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.

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.

Proposal and validation of polyconvex strain-energy function for biological soft tissues

2021 ◽  
pp. 1-14
Author(s):  
Takashi Funai ◽  
Hiroyuki Kataoka ◽  
Hideo Yokota ◽  
Taka-aki Suzuki
Keyword(s):  
Curve Fitting ◽  
Energy Function ◽  
Strain Energy ◽  
Soft Tissues ◽  
Strain Energy Function ◽  
Biological Tissues ◽  
Stress Strain ◽  
Increasing Trend ◽  
Strain Energy Functions ◽  
Derived Function

BACKGROUND: Mechanical simulations for biological tissues are effective technology for development of medical equipment, because it can be used to evaluate mechanical influences on the tissues. For such simulations, mechanical properties of biological tissues are required. For most biological soft tissues, stress tends to increase monotonically as strain increases. OBJECTIVE: Proposal of a strain-energy function that can guarantee monotonically increasing trend of biological soft tissue stress-strain relationships and applicability confirmation of the proposed function for biological soft tissues. METHOD: Based on convexity of invariants, a polyconvex strain-energy function that can reproduce monotonically increasing trend was derived. In addition, to confirm its applicability, curve-fitting of the function to stress-strain relationships of several biological soft tissues was performed. RESULTS: A function depending on the first invariant alone was derived. The derived function does not provide such inappropriate negative stress in the tensile region provided by several conventional strain-energy functions. CONCLUSIONS: The derived function can reproduce the monotonically increasing trend and is proposed as an appropriate function for biological soft tissues. In addition, as is well-known for functions depending the first invariant alone, uniaxial-compression and equibiaxial-tension of several biological soft tissues can be approximated by curve-fitting to uniaxial-tension alone using the proposed function.

scholarly journals Effects of Large Deformation and Velocity Impacts on the Mechanical Behavior of Filled Rubber: Microstructure-Based Constitutive Modeling and Mechanical Testing

Polymers ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 2322
Author(s):  
Wei Wei ◽  
Yong Yuan ◽  
Xiaoyu Gao
Keyword(s):  
Mechanical Behavior ◽  
Large Deformation ◽  
Energy Function ◽  
Constitutive Modeling ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Shear Loading ◽  
Stress Strain ◽  
Cyclic Shear ◽  
Filled Rubber

Filled rubber has been extensively used in the repairing, retrofitting, and protecting of civil infrastructures due to its superior physical and mechanical properties. However, effects of large deformation and velocity impacts on the mechanical behavior of filled rubber are not well recognized, one of the major challenges in the past investigations is that the material exhibits significant nonlinearity and sensitivity to velocity. This paper presents a hyper-viscoelastic constitutive modeling and experimental study to capture both the hyperelastic and viscoelastic behaviors of filled rubber under large shear deformation and velocity impacts. Motivated by the micro-mechanism of filled rubber, the constitutive modeling consists of an equilibrium element in parallel with an improved Maxwell element to incorporate both nonlinear hyperelasticity and rate-dependent performance governed by the readjustment and rearrangement of molecular chains in the material. A new strain energy function is developed and the physical description of parameters in the strain energy function is highlighted. The Clausius-Duhem inequality is employed to consider the thermodynamic consistency of the model. Then, stress relaxation property and stress-strain response of filled rubber upon cyclic shear loading with different strain rates (ranging from 0.08 to 12.0 s−1) are experimentally studied, and some key observations are summarized. Subsequently, a “Gau-Poly” function is proposed based on the experimental data to describe the viscoelastic property of filled rubber versus strain and strain rate. Finally, stress-strain relationship and hysteretic area obtained from the experimental results were compared with the numerical results of the model, good agreement was achieved and the capacity of the model to accurately reproduce the mechanical behavior of filled rubber under a wide range of deformation and velocity impacts was verified.

Characterization of Elastic Properties of Carbon-Black-Filled Rubber Vulcanizates

1990 ◽  
Vol 63 (5) ◽  
pp. 792-805 ◽  
Author(s):  
O. H. Yeoh
Keyword(s):  
Carbon Black ◽  
Shear Modulus ◽  
Elastic Properties ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Stress Strain ◽  
Filled Rubber ◽  
Filled Rubbers

Abstract A novel strain-energy function which is a simple cubic equation in the invariant (I1−3) is proposed for the characterization of the elastic properties of carbon-black-filled rubber vulcanizates. Conceptually, the proposed function is a material model with a shear modulus which varies with deformation. This contrasts with the neo-Hookean and Mooney-Rivlin models which have a constant shear modulus. The variation of shear modulus with deformation is commonly observed with filled rubbers. Initially, the modulus falls with increasing deformation, leading to a flattening of the shear stress/strain curve. At large deformations, the modulus rises again due to finite extensibility of the network, accentuated by the strain amplication effect of the filler. This characteristic behavior of filled rubbers may be described approximately by the proposed strain-energy function by requiring the coefficient C20 to be negative, while the coefficients C10 and C30 are positive. The use of the proposed strain-energy function has been shown to permit the prediction of stress/strain behavior in different deformation modes from data obtained in one simple deformation mode. This circumvents the need for a rather difficult experiment in general biaxial extension. The simple form of the proposed function also simplifies the regression analysis. This strain-energy function is consistent with the general Rivlin strain-energy function and is easily obtained from the popular third-order deformation approximation. Thus, it is already available in many existing finite-element analysis programs.

Mechanical properties of pleural membrane

1984 ◽  
Vol 57 (4) ◽  
pp. 1189-1194 ◽  
Author(s):  
D. Stamenovic
Keyword(s):  
Energy Function ◽  
Strain Energy ◽  
Large Deformations ◽  
Strain Energy Function ◽  
Shear Forces ◽  
Stress Strain ◽  
Oriented Line ◽  
Strain Equation ◽  
Line Elements ◽  
Good Agreement

The pleural membrane is modeled as a planar collection of interconnected randomly oriented line elements. By assuming that the line elements follow the strain field of a continuum, a strain-energy function is formulated. From the strain-energy function, an explicit stress-strain equation for large deformations is derived. In the linear approximation of the stress-strain equation the shear modulus and the area modulus of the membrane are respectively found to be 2.4 and 2.8 times the tension at the reference state. The stress-strain equation for large deformations is used to predict the displacement field around a circular hole in pleura. Good agreement is found between these predictions and measurements made on ablated pleura from dog lungs. From these theoretical and experimental results the conclusion is drawn that the pleura has a significant role in carrying shear forces and maintaining the lung's shape.

Inversion of a Class of Nonlinear Stress-Strain Relationships of Biological Soft Tissues

1979 ◽  
Vol 101 (1) ◽  
pp. 23-27 ◽  
Author(s):  
Y. C. Fung
Keyword(s):  
Stress Tensor ◽  
Energy Function ◽  
Strain Energy ◽  
Soft Tissues ◽  
Strain Tensor ◽  
Nonlinear Function ◽  
Strain Energy Function ◽  
Stress Strain ◽  
Highly Nonlinear ◽  
Nonlinear Stress

The mechanical properly of soft tissues is highly nonlinear. Normally, the stress tensor is a nonlinear function of the strain tensor. Correspondingly, the strain energy function is not a quadratic function of the strain. The problem resolved in the present paper is to invert the stress-strain relationship so that the strain tensor can be expressed as a nonlinear function of the stress tensor. Correspondingly, the strain energy function is inverted into the complementary energy function which is a function of stresses. It is shown that these inversions can be done quite simply if the strain energy function is an analytic function of a polynomial of the strain components of the second degree. We have shown previously that experimental results on the skin, the blood vessels, the mesentery, and the lung tissue can be best described by strain energy functions of this type. Therefore, the inversion presented here is applicable to these tissues. On the other hand, a popular strain energy function, a polynomial of third degree or higher, cannot be so inverted.

scholarly journals Biaxial vasoactivity of porcine coronary artery

2012 ◽  
Vol 302 (10) ◽  
pp. H2058-H2063 ◽  
Author(s):  
Yunlong Huo ◽  
Yana Cheng ◽  
Xuefeng Zhao ◽  
Xiao Lu ◽  
Ghassan S. Kassab
Keyword(s):  
Coronary Arteries ◽  
Strain Energy ◽  
Error Function ◽  
Strain Energy Function ◽  
Mechanical Tests ◽  
Biaxial Stress ◽  
Stress Strain ◽  
Porcine Coronary Artery ◽  
Strain Relationship ◽  
The Mean

The passive mechanical properties of blood vessel mainly stem from the interaction of collagen and elastin fibers, but vessel constriction is attributed to smooth muscle cell (SMC) contraction. Although the passive properties of coronary arteries have been well characterized, the active biaxial stress-strain relationship is not known. Here, we carry out biaxial (inflation and axial extension) mechanical tests in right coronary arteries that provide the active coronary stress-strain relationship in circumferential and axial directions. Based on the measurements, a biaxial active strain energy function is proposed to quantify the constitutive stress-strain relationship in the physiological range of loading. The strain energy is expressed as a Gauss error function in the physiological pressure range. In K+-induced vasoconstriction, the mean ± SE values of outer diameters at transmural pressure of 80 mmHg were 3.41 ± 0.17 and 3.28 ± 0.24 mm at axial stretch ratios of 1.3 and 1.5, respectively, which were significantly smaller than those in Ca2+-free-induced vasodilated state (i.e., 4.01 ± 0.16 and 3.75 ± 0.20 mm, respectively). The mean ± SE values of the inner and outer diameters in no-load state and the opening angles in zero-stress state were 1.69 ± 0.04 mm and 2.25 ± 0.08 mm and 126 ± 22°, respectively. The active stresses have a maximal value at the passive pressure of 80–100 mmHg and at the active pressure of 140–160 mmHg. Moreover, a mechanical analysis shows a significant reduction of mean stress and strain (averaged through the vessel wall). These findings have important implications for understanding SMC mechanics.

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