A Mathematical Model of Lung Parenchyma

1980 ◽  
Vol 102 (2) ◽  
pp. 124-136 ◽  
Author(s):  
A. D. Karakaplan ◽  
M. P. Bieniek ◽  
R. Skalak
Keyword(s):  
Strain Energy ◽  
Strain Energy Function ◽  
Strain Curve ◽  
Lung Parenchyma ◽  
The Finite Element Method ◽  
Stress Strain Curve ◽  
Proposed Model ◽  
Elastic Membranes ◽  
Mammalian Lung ◽  
Nonlinear Elastic

The geometry of the proposed model of the parenchyma of a mammalian lung reproduces a cluster of alveoli arranged around a lowest-level air duct. The alveolar walls are assumed to be nonlinear elastic membranes, whose properties are described in terms of a strain energy function which reflects the hardening character of the stress-strain curve. The effect of the surfactant is included in terms of a variable (area-dependent) surface tension. Analyses of various mechanical processes in the parenchyma are performed with the aid of the finite element method, with the geometric and physical nonlinearities of the problem taken into account.

The Strain Dependence of Rubber Viscoelasticity. III. Natural and Butyl Rubber at High Extensions

1962 ◽  
Vol 35 (4) ◽  
pp. 927-936
Author(s):  
P. Mason
Keyword(s):  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Strain Curve ◽  
Wide Frequency Range ◽  
Butyl Rubber ◽  
Frequency Range ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Strain Dependence

Abstract In previous papers in this series the linear viscoelastic behavior of gum and filled rubbers has been studied at mean extensions up to 100%. Linearity was assured by allowing each specimen to relax at the required extension to its equilibrium state and then measuring the complex Young's modulus for very small strains superimposed upon this equilibrium extension. Analysis of the data was made either in terms of a Mooney strain-energy function or, more generally, by relation to the experimentally determined equilibrium stress-strain curve of the material. At much higher strains, however, the use of a strain-energy function is invalidated by the hysteretic behavior of the rubber, and the determination of a stress-strain curve at anything resembling equilibrium becomes increasingly difficult. Consequently, in the region of high strain it is preferable to examine the strain dependence of the viscoelasticity without involving a direct comparison with the equilibrium behavior. In principle, the most significant analysis would be obtained from a study of the strain dependence of the relaxation or retardation spectrum. The long-time end of the spectrum could perhaps be measured using a refined creep or stress relaxation technique, although considerable care would be required to separate the effects from the residual behavior resulting from the initial large elongation. In the rubber-glass transition region, with which this work is primarily concerned, the difficulty lies in making measurements over a sufficiently wide frequency range. Normally the Williams—Landel—Ferry (WLF) equation would be used to transform constant-frequency data from a wide temperature range to the equivalent isothermal spectrum over a wide frequency range; however, the validity of this equation has been confirmed only for amorphous polymers, and its application to highly stretched, anisotropic rubber involves several untested assumptions as discussed further below. The main object of the present paper is to describe the observed variations in the viscoelasticity of natural and butyl rubber over a wide range of extension and temperature, although, of necessity, over a limited range of frequency. In addition, a tentative indication of the influence of strain upon the relaxation spectra is given, and the implications of this are examined.

Bifurcation of rotating circular cylindrical elastic membranes

1980 ◽  
Vol 87 (2) ◽  
pp. 357-376 ◽  
Author(s):  
D. M. Haughton ◽  
R. W. Ogden
Keyword(s):  
Axial Force ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Strain Energy Function ◽  
Angular Speed ◽  
Elastic Membrane ◽  
Axial Extension ◽  
End Conditions ◽  
Elastic Membranes ◽  
Realistic Choice

SummaryBifurcation from a finitely deformed circular cylindrical configuration of a rotating circular cylindrical elastic membrane is examined. It is found (for a physically realistic choice of elastic strain-energy function) that the angular speed attains a maximum followed by a minimum relative to the increasing radius of the cylinder for either a fixed axial extension or fixed axial force.At fixed axial extension (a) a prismatic mode of bifurcation (in which the cross-section of the cylinder becomes uniformly non-circular) may occur at a maximum of the angular speed provided the end conditions on the cylinder allow this; (b) axisyim-metric modes may occur before, at or after the angular speed maximum depending on the length of the cylinder and the magnitude of the axial extension; (c) an asymmetric or ‘wobble’ mode is always possible before either (a) or (b) as the angular speed increases from zero for any length of cylinder or axial extension. Moreover, ‘wobble’ occurs at lower angular speeds for longer cylinders.At fixed axial force the results are similar to (a), (b) and (c) except that an axisym-metric mode necessarily occurs between the turning points of the angular speed.

scholarly journals Modelling of the behaviour of metal foams under shock compression

2018 ◽  
Vol 183 ◽  
pp. 01041
Author(s):  
Nicolas Jacques ◽  
Romain Barthélémy
Keyword(s):  
Experimental Data ◽  
Excellent Agreement ◽  
Strain Curve ◽  
Metal Foams ◽  
Cellular Materials ◽  
Theoretical Modelling ◽  
Stress Strain Curve ◽  
Open Cell ◽  
Proposed Model ◽  
Shock Response

A theoretical modelling is proposed to describe the shock response of foam materials. This model is based on micromechanical and energetic arguments, and takes into account the contribution of microscale inertia. Within this framework, an analytical expression of the Hugoniot stress-strain curve is proposed for elastic-plastic cellular materials. The predictions derived from the proposed model are in excellent agreement with experimental data for open-cell aluminium foams. The case of viscoplastic foams is also considered.

Coherency Strain and a New Yield Criterion

2000 ◽  
Vol 634 ◽  
Author(s):  
N.B. Jayaweera ◽  
J.R. Downes ◽  
D.J. Dunstan ◽  
A.J. Bushby ◽  
P. Kidd ◽  
...  
Keyword(s):  
Strain Energy ◽  
Yield Criterion ◽  
Point Contact ◽  
Elastic Strain Energy ◽  
Strain Curve ◽  
Coherency Strain ◽  
Rate Of Change ◽  
Stress Strain Curve ◽  
Strain Fields ◽  
Nano Indentation

ABSTRACTWe have studied the onset of plasticity in coherently-strained semiconductor superlattices, using nano-indentation with spherical indenter tips to observe the full stress-strain curve. The yield pressure is reduced by as much as a factor of two by the presence of the coherency strain. By varying the thicknesses and strains of the superlattice layers, we provide a proof that yield commences over a finite volume. It is properties averaged or summed over this volume which determine the yield pressure. We show that the relevant yield criterion for our experimental data is the rate of change of elastic strain energy with plastic relaxation, integrated over a volume of the order of a micron across. This result is expected to be valid for other systems with highly inhomogenous strain fields, and hence to be applicable to modelling of point contact, and to the design and understanding of structural materials which have coherently-strained microstructure.

A Strain Energy Function for Lung Parenchyma

1985 ◽  
Vol 107 (1) ◽  
pp. 81-86 ◽  
Author(s):  
D. Stamenovic ◽  
T. A. Wilson
Keyword(s):  
Surface Energy ◽  
Strain Energy ◽  
Large Deformations ◽  
Strain Energy Function ◽  
Lung Parenchyma ◽  
Elastic Behavior ◽  
Recoil Pressure ◽  
Linear Elastic ◽  
Tissue System ◽  
Line Elements

The strain energy for the air-filled lung is calculated from a model of the parenchymal microstructure. The energy is the sum of the surface energy and the elastic energies of two tissue components. The first of these is the peripheral tissue system that provides the recoil pressure of the saline-filled lung, and the second is the system of line elements that form the free edges of the alveolar walls bordering the alveolar ducts. The computed strain energy is consistent with the observed linear elastic behavior of parenchyma and the data on large deformations around blood vessels.

scholarly journals A Stress-Strain Model for Brick Prism under Uniaxial Compression

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Keun-Hyeok Yang ◽  
Yongjei Lee ◽  
Yong-Ha Hwang
Keyword(s):  
Strain Curve ◽  
Peak Stress ◽  
Test Results ◽  
Compression Tests ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Proposed Model ◽  
Relationship Model ◽  
Strain Relationship ◽  
Strain Model

This study proposes a simple and rational stress-strain relationship model applicable to brick masonry under compression. The brick prism compression tests were conducted with different mortar strengths and with constant brick strength. From the observation of the test results, shape of the stress-strain curve is assumed to be parabola. In developing the stress-strain model, the modulus of elasticity, the strain at peak stress, and the strain at 50% of the peak stress on the descending branch were formulated from regression analysis using test data. Numerical and statistical analyses were then performed to derive equations for the key parameter to determine the slopes at the ascending and descending branches of the stress-strain curve shape. The reliability of the proposed model was examined by comparisons with actual stress-strain curves obtained from the tests and the existing model. The proposed model in this study turned out to be more accurate and easier to handle than previous models so that it is expected to contribute towards the mathematical simplicity of analytical modeling.

A Simplified Method for Calculating Ultimate Strength of Pressure Hull in Deep-Sea Manned Submersible

2012 ◽  
Vol 160 ◽  
pp. 17-24
Author(s):  
Li Hao Yuan ◽  
Zhi Xin Xiong ◽  
Lei Song ◽  
Zhi Hui Dong
Keyword(s):  
Strain Energy ◽  
Strain Curve ◽  
Initial Imperfection ◽  
Dimensionless Number ◽  
Stress Strain Curve ◽  
Critical Equilibrium ◽  
Simplified Method ◽  
Manned Submersible ◽  
Utilization Ratio ◽  
Strain Energy Density Theory

Based on the strain energy density theory, the connotation of tangent modulus theory is developed. At critical equilibrium state, a dimensionless number Φt of a structure under pressure is introduced in this paper. Derived from the stress-strain curve of material, a four-parameter formula that contains Φt is established. This formula is referred to as the function of strength utilization ratio that may be used for calculating the inelastic buckling of deep submersible pressure hull.Φt can be used to express the effect of initial imperfection of the shell and to guide the experimental study. Compared with the data from some experiments or other methods, it has demonstrated that the method given by this paper is more precise and convenient for predicting the failure of thin and moderately thick shell under pressure.

Nonlinear Elastic Constitutive Relations of Auxetic Honeycombs

2009 ◽  
Author(s):  
Jaehyung Ju ◽  
Joshua D. Summers ◽  
John Ziegert ◽  
Georges Fadel
Keyword(s):  
Cell Walls ◽  
Strain Energy ◽  
Constitutive Relations ◽  
Effective Strain ◽  
Strain Energy Function ◽  
Periodic Boundary Conditions ◽  
Plane Shear ◽  
Local Cell ◽  
Nonlinear Elastic ◽  
Nonlinear Constitutive Relation

When designing a flexible structure consisting of cellular materials, it is important to find the maximum effective strain of the cellular material resulting from the deformed cellular geometry and not leading to local cell wall failure. In this paper, a finite in-plane shear deformation of auxtic honeycombs having effective negative Poisson’s ratio is investigated over the base material’s elastic range. An analytical model of the inplane plastic failure of the cell walls is refined with finite element (FE) micromechanical analysis using periodic boundary conditions. A nonlinear constitutive relation of honeycombs is obtained from the FE micromechanics simulation and is used to define the coefficients of a hyperelastic strain energy function. Auxetic honeycombs show high shear flexibility without a severe geometric nonlinearity when compared to their regular counterparts.

Antiplane Wave Scattering from a Cylindrical Void in a Pre-Stressed Incompressible Neo-Hookean Material

2012 ◽  
Vol 11 (2) ◽  
pp. 367-382 ◽  
Author(s):  
William J. Parnell ◽  
I. David Abrahams
Keyword(s):  
Wave Scattering ◽  
Small Amplitude ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Incident Field ◽  
Constitutive Behaviour ◽  
Void Size ◽  
Scattering Coefficients ◽  
Nonlinear Elastic Medium ◽  
Nonlinear Elastic

AbstractAn isolated cylindrical void is located inside an incompressible nonlinear-elastic medium whose constitutive behaviour is governed by a neo-Hookean strain energy function. In-plane hydrostatic pressure is applied in the far-field so that the void changes its radius and an inhomogeneous region of deformation arises in the vicinity of the void. We consider scattering from the void in the deformed configuration due to an incident field (of small amplitude) generated by a horizontally polarized shear (SH) line source, a distance r0 (R0) away from the centre of the void in the deformed (undeformed) configuration. We show that the scattering coefficients of this scattered field are unaffected by the pre-stress (initial deformation). In particular, they depend not on the deformed void radius a or distance r0, but instead on the original void size A and original distance R0.

Effect of Constitutive Parameters on Formation of a Spherical Void in a Compressible Nonlinear Elastic Material

1994 ◽  
Vol 61 (2) ◽  
pp. 395-401 ◽  
Author(s):  
Shiro Biwa ◽  
Eiji Matsumoto ◽  
Toshinobu Shibata
Keyword(s):  
Strain Energy ◽  
Finite Elasticity ◽  
Void Formation ◽  
Strain Energy Function ◽  
Elastic Materials ◽  
Spherical Void ◽  
Nonlinear Elastic Material ◽  
Nonlinear Elastic ◽  
Constitutive Parameters ◽  
Bifurcation Behavior

Void formation in materials under isotropic tension is considered within the theory of finite elasticity. This phenomenon is described as the bifurcation of the solution containing a spherical cavity from the state of homogeneous deformation of a solid hyperelastic sphere. The equation giving the bifurcation point is derived, and the critical stretch and stress are numerically calculated for a special class of compressible nonlinear elastic materials for which the strain energy function was proposed by Hill. The effects of constitutive parameters on the post-bifurcation behavior as well as on the critical stretch and stress are discussed.

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