scholarly journals The Exponentiated Hencky Strain Energy in Modeling Tire Derived Material for Moderately Large Deformations

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Giuseppe Montella ◽  
Sanjay Govindjee ◽  
Patrizio Neff
Keyword(s):  
Constitutive Model ◽  
Strain Energy ◽  
Large Deformations ◽  
Large Strain ◽  
Strain Tensor ◽  
Strain Energy Function ◽  
Cold Forging ◽  
Central Feature ◽  
Hencky Strain ◽  
Highly Nonlinear

This work presents a hyperviscoelastic model, based on the Hencky-logarithmic strain tensor, to model the response of a tire derived material (TDM) undergoing moderately large deformations. The TDM is a composite made by cold forging a mix of rubber fibers and grains, obtained by grinding scrap tires, and polyurethane binder. The mechanical properties are highly influenced by the presence of voids associated with the granular composition and low tensile strength due to the weak connection at the grain–matrix interface. For these reasons, TDM use is restricted to applications involving a limited range of deformations. Experimental tests show that a central feature of the response is connected to highly nonlinear behavior of the material under volumetric deformation which conventional hyperelastic models fail in predicting. The strain energy function presented here is a variant of the exponentiated Hencky strain energy, which for moderate strains is as good as the quadratic Hencky model and in the large strain region improves several important features from a mathematical point of view. The proposed form of the exponentiated Hencky energy possesses a set of parameters uniquely determined in the infinitesimal strain regime and an orthogonal set of parameters to determine the nonlinear response. The hyperelastic model is additionally incorporated in a finite deformation viscoelasticity framework that accounts for the two main dissipation mechanisms in TDMs, one at the microscale level and one at the macroscale level. The new model is capable of predicting different deformation modes in a certain range of frequency and amplitude with a unique set of parameters with most of them having a clear physical meaning. This translates into an important advantage with respect to overcoming the difficulties related to finding a unique set of optimal material parameters as are usually encountered fitting the polynomial forms of strain energies. Moreover, by comparing the predictions from the proposed constitutive model with experimental data we conclude that the new constitutive model gives accurate prediction.

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.

A Corotational Elastoplastic Formulation With Subloading Surface Model for Hardening Materials

Volume 1 ◽  
2004 ◽  
Author(s):  
Ali Reza Saidi ◽  
Koichi Hashiguchi
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Simple Shear ◽  
Deformation Theory ◽  
Elastoplastic Deformation ◽  
Strain Tensor ◽  
Surface Model ◽  
Strain Rate Tensor ◽  
Hencky Strain ◽  
Stress Components

In this paper a corotational constitutive model for the large elastoplastic deformation of hardening materials using subloading surface model is formulated. This formulation is obtained by refining the large deformation theory of Naghdabadi and Saidi (2002) adopting the corotational logarithmic (Hencky) strain rate tensor and incorporating it into the subloading surface model of Hashiguchi (1980, 2003) falling within the framework of the unconventional plasticity. As an application of the proposed constitutive model, the large Elastoplastic deformation of simple shear example has been solved and the results have been compared with classical elasto-plastic model using the Hencky strain tensor. Also the effect of the choice of corotational rates on stress components has been studied.

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.

Some Forms of the Strain Energy Function for Rubber

1993 ◽  
Vol 66 (5) ◽  
pp. 754-771 ◽  
Author(s):  
O. H. Yeoh
Keyword(s):  
Energy Function ◽  
Strain Energy ◽  
Large Strain ◽  
Strain Energy Function ◽  
Phenomenological Theory ◽  
Material Model ◽  
Elastic Behavior ◽  
Strain Behavior ◽  
Strain Invariants ◽  
Infinite Power

Abstract According to Rivlin's Phenomenological Theory of Rubber Elasticity, the elastic properties of a rubber may be described in terms of a strain energy function which is an infinite power series in the strain invariants I1, I2 and I3. The simplest forms of Rivlin's strain energy function are the neo-Hookean, which is obtained by truncating the infinite series to just the first term in I1, and the Mooney-Rivlin, which retains the first terms in I1 and I2. Recently, we proposed a strain energy function which is a cubic in I1. Conceptually, the proposed function is a material model with a shear modulus that varies with deformation. In this paper, we compare the large strain behavior of rubber as predicted by these forms of the strain energy function. The elastic behavior of swollen rubber is also discussed.

Large Deformation Analysis for Soft Foams Based on Hyperelasticity

2010 ◽  
Vol 26 (3) ◽  
pp. 327-334 ◽  
Author(s):  
G. Silber ◽  
M. Alizadeh ◽  
M. Salimi
Keyword(s):  
Experimental Data ◽  
Constitutive Equation ◽  
Uniaxial Compression ◽  
Compression Test ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Uniaxial Compression Test ◽  
Highly Nonlinear ◽  
Non Linear

AbstractIn Elastomeric foam materials find wide applications for their excellent energy absorption properties. The mechanical property of elastomeric foams is highly nonlinear and it is essential to implement mathematical constitutive models capable of accurate representation of the stress-strain responses of foams. A constitutive modeling method of defining hyperfoam strain energy function by a Simplex Strategy is presented in this work. This study will demonstrate that a strain energy function of finite hyperelasticity for compressible media is applicable to describe the elastic properties of open cell soft foams. This strain energy function is implemented in the FE-tool ABAQUS and proposed for high compressible soft foams. To determine this constitutive equation, experimental data from a uniaxial compression test are used. As the parameters in the constitutive equation are linked in a non-linear way, non-linear optimization routines are adopted. Moreover due to the in homogeneities of the deformation field of the uniaxial compression test, the quality function of the optimization routine has to be determined by an FE-tool. The appropriateness of the strain energy function is tested by a complex loading test.By using the optimized parameters the FE-simulation of this test is in good accordance with the experimental data.

On H. Hencky’s Approximate Strain-Energy Function for Moderate Deformations

1979 ◽  
Vol 46 (1) ◽  
pp. 78-82 ◽  
Author(s):  
L. Anand
Keyword(s):  
Energy Function ◽  
Strain Energy ◽  
Finite Strain ◽  
Large Deformations ◽  
Strain Energy Function ◽  
Strain Measure ◽  
Logarithmic Measure ◽  
Infinitesimal Strain ◽  
Isotropic Elasticity ◽  
Good Agreement

It is shown that the classical strain-energy function of infinitesimal isotropic elasticity is in good agreement with experiment for a wide class of materials for moderately large deformations, provided the infinitesimal strain measure occurring in the strain-energy function is replaced by the Hencky or logarithmic measure of finite strain.

A New Viscous Potential Function for Developing the Viscohyperelastic Constitutive Model for Bovine Liver Tissue: Continuum Formulation and Finite Element Implementation

2020 ◽  
Vol 12 (03) ◽  
pp. 2050029 ◽  
Author(s):  
Zahra Matin Ghahfarokhi ◽  
Mehdi Salmani-Tehrani ◽  
Mahdi Moghimi Zand ◽  
Sara Esmaeilian
Keyword(s):  
Constitutive Model ◽  
Strain Energy ◽  
Soft Tissues ◽  
Short Term Memory ◽  
Strain Energy Function ◽  
Bovine Liver ◽  
Material Behavior ◽  
Compression Tests ◽  
Continuum Formulation ◽  
Linear Viscoelastic

The mechanical behavior of very soft tissues, such as liver, brain, kidney, etc. is assumed to be viscohyperelastic. The conventional approaches like quasi-linear viscoelastic (QLV) are limited to low strain rates and are unable to capture the short-term memory effects. In this paper, a new viscohyperelastic constitutive model is presented in which the strain energy function is decomposed into an elastic and a viscous part. The elastic part of the strain energy is assumed as a Mooney–Rivlin model, while a new viscous potential, as a function of strain and its rate, is proposed. Unconfined uniaxial compression tests are conducted up to 10% compression at two loading velocities of 1.3 and 10.56[Formula: see text](mm/min), to determine the material constants. A numerical simulation is also used to investigate the model-predicted material behavior. It is shown that the model is more sensitive to the hyperelastic parameters than the viscous parameters. This model is also able to predict the stress relaxation and hysteresis; however, an instantaneous relaxation is observed.

3D Mechanical Properties of the Layered Esophagus: Experiment and Constitutive Model

2006 ◽  
Vol 128 (6) ◽  
pp. 899-908 ◽  
Author(s):  
W. Yang ◽  
T. C. Fung ◽  
K. S. Chian ◽  
C. K. Chong
Keyword(s):  
Constitutive Model ◽  
Fiber Orientation ◽  
Strain Energy ◽  
Physiological State ◽  
Three Dimensional ◽  
Strain Energy Function ◽  
Esophageal Wall ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Esophageal Diseases

The identification of a three dimensional constitutive model is useful for describing the complex mechanical behavior of a nonlinear and anisotropic biological tissue such as the esophagus. The inflation tests at the fixed axial extension of 1, 1.125, and 1.25 were conducted on the muscle and mucosa layer of a porcine esophagus separately and the pressure-radius-axial force was recorded. The experimental data were fitted with the constitutive model to obtain the structure-related parameters, including the collagen amount and fiber orientation. Results showed that a bilinear strain energy function (SEF) with four parameters could fit the inflation data at an individual extension very well while a six-parameter model had to be used to capture the inflation behaviors at all three extensions simultaneously. It was found that the collagen distribution was axial preferred in both layers and the mucosa contained more collagen, which were in agreement with the findings through a pair of uniaxial tensile test in our previous study. The model was expected to be used for the prediction of stress distribution within the esophageal wall under the physiological state and provide some useful information in the clinical studies of the esophageal diseases.

Nonlinear Thermohyperviscoelastic Constitutive Model for Soft Materials with Strain Rate and Temperature Dependency

2020 ◽  
Vol 12 (06) ◽  
pp. 2050059
Author(s):  
Zahra Matin Ghahfarokhi ◽  
Mehdi Salmani-Tehrani ◽  
Mahdi Moghimi Zand
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Soft Materials ◽  
Material Behavior ◽  
Temperature Dependent ◽  
Dependent Behavior ◽  
Temperature Dependent Behavior

Soft materials, such as polymeric materials and biological tissues, often exhibit strain rate and temperature-dependent behavior when subjected to external loads. To characterize the thermomechanical behavior of isotropic soft material, a thermohyperviscoelastic constitutive model has been developed through an additive decomposition of strain energy function into elastic and viscous parts. A three-term generalized Rivlin strain energy function is utilized to formulate the hyperelastic part of the model, while a new viscous potential function is proposed to describe the effect of strain rate and temperature on material behavior. Toward this end, a new procedure has been proposed to determine the viscous mechanical properties as a function of strain-rate and temperature. Comparing with the previously published experimental data for linear low-density polyethylene reveals that the proposed model can sufficiently capture the nonlinearity, rate- and temperature-dependent behavior of the soft materials.

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.

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