scholarly journals Joined dissimilar orthotropic elastic cylindrical membranes under internal pressure and longitudinal tension

1993 ◽  
Vol 34 (3) ◽  
pp. 296-317 ◽  
Author(s):  
V. G. Hart ◽  
Jingyu Shi
Keyword(s):  
Internal Pressure ◽  
Energy Function ◽  
Strain Energy ◽  
Numerical Solutions ◽  
Circumferential Stress ◽  
Strain Energy Function ◽  
The Body ◽  
Surgical Implants ◽  
Elastic Membranes ◽  
Preliminary Study

AbstractFollowing work in an earlier paper, the theory of finite deformation of elastic membranes is applied to the problem of two initially-circular semi-infinite cylindrical membranes of the same radius but of different material, joined longitudinally at a cross-section. The body is inflated by constant interior pressure and is also extended longitudinally. The exact solution found for an arbitrary material is now specialised to the orthotropic case, and the results are interpreted for forms of the strain-energy function introduced by Vaishnav and by How and Clarke in connection with the study of arteries. Also considered in this context is the similar problem where two semi-infinite cylindrical membranes of the same material are separated by a cuff of different material. Numerical solutions are obtained for various pressures and longitudinal extensions. It is shown that discontinuities in the circumferential stress at the joint can be reduced by suitable choice of certain coefficients in the expression defining the strain-energy function. The results obtained here thus solve the problem of static internal pressure loading in extended dissimilar thin orthotropic tubes, and may also be useful in the preliminary study of surgical implants in arteries.

Finite Axisymmetric Deformations of Initially Cylindrical Reinforced Membranes

1972 ◽  
Vol 45 (6) ◽  
pp. 1677-1683 ◽  
Author(s):  
A. D. Kydoniefs
Keyword(s):  
Stress Field ◽  
Internal Pressure ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Incompressible Material ◽  
Parameter System ◽  
Axial Section ◽  
Variable Pitch ◽  
Two Parameter

Abstract We consider the axisymmetrie deformations of an initially cylindrical membrane composed of an elastic, homogeneous, isotropic and incompressible material reinforced with a two-parameter system of perfectly flexible and inextensible helicoidal cords of variable pitch. The undeformed configuration is determined so that the deformed membrane has a given axial section under specified internal pressure. The corresponding stress field and cord tensions are obtained. The solution given is exact and valid for the general form of the strain—energy function.

Finite Deformation Analysis and Numerical Simulation of Arterial Wall

2013 ◽  
Vol 300-301 ◽  
pp. 1636-1639
Author(s):  
Jian Bing Sang ◽  
Li Fang Sun ◽  
Lan Lan Ge ◽  
Zhong Kai Zhang ◽  
Dong Ling Zhang ◽  
...  
Keyword(s):  
Theoretical Analysis ◽  
Energy Function ◽  
Finite Deformation ◽  
Radial Stress ◽  
Strain Energy ◽  
Arterial Wall ◽  
Circumferential Stress ◽  
Strain Energy Function ◽  
Deformation Analysis ◽  
Gent Model

Based on Gent model, a new strain energy function is developed for the description of mechanical response of arterial wall, which fulfills the requirement that in the rigid condition and will thansform into Gent model when . By utilizing the modified strain energy function, inflation of arterial wall by internal pressure is researched. Stress distribution through the deformed arterial wall at cylindrical system is achieved based finite deformation theory. In order to analyze the deformation and stress field of arterial wall at different blood pressure, a user subroutine is programmed to implement the modified strain energy function from Gent into the program of MSC.Marc,. The results show that maximum radial stress and maximum circumferential stress all appear at inside wall. In the meanwhile, radial stress and circumferential stress become smaller along the wall thickness from inside to outside. It can seen the results of finite element analysis of arterial wall are accordant to the result of theoretical analysis, which approves that theoretical analysis is correct.

Finite elastic deformation of incompressible isotropic bodies

1950 ◽  
Vol 202 (1070) ◽  
pp. 407-419 ◽  
Keyword(s):  
Elastic Deformation ◽  
Simple Form ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
General System ◽  
Rotating Cylinder ◽  
The Body ◽  
External Pressures ◽  
Isotropic Bodies

The theory of finite elastic deformation of incompressible isotropic bodies is expressed in a simple form in tensor notation, using a general system of co-ordinates which move with the body as it is deformed. In order to illustrate the advantages of the present methods one problem, previously solved by Rivlin, is re-examined. Two new problems are then solved using a completely general form for the strain energy function, the first problem being that of a rotating cylinder, and the second a uniform spherical shell under symmetrical internal and external pressures.

Finite Inflation of a Bonded Toroid

1972 ◽  
Vol 39 (2) ◽  
pp. 491-494 ◽  
Author(s):  
K. H. Hsu
Keyword(s):  
Differential Equations ◽  
Energy Function ◽  
Strain Energy ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Strain Energy Function ◽  
Axially Symmetric ◽  
Various Boundary Conditions ◽  
Runge Kutta Method ◽  
Membrane Problem

A general approach to the numerical solutions for axially symmetric membrane problem is presented. The formulation of the problem leads to a system of first-order nonlinear differential equations. These equations are formulated such that the numerical integration can be carried out for any form of strain-energy function. Solutions to these equations are feasible for various boundary conditions. In this paper, these equations are applied to the problem of a bonded toroid under inflation. A bonded toroid, which is in the shape of a tubeless tire, has its two circular edges rigidly bonded to a rim. The Runge-Kutta method is employed to solve the system of differential equations, in which Mooney’s form of strain-energy function is adopted.

Mechanical power and hyperelasticity

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Mechanical Power ◽  
Elastic Materials ◽  
Cyclic Motion

This chapter covers the notion of hyperelasticity—the concept that stress is derived from a strain—energy function–by invoking an analogy between elastic materials and springs. Alternatively, it can be derived by invoking a work inequality; the notion that work is required to effect a cyclic motion of the material.

scholarly journals Modelling the Inflation and Elastic Instabilities of Rubber-Like Spherical and Cylindrical Shells Using a New Generalised Neo-Hookean Strain Energy Function

2021 ◽  
Author(s):  
Afshin Anssari-Benam ◽  
Andrea Bucchi ◽  
Giuseppe Saccomandi
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Limit Point ◽  
Strain Energy ◽  
Cylindrical Shells ◽  
Strain Energy Function ◽  
Model Parameters ◽  
Wide Range ◽  
Cylindrical Tubes ◽  
Gent Model

AbstractThe application of a newly proposed generalised neo-Hookean strain energy function to the inflation of incompressible rubber-like spherical and cylindrical shells is demonstrated in this paper. The pressure ($P$ P ) – inflation ($\lambda $ λ or $v$ v ) relationships are derived and presented for four shells: thin- and thick-walled spherical balloons, and thin- and thick-walled cylindrical tubes. Characteristics of the inflation curves predicted by the model for the four considered shells are analysed and the critical values of the model parameters for exhibiting the limit-point instability are established. The application of the model to extant experimental datasets procured from studies across 19th to 21st century will be demonstrated, showing favourable agreement between the model and the experimental data. The capability of the model to capture the two characteristic instability phenomena in the inflation of rubber-like materials, namely the limit-point and inflation-jump instabilities, will be made evident from both the theoretical analysis and curve-fitting approaches presented in this study. A comparison with the predictions of the Gent model for the considered data is also demonstrated and is shown that our presented model provides improved fits. Given the simplicity of the model, its ability to fit a wide range of experimental data and capture both limit-point and inflation-jump instabilities, we propose the application of our model to the inflation of rubber-like materials.

Mechanical characterization of a woven multi-layered hyperelastic composite laminate under uniaxial loading

2021 ◽  
pp. 002199832110115
Author(s):  
Shaikbepari Mohmmed Khajamoinuddin ◽  
Aritra Chatterjee ◽  
MR Bhat ◽  
Dineshkumar Harursampath ◽  
Namrata Gundiah
Keyword(s):  
Composite Materials ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Mechanical Tests ◽  
Stress Strain ◽  
Aerospace Applications ◽  
Envelope Material ◽  
The Individual ◽  
High Dielectric

We characterize the material properties of a woven, multi-layered, hyperelastic composite that is useful as an envelope material for high-altitude stratospheric airships and in the design of other large structures. The composite was fabricated by sandwiching a polyaramid Nomex® core, with good tensile strength, between polyimide Kapton® films with high dielectric constant, and cured with epoxy using a vacuum bagging technique. Uniaxial mechanical tests were used to stretch the individual materials and the composite to failure in the longitudinal and transverse directions respectively. The experimental data for Kapton® were fit to a five-parameter Yeoh form of nonlinear, hyperelastic and isotropic constitutive model. Image analysis of the Nomex® sheets, obtained using scanning electron microscopy, demonstrate two families of symmetrically oriented fibers at 69.3°± 7.4° and 129°± 5.3°. Stress-strain results for Nomex® were fit to a nonlinear and orthotropic Holzapfel-Gasser-Ogden (HGO) hyperelastic model with two fiber families. We used a linear decomposition of the strain energy function for the composite, based on the individual strain energy functions for Kapton® and Nomex®, obtained using experimental results. A rule of mixtures approach, using volume fractions of individual constituents present in the composite during specimen fabrication, was used to formulate the strain energy function for the composite. Model results for the composite were in good agreement with experimental stress-strain data. Constitutive properties for woven composite materials, combining nonlinear elastic properties within a composite materials framework, are required in the design of laminated pretensioned structures for civil engineering and in aerospace applications.

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.

Viscohyperelastic Strain Energy Function

2017 ◽  
pp. 59-78 ◽  
Author(s):  
Arne Vogel ◽  
Lalao Rakotomanana ◽  
Dominique P. Pioletti
Keyword(s):  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function
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