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.

Constitutive Modeling of the Finite Deformation Behavior of Membranes Possessing a Triangulated Network Microstructure

2005 ◽  
Vol 73 (4) ◽  
pp. 536-543 ◽  
Author(s):  
M. Arslan ◽  
M. C. Boyce
Keyword(s):  
Blood Cell ◽  
Mechanical Behavior ◽  
Lipid Bilayer ◽  
Red Blood Cell ◽  
Finite Deformation ◽  
Constitutive Modeling ◽  
Strain Energy ◽  
Shear Loading ◽  
Stress Strain ◽  
Spectrin Network

The mechanical behavior of the membrane of the red blood cell is governed by two primary microstructural features: the lipid bilayer and the underlying spectrin network. The lipid bilayer is analogous to a two-dimensional fluid in that it resists changes to its surface area, yet poses little resistance to shear. A skeletal network of spectrin molecules is cross-linked to the lipid bilayer and provides the shear stiffness of the membrane. Here, a general continuum level constitutive model of the large stretch behavior of the red blood cell membrane that directly incorporates the microstructure of the spectrin network is developed. The triangulated structure of the spectrin network is used to identify a representative volume element (RVE) for the model. A strain energy density function is constructed using the RVE together with various representations of the underlying molecular chain force-extension behaviors where the chain extensions are kinematically determined by the macroscopic deformation gradient. Expressions for the nonlinear finite deformation stress-strain behavior of the membrane are obtained by proper differentiation of the strain energy function. The stress-strain behaviors of the membrane when subjected to tensile and simple shear loading in different directions are obtained, demonstrating the capabilities of the proposed microstructurally detailed constitutive modeling approach in capturing the small to large strain nonlinear, anisotropic mechanical behavior. The sources of nonlinearity and evolving anisotropy are delineated by simultaneous monitoring of the evolution in microstructure including chain extensions, forces and orientations as a function of macroscopic stretch. The model captures the effect of pretension on the mechanical response where pretension is found to increase the initial modulus and decrease the limiting extensibility of the networked membrane.

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 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.

ON THE DEVELOPMENT OF COMPRESSIBLE PSEUDO-STRAIN ENERGY DENSITY FUNCTION FOR HYPERELASTIC MATERIAL: EXPERIMENT, THEORY AND FEM

2005 ◽  
Vol 29 (3) ◽  
pp. 459-475
Author(s):  
Hamid Ghaemi ◽  
A. Spence ◽  
K. Behdinan
Keyword(s):  
Mechanical Behavior ◽  
Density Function ◽  
Energy Function ◽  
Strain Energy ◽  
Three Dimensional ◽  
Strain Energy Function ◽  
Material Parameter Identification ◽  
Constitutive Function ◽  
Strain Energy Density Function ◽  
Biaxial Tests

This study was carried out to develop a compressible pseudo-strain energy function that describes the mechanical behavior of rubber-like materials. The motivation for this work was two fold; first was to define a single-term strain energy function derived from constitutive equations that can describe the mechanical behavior of rubber-like materials and taking into account the coupling between principal stretches and the nearly incompressibility characteristic of elastomers. Second was to implement this strain energy function into the Finite Element Method (FEM) to study the suitability of the model in FEM. A one-term three-dimensional strain energy function based on the principal stretch ratios was proposed. The three dimensional constitutive function was then reduced to describe the behavior of rubber-like materials under biaxial and uniaxial loading condition based on the membrane theory. The work presented here was based on the decoupling of the strain density function into a deviatoric and a volumetric part. Using pure gum, GMS-SS-A40, uniaxial and equi-biaxial experiments were conducted employing different strain rate protocols. The material was assumed to be isotropic and homogenous. The experimental data from uniaxial and biaxial tests were used simultaneously to determine the material parameters of the proposed strain energy function. A GA curve fitting technique was utilized in the material parameter identification. The proposed strain energy function was compared to a few well-known strain energy functions as well as the experimental results. It was determined that the proposed strain energy function predicted the mechanical behavior of rubber-like material with greater accuracy as compared to other models both analytical and numerical results.

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 Constitutive Modeling of Skeletal Muscle Tissue With an Explicit Strain-Energy Function

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
G. M. Odegard ◽  
T. L. Haut Donahue ◽  
D. A. Morrow ◽  
K. R. Kaufman
Keyword(s):  
Skeletal Muscle ◽  
Muscle Tissue ◽  
Energy Function ◽  
Constitutive Modeling ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Skeletal Muscle Tissue ◽  
Design Consideration ◽  
Active Response ◽  
Tension Properties

While much work has previously been done in the modeling of skeletal muscle, no model has, to date, been developed that describes the mechanical behavior with an explicit strain-energy function associated with the active response of skeletal muscle tissue. A model is presented herein that has been developed to accommodate this design consideration using a robust dynamical approach. The model shows excellent agreement with a previously published model of both the active and passive length-tension properties of skeletal muscle.

A Simplified Strain Energy Function to Represent the Mechanical Behavior of the Annulus Fibrosus

2009 ◽  
Author(s):  
Jose J. García ◽  
Christian Puttlitz
Keyword(s):  
Finite Element ◽  
Mechanical Behavior ◽  
Energy Function ◽  
Annulus Fibrosus ◽  
Strain Energy ◽  
Degrees Of Freedom ◽  
Strain Energy Function ◽  
Efficient Simulation ◽  
Matrix Interactions ◽  
Complex Functions

Models to represent the mechanical behavior of the annulus fibrosus are important tools to understand the biomechanics of the spine. Many hyperelastic constitutive equations have been proposed to simulate the mechanical behavior of the annulus that incorporate the anisotropic nature of the tissue. Recent approaches [1,2] have included terms into the energy function which take into account fiber-fiber and fiber-matrix interactions, leading to complex functions that cannot be readily implemented into commercial finite element codes for an efficient simulation of nonlinear realistic models of the spine (which are generally composed of 100,000+ degrees of freedom). An effort is undertaken here to test the capability of a relatively simple strain energy function [3] for the description of the annulus fibrosus. This function has already been shown to successfully represent the mechanical behavior of the arterial tissue and can be readily implemented into existing finite element codes.

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