Bending of Blood Vessel Wall: Stress-Strain Laws of the Intima-Media and Adventitial Layers

1995 ◽  
Vol 117 (1) ◽  
pp. 136-145 ◽  
Author(s):  
Jiaping Xie ◽  
Jianbo Zhou ◽  
Y. C. Fung
Keyword(s):  
Experimental Data ◽  
Stress State ◽  
Beam Theory ◽  
Nonlinear Least Squares ◽  
Wall Stress ◽  
Wall Material ◽  
Stress Strain ◽  
Strain Relationship ◽  
Residual Strains ◽  
Residual Stresses And Strains

In order to determine the stress-strain relationship of the inner (intima and media) and outer (adventitia) layers of blood vessels in the neighborhood of the zero-stress state, bending experiments were performed on aortic strips of rats. In the experiments, one end of a strip was clamped, and a force was applied on the other end. The deflection curves of the strips were measured. By regarding the aortic strip as a curved beam, the classical beam theory was employed to analyze the strain distribution from the experimental data. A computer program dealing with nonlinear equations and nonlinear least squares optimization was developed. Strains were referred to the zero-stress state. The load-deflection relationship was then used to determine the stress-strain relationship. Certain forms of the stress-strain laws were assumed. The linear laws fit the experimental data accurately, probably because the strains during bending are quite small, although the rotations are large. The Young’s modulus of the inner layer, which consists of endothelial and smooth muscle cells and elastic lamina, was found to be three to four times larger than that of the outer layer which consists of collagen with a small amount of fibroblasts and elastin. The residual stresses and strains at the no-load state were calculated from the deduced stress-strain relationship. It is shown that large errors (up to 50 percent) in the values of the residual strains will occur if the wall material was treated as homogeneous, i.e., if the layered constitution was ignored.

scholarly journals An Incremental Formulation of Constitutive Equations for Deposited Snow

1980 ◽  
Vol 25 (92) ◽  
pp. 289-307 ◽  
Author(s):  
J. Desrues ◽  
F. Darve ◽  
E. Flavigny ◽  
J.P. Navarre ◽  
A. Taillefer
Keyword(s):  
Experimental Data ◽  
Axial Strain ◽  
Triaxial Tests ◽  
Stress Strain ◽  
Theoretical Formulation ◽  
Non Linear ◽  
Incremental Formulation ◽  
Strain Relationship ◽  
Strain Paths ◽  
Incremental Form

Abstract The behaviour of a snow mass under natural loadings (gravity forces, boundary conditions) can be computed by the finite-element method, in so far as a convenient formulation of the stress–strain relationship for snow is available. This paper deals with such a formulation given in incremental form. Experiments have been performed, which show that deposited snow can be considered as a non-linear visco-elastic material with memory effect. The proposed theoretical formulation takes into account these properties. The elastic part of the deformation is assumed to be isotropic and non-linear; the viscous part is expressed in terms of a creep-rate, which results from a superposition of elementary creep-rates according to Boltzmann’s principle. The values of parameters can be obtained from isotropic creep experiments. The experimental data and the resulting parameters are reported. Since the parameters were determined, the formulation of the rheological law was then tested by integration on “stress–strain paths" corresponding to other experiments of a different type, performed on the same snow. The experiments are triaxial tests at constant axial strain-rate, with a preliminary stage of isotropic compression. Experimental data are compared to theoretical curves obtained by integration of the rheological law. The calculated behaviour is consistent with the experimental results.

scholarly journals Modeling the stress-strain state of a circular plate subject to general corrosion according to various models

2021 ◽  
Vol 263 ◽  
pp. 03009
Author(s):  
Ilya Ovchinnikov ◽  
Vladimir Avzovin
Keyword(s):  
Experimental Data ◽  
Stress State ◽  
Circular Plate ◽  
Strain State ◽  
Corrosive Wear ◽  
Operating Conditions ◽  
General Corrosion ◽  
Stress Strain ◽  
Stress Strain State ◽  
Kinetics Of

Quite a lot of works have been devoted to the problem of modeling the behavior of thin-walled structures exposed to an aggressive environment leading to corrosive wear of their surface. Researchers have proposed a fairly large set of models of corrosive wear, taking into account the influence of various factors on the kinetics of corrosion (time, material, temperature, the nature of the corrosive environment, the stress-strain state of the structure). Moreover, different authors often propose different models for the same conditions. In the article under consideration, a rather unique comparative study of three corrosion models proposed by different authors (Dolinsky V.M., Gutman E.M., Ovchinnikov I.G.) was carried out to simulate the behavior of the same circular plate subjected to the combined action of load and corrosion wear and tear. Moreover, the identification of the models, that is, the determination of the coefficients included in them, was carried out using the same experimental data. These models were then used to simulate the behavior of plates subject to corrosive wear under various loads. The results of numerical simulation were compared with experimental data obtained during testing of corrosive plates. Interestingly, in the models used, the effect of the stress state on the kinetics of corrosion was taken into account using different invariants of the stress state: the stress intensity in V.M. Dolinsky, medium voltage in the model of E.M. Gutman, and the specific energy in the model of I.G. Ovchinnikov. The analysis showed that the difference from the experiment when using the three models considered does not exceed 9.3%. The discrepancy between the results obtained using different models is also within the acceptable range, which suggests that all three models can be used to predict the behavior of plates under corrosive wear conditions. However, it is of interest to conduct research on the predictive capabilities of models on large forecast arms that go beyond the scope of experimental studies. At the same time, carrying out numerical experiments to simulate the behavior of complex structures in a stressed state and subject to corrosive wear, using several models that allow a good description of the experimental data and the most complete consideration of the operating conditions, makes it possible to obtain a more complete and versatile picture of what is happening in design processes, in comparison with the calculations performed according to one model, even if it describes the experimental data well.

Chronic hypoxia augments uterine artery distensibility and alters the circumferential wall stress-strain relationship during pregnancy

2006 ◽  
Vol 100 (6) ◽  
pp. 1842-1850 ◽  
Author(s):  
Stephanie N. Mateev ◽  
Rhonda Mouser ◽  
David A. Young ◽  
Robert P. Mecham ◽  
Lorna G. Moore
Keyword(s):  
Blood Flow ◽  
Guinea Pigs ◽  
Uterine Artery ◽  
Chronic Hypoxia ◽  
Wall Stress ◽  
Myogenic Tone ◽  
Stress Strain ◽  
Circumferential Wall Stress ◽  
Strain Relationship ◽  
Resting Tone

Pregnancy-associated increases in uterine artery (UA) blood flow are due, in part, to vasoactive and growth-related changes that enlarge UA diameter. Although active and passive mechanical factors can contribute to this enlargement, their role is less well understood. We hypothesized that pregnancy increased UA distensibility and/or decreased myogenic tone. Given the fetal growth restriction and lower UA flow seen under chronic hypoxia, we further hypothesized that chronic hypoxia opposed these normal active and passive mechanical changes. UA were isolated from 12 nonpregnant and 12 pregnant (0.7 gestation) guinea pigs housed under normoxia or chronic hypoxia (3,960 m) and studied by pressure myography. Pregnancy increased UA diameter similarly under normoxia and hypoxia. Although chronic hypoxia raised resting tone in UA from nonpregnant guinea pigs to ∼20% and tone was greater in preconstricted pregnant chronically hypoxic vs. normoxic UA (both P < 0.01), there was an absence of myogenic response (i.e., an increase in tone with rising pressure) in all groups. Pregnancy increased UA distensibility 1.5-fold but did not change stiffness or the stress-strain relationship. Compared with vessels from normoxic pregnant animals, hypoxic pregnancy raised UA distensibility fourfold, decreased stiffness (rate constant b = 3.80 ± 1.06 vs. 8.92 ± 1.25, respectively, P < 0.01), lowered elastin by 50%, and shifted the stress-strain relationship upward such that four times as much strain was present at a given stress. We concluded that increased distensibility and low myogenic tone contribute to enlarging UA diameter and raising UA blood flow during pregnancy. Chronic hypoxia exaggerates the rise in distensibility and alters the stress-strain relationship in ways that may provoke vascular injury.

Mechanical Behavior of FRP-Confined Rectangular Concrete Column

2010 ◽  
Vol 163-167 ◽  
pp. 3804-3807
Author(s):  
Ping Wu ◽  
Feng Yu
Keyword(s):  
Experimental Data ◽  
Experimental Study ◽  
Cross Section ◽  
Strain Softening ◽  
Axial Strain ◽  
Concrete Column ◽  
Stress Strain ◽  
Strain Relationship ◽  
Rectangular Concrete Column ◽  
Strain Model

According to the analysis of existing experimental data, it is well known that the behavior of FRP-confined rectangular concrete column were mainly related to the cross section coefficient of concrete, the confinement effect coefficient and the strength of concrete. Based on experimental study and theoretical analysis, the formula for bearing capacity and ultimate axial strain of FRP-confined rectangular concrete column were proposed, and the stress-strain model with strain-hardening components or strain-softening components. The effects of every parameter on the stress-strain relationship were carefully considered. The predictions of the model agree well with test data.

Mathematical and mechanical modeling of stress-strain relationship of pericardium

1975 ◽  
Vol 229 (4) ◽  
pp. 896-900 ◽  
Author(s):  
SW Rabkin ◽  
PH Hsu
Keyword(s):  
Experimental Data ◽  
Mechanical Model ◽  
Soft Tissues ◽  
Mechanical Modeling ◽  
Stress Strain ◽  
Mathematical Expressions ◽  
Strain Relationship ◽  
Relationship Of

Several mathematical expressions (models) were compared for use in describing the stress-strain (sigma - epsilon) relationship of pericardium. The expression sigma = alpha[ebeta epsilon - 1] was preferred because of its simpler form, theoretical consistency, and "good fit" of experimental data. A method was developed for estimating the precisions of the estimates of the parameters alpha and beta. This approach can have general usefulness in assessing the significance of a change in stress-strain relationship of various soft tissues following different interventions. A mechanical model was formulated for the pericardium which consisted of springs representing the collagen and elastin fibers connected in parallel. It could be simulated by the above equation and could describe the behavior of the pericardium.

End-systolic pressure-volume, pressure-length, and stress-strain relations in canine hearts

1985 ◽  
Vol 249 (3) ◽  
pp. H648-H654 ◽  
Author(s):  
S. Kaseda ◽  
H. Tomoike ◽  
I. Ogata ◽  
M. Nakamura
Keyword(s):  
Systolic Pressure ◽  
Wall Stress ◽  
Regional Wall Motion ◽  
Stress Strain ◽  
Contractile State ◽  
Inotropic State ◽  
Inferior Caval Vein ◽  
Strain Relationship ◽  
Pressure Volume Relationship ◽  
Lv Volume

End-systolic pressure-volume relationship (ESPVR) of the in situ heart in the dog was measured during changes in contractile state and was compared with end-systolic pressure-length (ESPLR) or stress-strain relationship (ESSSR). Circumferential segmental length and wall thickness at the equator and external long and short axis diameters of the left ventricle (LV) were determined sonomicrometrically, and LV volume was calculated by an ellipsoidal model. Circumferential wall stress at the equator was calculated by a very thin shell model. Contractile state was enhanced by an intravenous infusion of dobutamine and was suppressed by propranolol. ESPVR, ESPLR, and ESSSR were determined during a reduction of arterial pressure by occluding temporarily the inferior caval vein (IVC). ESPVR, ESPLR, and ESSSR during changes in end-systolic pressure from 108 +/- 3 to 71 +/- 2 mmHg were linear, irrespective of inotropic states (r greater than 0.92). Slopes of these relationships increased similarly in case of dobutamine and were reduced after propranolol, yet the extrapolated X-axis intercept of ESPVR, ESPLR, and ESSSR remained unchanged. Thus the slope of ESPVR is unique to the inotropic state, and both ESPLR and ESSSR are useful as a substitute for ESPVR when there is no regional wall motion abnormality.

scholarly journals In vivo characterization of the aortic wall stress–strain relationship

Ultrasonics ◽  
2010 ◽  
Vol 50 (7) ◽  
pp. 654-665 ◽  
Author(s):  
Asawinee Danpinid ◽  
Jianwen Luo ◽  
Jonathan Vappou ◽  
Pradit Terdtoon ◽  
Elisa E. Konofagou
Keyword(s):  
Aortic Wall ◽  
Wall Stress ◽  
Stress Strain ◽  
Strain Relationship ◽  
In Vivo Characterization

scholarly journals Comparing thixotropic and Herschel–Bulkley parameterizations for continuum models of avalanches and subaqueous debris flows

2018 ◽  
Vol 18 (1) ◽  
pp. 303-319 ◽  
Author(s):  
Chan-Hoo Jeon ◽  
Ben R. Hodges
Keyword(s):  
Experimental Data ◽  
Debris Flows ◽  
Fluid Model ◽  
Liquid Mixtures ◽  
High Yield ◽  
Aging Effects ◽  
Stress Strain ◽  
Experimental Conditions ◽  
Wide Range ◽  
Strain Relationship

Abstract. Avalanches and subaqueous debris flows are two cases of a wide range of natural hazards that have been previously modeled with non-Newtonian fluid mechanics approximating the interplay of forces associated with gravity flows of granular and solid–liquid mixtures. The complex behaviors of such flows at unsteady flow initiation (i.e., destruction of structural jamming) and flow stalling (restructuralization) imply that the representative viscosity–stress relationships should include hysteresis: there is no reason to expect the timescale of microstructure destruction is the same as the timescale of restructuralization. The non-Newtonian Herschel–Bulkley relationship that has been previously used in such models implies complete reversibility of the stress–strain relationship and thus cannot correctly represent unsteady phases. In contrast, a thixotropic non-Newtonian model allows representation of initial structural jamming and aging effects that provide hysteresis in the stress–strain relationship. In this study, a thixotropic model and a Herschel–Bulkley model are compared to each other and to prior laboratory experiments that are representative of an avalanche and a subaqueous debris flow. A numerical solver using a multi-material level-set method is applied to track multiple interfaces simultaneously in the simulations. The numerical results are validated with analytical solutions and available experimental data using parameters selected based on the experimental setup and without post hoc calibration. The thixotropic (time-dependent) fluid model shows reasonable agreement with all the experimental data. For most of the experimental conditions, the Herschel–Bulkley (time-independent) model results were similar to the thixotropic model, a critical exception being conditions with a high yield stress where the Herschel–Bulkley model did not initiate flow. These results indicate that the thixotropic relationship is promising for modeling unsteady phases of debris flows and avalanches, but there is a need for better understanding of the correct material parameters and parameters for the initial structural jamming and characteristic time of aging, which requires more detailed experimental data than presently available.

STUDY ON STRESS-STRAIN RELATIONSHIP OF LOESS BASED ON TWIN SHEAR UNIFIED DAMAGE CONSTITUTIVE MODEL

2008 ◽  
Vol 22 (31n32) ◽  
pp. 5838-5843
Author(s):  
BO HAN ◽  
HANGZHOU LI ◽  
HONG-JIAN LIAO ◽  
ZHENGHUA XIAO
Keyword(s):  
Stress State ◽  
Constitutive Model ◽  
Triaxial Test ◽  
Test Results ◽  
Stress Strain ◽  
Statistical Probability ◽  
Unified Strength Theory ◽  
Strain Relationship ◽  
Damage Constitutive Model ◽  
Relationship Of

To investigate the change of loess stress state, a series of triaxial shear tests were performed on normal consolidation and over consolidation loess. From the test results, the stress-strain relationships of loess were obtained and discussed. Based on unified strength theory, the statistical damage constitutive equation was obtained under triaxial stress state assuming distribution statistical probability of micro-units strength. Then the proposed formulation was adopted to study on stress-strain constitutive relationships of loess and to simulate consolidation undrained triaxial test and consolidation drained triaxial test for normal consolidated and over-consolidated specimens. Compared between experimental and theoretical results, it was shown that the proposed constitutive model can well describe stress-strain relationship of loess, whatever the characteristic of strain softening or stain hardening.

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