scholarly journals An Anisotropic Hyperelastic Constitutive Model with Bending Stiffness Interaction for Cord-Rubber Composites: Comparison of Simulation Results with Experimental Data

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Shulei Sun ◽  
Wenguo Chen
Keyword(s):  
Strain Energy ◽  
Tensile Deformation ◽  
Strain Energy Function ◽  
Deformation Energy ◽  
Bending Stiffness ◽  
Fiber Direction ◽  
Rubber Composites ◽  
Bending Deformation ◽  
Current Configuration ◽  
Nonsymmetric Stress

Based on the invariant theory of continuum mechanics by Spencer, the strain energy depends on deformation, fiber direction, and the gradients of the fiber direction in the deformed configuration. The resulting extended theory is very complicated and brings a nonsymmetric stress and couple stress. By introducing the gradient of fiber vector in the current configuration, the strain energy function can be decomposed into volumetric, isochoric, anisotropic, and bending deformation energy. Due to the particularity of bending deformation, the reinforced material has tensile deformation and compression deformation. The bending stiffness should be taken into consideration, and it is further verified by the bending simulation.

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.

Continuum Description of the Time- and Strain-Dependent Poisson’s Ratio of Ligament Under Finite Deformation

2013 ◽  
Author(s):  
Aaron M. Swedberg ◽  
Shawn P. Reese ◽  
Steve A. Maas ◽  
Benjamin J. Ellis ◽  
Jeffrey A. Weiss
Keyword(s):  
Large Scale ◽  
Mechanical Response ◽  
Tensile Deformation ◽  
Large Strain ◽  
Fiber Direction ◽  
Strain Behavior ◽  
Nonlinear Stress ◽  
Poisson's Ratios ◽  
Poisson’S Ratios ◽  
Strain Dependent

Ligament volumetric behavior controls fluid and thus nutrient movement as well as the mechanical response of the tissue to applied loads. The reported Poisson’s ratios for tendon and ligament subjected to tensile deformation loading along the fiber direction are large, ranging from 0.8 ± 0.3 in rat tail tendon fascicles [1] to 2.98 ± 2.59 in bovine flexor tendon [2]. These Poisson’s ratios are indicative of volume loss and thus fluid exudation [3,4]. We have developed micromechanical finite element models that can reproduce both the characteristic nonlinear stress-strain behavior and large, strain-dependent Poisson’s ratios seen in tendons and ligaments [5], but these models are computationally expensive and unfeasible for large scale, whole joint models. The objectives of this research were to develop an anisotropic, continuum based constitutive model for ligaments and tendons that can describe strain-dependent Poisson’s ratios much larger than the isotropic limit of 0.5. Further, we sought to demonstrate the ability of the model to describe experimental data, and to show that the model can be combined with biphasic theory to describe the rate- and time-dependent behavior of ligament and tendon.

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.

Three-Dimensional Stress Distribution in Arteries

1983 ◽  
Vol 105 (3) ◽  
pp. 268-274 ◽  
Author(s):  
C. J. Chuong ◽  
Y. C. Fung
Keyword(s):  
Experimental Data ◽  
Stress Distribution ◽  
Vessel Wall ◽  
Strain Energy ◽  
Arterial Wall ◽  
Three Dimensional ◽  
Strain Energy Function ◽  
Exponential Form ◽  
Strain Relationship ◽  
Longitudinal Stretch

A three-dimensional stress-strain relationship derived from a strain energy function of the exponential form is proposed for the arterial wall. The material constants are identified from experimental data on rabbit arteries subjected to inflation and longitudinal stretch in the physiological range. The objectives are: 1) to show that such a procedure is feasible and practical, and 2) to call attention to the very large variations in stresses and strains across the vessel wall under the assumptions that the tissue is incompressible and stress-free when all external load is removed.

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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