 0.0, 1.0, 2.5, 5.0, 7.5, and 10.0% by dry weight of clay. Fiber was included in the sand–clay mixture at four different percentages, namely 0.0, 0.25, 0.5, and 1.0% by dry weight of clay. Compaction characteristics of the sand–clay mixtures were evaluated at standard compaction energy. According to fiber content, four groups of samples were prepared at maximum dry unit weight and optimum water content. For each of the four sample groups, unconfined compressive stress-axial strain and split tensile stress-diametrical strain behavior of the fiber–sand–clay mixtures were investigated. The test results showed that unconfined compressive strength (UCS) reached its maximum value at a fiber/clay ratio of 1.0% and sand/clay ratio of 7.5%. There was a reasonably strong linear correlation (R2≈ 1.0) between UCS and average initial tangent modulus values. The ratio of UCS to split tensile strength (STS) for all fiber–sand–clay mixtures varied between 3.2- and 5.8-fold.

A Microstructural Hyperelastic Model of Pulmonary Arteries Under Normo- and Hypertensive Conditions

This work represents the first application of a statistical mechanics based microstructural orthotropic hyperelastic model to pulmonary artery mechanics under normotensive and hypertensive conditions. The model provides an analogy between the entangled network of long molecular chains and the structural protein framework seen in the medial layer, and relates the mechanical response at macro-level to the deformation (entropy change) of individual molecular chains at the micro-level. A finite element approach was adopted to implement the model. Material parameters were determined via comparing model output to measured pressure-stretch results from normotensive and hypertensive trunks and branches obtained from a rat model of pulmonary arterial hypertension. Results from this initial study show that this model appears reasonable for the study of hyperelastic and anisotropic pulmonary artery mechanics. Typical tangent modulus values ranged from 200 to 800 kPa for normotensive arteries-this increased to beyond 1 MPa for hypertensive vessels. Our study also provokes the hypothesis that increase of cross-linking density may be one mechanism by which the pulmonary artery stiffens in hypertension.

A study of sand stabilization in Eastern Saudi Arabia

Saudi Arabia as well as many of the Arabian Gulf countries have witnessed extensive programmes of industrialization and urbanization in the last few decades. In the eastern part of Saudi Arabia these unprecedented activities have resulted in some unexpected constructional problems attributed to the lack of proper quality soil and unfamiliarity with the inferior properties of these soils. The abundance of fine to medium, non-plastic, wind-blown sand deposits at shallow depths makes such soils attractive for construction purposes. However, the poor quality of these soils, especially their low bearing capacity, makes it necessary to improve their properties by stabilization. In an attempt to assess the strength properties of stabilized granular soils and to evaluate the behaviour of cement-treated sands, stabilized samples were prepared and tested in the laboratory under controlled conditions. Two types of cementing agent were used: Portland cement and calcium carbonate. The effects of some of the variables encountered in the field such as curing type and time, confining pressure, cementing agent content, density, saturation and reconstitution on the behaviour of stabilized soils, were studied. Test results show that the addition of a cementing agent to a wind-blown sand (cohesionless material) with uniform size distribution produces a material with two strength components — that due to cementation or “true” cohesion and that due to friction. The angle of internal friction for the treated sands is not much different from that of the untreated sand. The results also show that the drying process is essential in the development of cementation, especially when calcium carbonate is used as the cementing agent. Peak strength as well as initial tangent modulus values, increase with an increase in curing period, confining pressure, cement content and density. Residual strength values seem to be independent of all parameters other than the confinement and density; a behaviour commonly observed for uncemented sands.

Micromechanical analysis of nonlinear thermal deformation of filamentary metal matrix composites

A micromechanical model was developed to predict the thermomechanical deformation of unidirectional filamentary metal matrix composites. The composite is represented by two concentric cylinders, the inner one simulating the fiber and the outer one the matrix. Both elastic and elastic-plastic analyses were performed. In the model the fiber was assumed to be linear-elastic and the matrix a work-hardening elastoplastic material. The elastoplastic analysis was based on the deformation theory of plasticity in conjunction with the von Mises yield criterion. The matrix cylinder in the model was divided into a number (N) of concentric layers with each layer having different values of tangent modulus and Poisson's ratio depending on the amount of plastic deformation. An elastic analysis of a composite cylinder with (N+1) layers was then performed and served as a subroutine for a computer program.

Design of tunnel support systems using ground freezing

One of the more promising techniques in soft ground tunneling through urbanized areas is the use of artificially frozen ground for temporary tunnel support. This paper describes the general design considerations involved in the ground freezing method. Various factors are discussed which influence the selection of the freezing temperature, the thickness of the frozen zones and the spacing of the freeze pipes. The time required to achieve freezing is discussed in addition to the amount and rate of frost heave caused by the freezing. To illustrate the applicability of the freezing method, various considerations in the design of an 8-ft. diameter tunnel in upstate New York, a 75-ft. diameter tunnel in Georgia, and a 12 1/2-ft. diameter tunnel in Washington, D.C. are discussed. All three of the tunnels were to pass immediately beneath mainline railroad tracks. A laboratory testing program was implemented to determine the effects of the repetitive train loads on the zone of frozen soil around the tunnel perimeter. Stress-controlled repeated load triaxial tests were performed on both undisturbed and remolded samples frozen from temperatures of −7°C for the New York tunnel to −10°C for the Atlanta and Washington tunnels. Static testing consisted of both quick triaxial tests and creep tests on frozen samples of the various soil types. It was found that there was little difference between the cumulative strain response from repeated load tests and static tests for the low frequencies investigated (one-quarter to one-half cycles per minute). Hyperbolic stress—strain functions were developed to simulate the stress—strain relationship for various cumulative loading times. The stresses and strains in the frozen soil tunnel configuration were computed by the finite element method, using both linear and hyperbolic stress—strain functions. Tangent modulus values were varied to reflect the decreasing modulus with increasing loading time. The analyses indicated that zones of frozen soil of approximately 3 ft. thick were required for both the New York and Washington tunnels. However, high tensile stresses were calculated for the Atlanta tunnel, precluding the use of the freezing method.

The effect of radial inertia on the plastic stress wave speeds in thin-walled tubes under combined stress

The plastic wave speeds in a thin-walled tube of rate insensitive material subject to combined axial and torsional loading may be calculated in closed form. For a given stress state the wave speeds are determined from theories which differ in their formulation only by the inclusion of radial inertia. For axial stress states it is shown that for specific values of the tangent modulus both the fast and slow wave speeds coincide with the elastic shear wave speed and that the inclusion of radial inertia markedly affects these critical values of tangent modulus.

Undrained Behaviour of Overconsolidated Saturated Clays during Shear

ABSTRACT A laboratory investigation is made on the undrained behaviour of two heavily overconsolidated saturated clays during shear. The effect of heavy overconsolidation on undrained behaviour of saturated clays is markedly different as compared to that for low degree of overconsolidation and it is function of clay type. The strength envelope is highly nonlinear for heavily overconsolidated clays at low stress levels. Increase of qf/σc' is much pronounced at high overconsolidation ratios. The pore water pressure parameter A at failure is very much dependent on the type of clay and the stress system used. For the first time development of shear stress, pore water pressure with strain and OCR is discussed. The pore water pressure parameter A increasing with strain at low OCR values converges to a low strain-independent value at a critical OCR value for each clay and then decreases with strain for high OCR values leading to a steady, strain-independent, A value. Tangent modulus values are given as a function of OCR and confining pressure for use in analysis of foundation engineering problems in the clay deposits under undrained condition. The investigation provides valuable information in the much needed high OCR range of low stress levels where very little data is available.