Tangent Elastic Modulus Research Articles

Effects of aging on mechanics and composition of cerebral arterioles in rats.

The purpose of this study was to examine effects of aging on the mechanics and composition of cerebral arterioles. We measured pressure (servo-null) and diameter in pial arterioles in anesthetized adult (9-12 months old) and aged (24-27 months old) Fischer 344 rats. After deactivation of smooth muscle with EDTA, diameter of pial arterioles at 70 mm Hg pial arteriolar pressure was less in aged than in adult rats (67 +/- 4 vs. 81 +/- 4 microns [mean +/- SEM], p less than 0.05). The stress-strain relation and the slope of tangential elastic modulus versus stress (6.8 +/- 0.6 vs. 5.3 +/- 0.3, p less than 0.05) indicated that distensibility of pial arterioles was reduced in aged rats. Cross-sectional area of the vessel wall, measured histologically, was less in aged than adult rats (1,239 +/- 91 vs. 1,832 +/- 180 microns2, p less than 0.05). Point counting stereology was used to quantitate smooth muscle, elastin, collagen, and basement membrane in the arteriolar wall. Cross-sectional areas of smooth muscle and elastin were significantly less in aged than adult rats (744 +/- 57 vs. 1,291 +/- 119 microns2 for smooth muscle, 52 +/- 6 vs. 113 +/- 15 microns2 for elastin; p less than 0.05), whereas cross-sectional areas of collagen and basement membrane were not significantly different in aged and adult rats (4 +/- 1 vs. 3 +/- 1 microns2 for collagen, 236 +/- 17 vs. 258 +/- 31 microns2 for basement membrane). The ratio of nondistensible (collagen and basement membrane) to distensible (smooth muscle and elastin) components was greater in aged than adult rats (0.30 +/- 0.01 vs. 0.18 +/- 0.01, p less than 0.05). Thus, we conclude that, during aging, cerebral arterioles undergo atrophy, distensibility of cerebral arterioles is reduced, and the relative proportion of distensible elements, elastin and smooth muscle, is reduced in the arteriolar wall.

高圧3軸圧縮応力下におけるコンクリートの応力-ひずみ関係 : その2 高速載荷

In order to clarify the strain rate effect on mechanical characteristics of concrete, rapid triaxial high compression tests and rapid hydrostatic loading tests are conducted for cylindrical concrete specimens in the same manner as the static tests in Part 1 except forloading rates. In the rapid loading tests, the loading rates are applied corresponded to average uniaxial strain rates (D1) ε_1=-1.44×10^<-3>/sec, (D2) ε_1=-2.40×10^<-2>/sec and (D3) ε_1=-2.54×10^<-1>/sec. The effect of strain rate magnitude on the initial elastic moduli and failure strength are discussed, then the rates of increase of them due to octahedral strain rates are expressed by empirical equations. The tangent elastic moduli, which are described below, are derived by introducing this effect to the static tangent moduli presented in Part 1. K^t=KO・κ(ε_<oct>)・α_v(ε_<oct>)-α_D(φ_d) G^t=GO・g(ε_<oct>, γ_<oct>)・β_v(ε_<oct>)・β_v(φ_d) in which, KO=initial bulk modulus, GO=initial shear modulus, ε_<oct>=octahedral normal strain, ε_<oct>=octahedral normal strain rate, γ_<oct>= octahedral shear strain rate, κ(ε_<oct>) and g(ε_<oct>, γ_<oct>) are the increase coefficients due to strain rates. φ_d is coresponded to φ defined by expanding failure curve due to strain rates. Then, α_v(ε_<oct>), β_v(ε_<oct>), α_v(φ), β_v(φ) and φ are given in Part 1.

Decreased vascular contraction and elastic stiffening after intramural lymphostasis.

Lymphatic obstruction leads to leakage of protein into the vessel wall that is coupled with edema formation and smooth muscle degeneration. To clarify the mechanical effect of these changes, lymphatic trunks, draining the femoral artery, were stained with Evans blue and then ligated in dogs anesthetized with pentobarbital sodium (n = 11). Sham ligation was performed on these lymphatic trunks in the opposite hindlimb (n = 11). Three days later, 7- to 30-mm segments of both femoral arteries were studied in vitro. Intraluminal pressure was cycled between 5 and 250 mmHg at 5 mmHg/s, and external diameter was recorded in both relaxed and activated (norepinephrine, 3 x 10(-5) mol/l) state of smooth muscle. Mechanical parameters were computed for 10-mmHg pressure increments. After lymphatic obstruction, strain energy density and distensibility of the passive wall components as well as isobaric active tangential strain were decreased by a maximum of 27, 59, and 54%, respectively; active tangential stress and elastic modulus, as a function of tangential stretch, was decreased by a maximum of 62%, and increased by 61%, respectively. These results indicate that short-term intramural lymphostasis reduces smooth muscle reactivity and induces vascular stiffening.

The effect of annealing at 135° on the mechanical properties of injection molded high density polyethylene‐polypropylene blends

AbstractThe effect of annealing at 135°C for 5 hours on the tensile properties of mechanically mixed and then injection molded high density polyethylene (HDPE) and polypropylene (PP) blends has been investigated. Both the tangent elastic modulus and the tensile strength at yield exhibit a non‐linear behavior versus blend composition with a minimum of properties typical for incompatible blends. Annealing substantially improves mechanical properties of pure components and blends (20 percent increase in the yield strength of pure components and blends and the modulus of pure components, and ∼40 percent increase in the modulus of 50/50 blends) but the property behavior versus composition is still nonlinear. Scanning electron microscopy studies of fracture surfaces of blends seems to indicate some improvement in bonding between phases as a result of annealing, Both the elastic modulus and yield strength fit extremely well to the modified “rule of mixtures” equation in the general form: Mb = MPEφPE + MPPφPP + ΔMPE/PPφPEφPP where Mb is the blend property, MPE and MPP are properties of pure PE and PP components, φPE and φPP are weight fractions of PE and PP, and ΔMPE/PP is the interaction term being a measure of the deviation from simple additivity.

高圧3軸圧縮応力下におけるコンクリートの応力-ひずみ関係 : その1 静的載荷

In order to clarify the strain rate effect on mechanical characteristics of concrete, rapid triaxial high compression tests and rapid hydrostatic loading tests are conducted for cylindrical concrete specimens in the same manner as the static tests in Part 1 except forloading rates. In the rapid loading tests, the loading rates are applied corresponded to average uniaxial strain rates (D1) epsilon/sub 1/ = -1.44 x 10/sup -3//sec, (D2) epsilon/sub 1/ = -2.40 x 10/sup -2//sec and (D3) epsilon/sub 1/ = -2.54 x 10/sup -1//sec. The effect of strain rate magnitude on the intial elastic moduli and failure strength are discussed, then the rates of increase of them due to octahedral strain rates are expressed by empirical equations. The tangent elastic moduli, which are described below, are derived by introducing this effect to the static tangent moduli presented in Part 1. K/sup t/ = K0center dotk(epsilon/sub oct/)center dot..cap alpha../sub V/(epsilon/sub oct/)center dot..cap alpha../sub D/(phi/sub d/) G/sup t/ = G0center dotg(epsilon/sub oct/, ..gamma../sub oct/)center dot..beta../sub V/(epsilon/sub oct/)center dot..beta../sub D/(phi/sub d/) in which, K0 = initial bulk modulus, G0 = initial shear modulus, epsilon/sub oct/ = octahedral normal strain, epsilon/sub oct/ = octahedral normal strain rate, ..gamma../sub oct/ = octahedral shear strain rate, k(epsilon/sub oct/) and g(epsilon/sub oct/, ..gamma../sub oct/) are the increase coefficients due to strain rates. phi/sub d/ is corresponded to phi defined by expanding failure curve due to strain rates. Then, ..cap alpha../sub V/(epsilon/sub oct/), ..beta../sub V/(epsilon/sub oct/), ..cap alpha../sub D/(phi), ..beta../sub D/(phi) and phi are given in Part 1.

Significance of right ventricular filling for left ventricular enddiastolic pressure-volume relationship under acute hypoxia in the dog.

In 14 closed-chest dogs, the significance of right ventricular filling for left ventricular enddiastolic pressure-volume relationship was investigated under acute hypoxia by means of single plane cineventriculography and simultaneous intraventricular pressure recording. Both after 5 min asphyxia (respirator switched off) (n = 5) and after 3 min hypoxia (ventilation with pure N2) (n = 9), there was a significant leftward shift (p less than 0.005) of the left ventricular enddiastolic pressure-volume curve as compared to the control curves under normoxia. To simulate the elevated filling of the right ventricle under acute hypoxia, rapid intraventricular infusion was applied under normoxic conditions to raise right ventricular enddiastolic pressure to the same values as that measured under hypoxia. The extent of the ensuing leftward shift of the left ventricular enddiastolic pressure-volume curve was on average 60% of the shift under hypoxia in both sets of experiments. Neither the slope of the relationship between volume stiffness and enddiastolic pressure, nor the relationship between tangent elastic modulus and left ventricular wall stress, was affected by hypoxia or asphyxia. Thus, the shift of the left ventricular enddiastolic pressure-volume curve in the early stage of hypoxia is predominantly due to the influence of increased right ventricular filling. Since the increased volume of the atria under acute hypoxia limits left ventricular distensibility additionally, the changes in left ventricular enddiastolic pressure-volume relationships observed in the early stage of hypoxia are mainly, or even entirely, the result of interaction of the various heart compartments, and not a reflection of alterations in myocardial tissue elasticity.

Effect of temperature on the residual compressive strength of laterized concrete

Abstract Tests are reported on 100 mm laterized concrete cubes, containing ordinary portland cement, crushed granite, sharp sand and fine laterite in varying proportions. The percentage of sand by weight of total fine aggregate was varied in steps of 25 % up to a maximum of 100 % corresponding to normal concrete. The mix proportion was 1:11/2:3 . The test specimens were exposed to varying temperatures ranging from 30 °C (i.e. room temperature) to 800 °C and allowed to cool for 24 hours before crushing. The results showed that unlike normal concrete the residual compressive strength of laterized concrete increaed, by up to 50 % of the nominal strength, with increasing temperature up to 200 °C before falling to about 20 % of the nominal strength at 800 °C. The gain in strength depended on the sand content. The results further showed that within the limits of water/cement ratios normally used in concrete works (i.e. 0.55 to 0.65 ), the residual strength of laterized concrete was independent of the water/cement ratio. Also, the density of laterized concrete was not significantly affected by changes in temperature but that the tangent modulus of elasticity was reduced from 18 kN/mm 2 at 30 °C to 0.12 kN/mm 2 at 600 °C.

A Unified Approach for Stability Bracing Requirements

Columns and beam flanges in compression often require intermediate lateral bracing to satisfactorily carry the required load. Usually this is a finite number of braces at a spacing S. Many engineers are familiar with the ideal stiffness needed to fully brace the compression member over the length S, and that the required stiffness is generally taken as twice the ideal stiffness. If the compression member does not need to be fully braced at each support point, due to either the magnitude of loading required or the size of member used, considerably less bracing stiffness may be required than would be calculated. A means to evaluate an accurate value of required stiffness is important for examining structural members whose integrity is questionable because of limited bracing stiffness and strength, and for obtaining economical bracing design for members repeated many times in a structure. No simple technique other than continuous bracing expressions, exists for obtaining the less-than-full bracing integrity. In this paper, the bracing stiffness required for the range from continuous point bracing to a single point brace is presented. The required brace strength is also summarized. The bracing expressions are given in the form most familiar for point bracing. The expressions provide an understanding of the relationship between bracing stiffness and buckling behavior of the compression member. Furthermore, an expression for tangent modulus of elasticity is proposed as a means to apply the bracing expressions for all levels of critical load less than the yield load.

Thermal Stresses in Steel Grain Bins Using the Tangent Modulus of Grain

ABSTRACT THE tangent modulus of elasticity for soft red winter wheat was determined as it was affected by the internal pressure on the grain and the moisture content of the grain. Using these values, the thermal stresses in a steel grain bin were calculated using Andersen's equation.

A practical classification of rocks for engineering purposes

A new method of classification of rocks is proposed based on rock material properties determined in the laboratory. Uniaxial compressive strength is plotted against the ratio of tangent elastic modulus to Poisson's ratio. For unweathered rocks this gives the horizontal strain of the rock at failure. It is convenient to plot the experimental values on log-log paper in order to assess the mean value.

Analytical stress calculations for magnetic field coils with anisotropic modulus of elasticity

Analytical solutions for the radial and tangential stresses in the midplane of long magnetic field coils are derived, for both constant current density and a 1/r current distribution. The elastic anisotropy is contained in the solution as the ratio of the axial and tangential modulus of elasticity. The critical tangential stress is largest at the inner surface for coils with radial transmission of stress; this is greatly reduced if the coil is softer in the radial direction. An outer reinforcing cylinder becomes quite ineffective in this case. The average axial stress in the midplane is calculated for inclusion in Timoshenko's criterion. The authors also calculate the critical stresses in polyhelix coils with equally distributed stress among the layers. These have a modest advantage over radially soft coils only for a large number of layers.

Diastolic tension of rat cardiac muscle during deficiency of oxygen and glucose. Stress-strain relationships and reversibility.

In the isometrically contracting rat trabecular muscle strip preparation, contracture tension was induced either by 10 min of hypoxia (low contracture tension) or by 30 min of joint oxygen and glucose withdrawal (severe contracture tension) at optimum length. Using stepwise 0.1 mm releases, length-tension relationships were recorded under control and contracture conditions in both types of contracture. Stress-strain relationships were evaluated as well as the linear function of the tangent elastic modulus delta sigma/delta epsilon versus stress sigma. The slope of the delta sigma/delta epsilon = f (sigma) function was not significantly changed in low contracture compared to control conditions (n = 8; p less than 0.001). When reversibility tests were performed by reoxygenation after 10 min hypoxia and reperfusion with oxygen and glucose after 30 min of glucose and oxygen withdrawal, low contracture tension was completely abolished after 15 min, whereas 28% of severe contracture was maintained even after 60 min of reperfusion. Additional morphological studies revealed uniform sarcomere lengths in low contracture, and two populations of sarcomere lengths in the severe contracture. On the basis of the present and earlier results, a model of contracture tension generation is proposed in which cross-bridges between actin and myosin cycle at a very low rate and are attached in a force-generating position for a long time.

Functional and structural changes in the rabbit ear artery after sympathetic denervation.

We studied the tissue weight, dimensions, contractility, elasticity, and sensitivity to exogenous norepinephrine (NE) of denervated and innervated segments of the central ear arteries of white New Zealand rabbits. Three different age groups received unilateral superior cervical ganglionectomies, "growing" at 3-4 weeks, "young adult" at 9-11 weeks, and "mature" at 16-20 weeks. In the growing group, 8 weeks after ganglionectomy, the denervated arteries showed mean decreases in tissue weight (11%), total wall thickness (12+), cross-sectional area of media (17%), contractility (16%), and increases in the tangential modulus of elasticity and sensitivity to NE (2.3-fold) compared to the contralateral control vessels. The change in medial cross-sectional area was significant in the growing and young adult but not the mature animals. The other changes, however, although consistently seen, differed quantitatively among the groups. These results indicate that an intact innervation is necessary for normal development and maintenance of the artery wall. However, the precise consequences of this influence vary at different ages. Whether this influence involves a special trophic factor is not known.

Age-related changes in mechanical indices of compact bone tissue

1. The mechanical indices of demineralized compact bone tissue upon tensile testing change with age. The greatest linear correlation was found for the initial modulus of elasticity E1 (r = 0.87). The mean tangential modulus of elasticity over the cross section doubles from age 24 to 52. The greatest linear correlation with age for strength indices is found for ultimate deformation ɛ11* (r = -0.94). Its mean value over the cross section decreases by a factor of 1.52. 2. The outer layer has higher mean strength indices and initial moduli of elasticity over the cross section, More regular and significant correlations with age are also found for the outer layer for all deformation and most strength indices. It is assumed that these differences in the age-related changes in the mechanical indices of the organic matrix over the thickness of the cortical layer of bone are mainly the result of structural nonuniformity. 3. The rate of change of the mechanical indices of demineralized compact bone tissue upon aging is nonuniform over the cross section. Biological aging has the greatest effect on the change in E1 and ɛ11* in zone 6 which, under normal physiological loads, functions primarily in tension.

Dynamic viscoelastic behaviour of the human tendon in vitro

In order to characterize the mechanical behaviour of human tendon in vitro, we have developed a testing apparatus which applies a small periodic displacement to a specimen pre-stretched at different extension ratios (1.005–1.05). The electropneumatic vibrator we have used in this device has a frequency range from 0.5 to 15 Hz. In the study, we measured the periodic displacements and stresses of flexor digitorum tendons of the human hand and calculated therefrom the dynamic tangential elastic modulus of this biological tissue. As expected, the tendon bahaves as a nonlinearly viscoelastic body, the influence of the initial elongation being more important than the influence of the frequency of the deformation. The data of the 15 tendons tested are compared by means of a t′ o-parameter linearization for the real and imaginary part of the dynamic tangential elastic modulus.

The mechanical properties of exposed human common carotid arteries in vivo.

In exposed common carotid arteries of 15 patients (36-74 years) undergoing neck surgery, the intra-arterial pressure (P) was recorded by means of a catheter-tip manometer and, at the same site, the external diameter (D) by means of a contact-free photoelectric device. On the average, the pulsatile diameter changes were 5.6% of the end-diastolic diameter at pulse pressures of about 50 mm Hg. Due to viscoelasticity, the P-D diagrams exhibited hysteresis loops. Using the criterion of loop elimination, an iterative procedure was applied which permitted, by the use of an appropriate computer program, the separation of the purely elastic and the purely viscous components of the P-D relationships. In all cases, the purely elastic P-D curves markedly deviated from linearity. The tangential elastic modulus (Et) and the pulse wave velocity (c) calculated from these curves were normalized by dividing these quantities by the respective end-diastolic values and plotted against the normalized external diameters. During each pulse cycle, Et increased, with increasing diameter, by a factor between 1.2 and 3.5, while c increased by a factor between 1.1 and 1.9 with reference to the respective end-diastolic values.

Drawing and annealing of polypropylene fibers: Structural changes and mechanical properties

AbstractA study has been carried out on the influence of cold drawing (25°C), hot drawing (140°C), and annealing (140°C) on the structure and mechanical properties of a series of four different well‐characterized melt spun polypropylene filaments. The influence of the interaction between melt spinning and drawing variables was given special attention. Cold drawing increased the orientation in the samples, disrupts the initial monoclinic crystal structure and the morphology of the filaments, and it results in extensive fibrillation. Annealing restored the monoclinic structure but eliminated only a small part of the fibrillation. Hot drawing produced changes which were qualitatively similar to the combined effects of cold drawing and annealing. The orientation and morphology of the asspun filaments were found to have major effects on drawing behavior and the mechanical properties of the drawn fibers for a given draw ratio. It was found, however, that the mechanical properties (tensile strength, tangent elastic modulus, and elongation to break) of the melt spun, hot drawn and cold drawn, and annealed fibers could all be correlated with birefringence measurements.

Pressure-volume relations, elastic modulus, and contractile behaviour of the hypertrophied left ventricle of rats with Goldblatt II hypertension.

In young male Wistar rats, an increase in systolic blood pressure to above 200 mm Hg was induced by constricting one renal artery (Goldblatt II). This led to cardiac hypertrophy with an increase in left ventricular weight of about 40% after 4 weeks as compared with controls of the same age. Four and 8 weeks after the operation, the systolic and enddiastolic pressure-volume relations of the left ventricle were determined under isovolumetric conditions in open-chest Goldblatt rats and in control animals of the same age. The systolic and diastolic wall stress and the tangential elastic modulus were calculated, assuming a thick-walled sphere.

Melt spinning of nylon 6: Structure development and mechanical properties of as‐spun filaments

AbstractThe structure of melt‐spun nylon 6 filaments was studied using on‐line x‐ray diffraction and birefringence measurements. Measurements were also made on as‐spun and treated filaments. On‐line wide‐angle x‐ray scattering measurements indicated that crystallization did not occur on the nylon 6 spinline at spinning rates up to 1000 m/min when spinning was done into either ambient air of 60% relative humidity or into wet saturated air. The filaments did crystalline gradually on the bobbin to a paracrystalline pseudohexagonal (γ) form. The rate of crystallization was dependent on the molecular orientation developed in the spun filaments. Crystalline orientation factors based on hexagonal symmetry were computed as a function of take‐up velocity for fibers which were conditioned 24 hr in air at 65% relative humidity. Annealing in air or treatment in water or 20% formic acid solution causes a transformation from the pseudohexagonal form to the α monoclinic form. The tangent modulus of elasticity and tensile strength of spun and conditioned filaments increase with increasing take‐up velocity and spinline stress, while elongation to break decreases with these variables.

Comparison of the visco-elastic properties of the tail artery in spontaneously hypertensive and normotensive rats.

The quasistatic and dynamic elastic behaviour of the tail artery of male normotensive (NCR) and spontaneously hypertensive (SHR) rats was determined in vitro. The tone of the smooth muscle was enhanced by norepinephrine and diminished by papaverine. The circumferential wall stress was changed by varying the transmural pressure level. The experimental procedure was the same as that used in a previous investigation (Bauer and Pasch, 1971). The circumferential (tangential) elastic wall modulus Et was calculated from the mean internal and external radii determined at each pressure level and from dynamic pressure-volume recordings in the frequency range between 0.03 and 20 HZ. The calculation was based on a formula valid for thick-walled, longitudinally constrained vessels.