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.

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.

Analytical and Experimental Study of Beam Torsional Stiffness With Large Axial Elongation

1988 ◽  
Vol 55 (1) ◽  
pp. 171-178 ◽  
Author(s):  
M. Degener ◽  
D. H. Hodges ◽  
D. Petersen
Keyword(s):  
Experimental Data ◽  
Axial Force ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Torsional Stiffness ◽  
Deformation Tensor ◽  
Axial Elongation ◽  
Green Strain ◽  
Strain Components

The axial force and effective torsional stiffness versus axial elongation are investigated analytically and experimentally for a beam of circular cross section and made of an incompressible material that can sustain large elastic deformation. An approach based on a strain energy function identical to that used in linear elasticity, except with its strain components replaced by those of some finite-deformation tensor, would be expected to provide only limited predictive capability for this large-strain problem. Indeed, such an approach based on Green strain components (commonly referred to as the geometrically nonlinear theory of elasticity) incorrectly predicts a change in volume and predicts the wrong trend regarding the experimentally determined axial force and effective torsional stiffness. On the other hand, use of the same strain energy function, only with the Hencky logarithmic strain components, correctly predicts constant volume and provides excellent agreement with experimental data for lateral contraction, tensile force, and torsional stiffness—even when the axial elongation is large. For strain measures other than Hencky, the strain energy function must be modified to consistently account for large strains. For comparison, theoretical curves derived from a modified Green strain energy function are added. This approach provides results identical to those of the Neo-Hookean formulation for incompressible materials yielding fair agreement with the experimental results for coupled tension and torsion. An alternative approach, proposed in the present paper and based on a modified Almansi strain energy function, provides very good agreement with experimental data and is somewhat easier to manage than the Hencky strain energy approach.

Finding the Constitutive Relation for a Specific Elastomer

1993 ◽  
Vol 115 (3) ◽  
pp. 329-336 ◽  
Author(s):  
Yun Ling ◽  
Peter A. Engel ◽  
Wm. L. Brodskey ◽  
Yifan Guo
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Strain Energy ◽  
Pure Shear ◽  
Strain Energy Function ◽  
Invariant Polynomial ◽  
Energy Functions ◽  
Finite Element Program ◽  
Biaxial Extension ◽  
Strain Energy Functions

The main purpose of this study was to determine a suitable strain energy function for a specific elastomer. A survey of various strain energy functions proposed in the past was made. For natural rubber, there were some specific strain energy functions which could accurately fit the experimental data for various types of deformations. The process of determining a strain energy function for the specific elastomer was then described. The second-order invariant polynomial strain energy function (James et al., 1975) was found to give a good fit to the experimental data of uniaxial tension, uniaxial compression, equi-biaxial extension, and pure shear. A new form of strain energy function was proposed; it yielded improved results. The equi-biaxial extension experiment was done in a novel way in which the moire techniques (Pendleton, 1989) were used. The obtained strain energy functions were then utilized in a finite element program to calculate the load-deflection relation of an electrometric spring used in an electrical connector.

scholarly journals Residually Stressed Fiber Reinforced Solids: A Spectral Approach

Materials ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 4076
Author(s):  
Mohd Halim Bin Mohd Shariff ◽  
Jose Merodio
Keyword(s):  
Constitutive Equation ◽  
Energy Function ◽  
Strain Energy ◽  
Finite Strain ◽  
Strain Energy Function ◽  
Spectral Approach ◽  
Fiber Reinforced ◽  
Elastic Solids ◽  
Preferred Direction ◽  
The Right

We use a spectral approach to model residually stressed elastic solids that can be applied to carbon fiber reinforced solids with a preferred direction; since the spectral formulation is more general than the classical-invariant formulation, it facilitates the search for an adequate constitutive equation for these solids. The constitutive equation is governed by spectral invariants, where each of them has a direct meaning, and are functions of the preferred direction, the residual stress tensor and the right stretch tensor. Invariants that have a transparent interpretation are useful in assisting the construction of a stringent experiment to seek a specific form of strain energy function. A separable nonlinear (finite strain) strain energy function containing single-variable functions is postulated and the associated infinitesimal strain energy function is straightforwardly obtained from its finite strain counterpart. We prove that only 11 invariants are independent. Some illustrative boundary value calculations are given. The proposed strain energy function can be simply transformed to admit the mechanical influence of compressed fibers to be partially or fully excluded.

scholarly journals A generalized strain approach to anisotropic elasticity

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
M. H. B. M. Shariff
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Single Variable ◽  
Energy Functions ◽  
Anisotropic Strain ◽  
Strain Energy Functions ◽  
Strain Function

AbstractThis work proposes a generalized Lagrangian strain function $$f_\alpha$$ f α (that depends on modified stretches) and a volumetric strain function $$g_\alpha$$ g α (that depends on the determinant of the deformation tensor) to characterize isotropic/anisotropic strain energy functions. With the aid of a spectral approach, the single-variable strain functions enable the development of strain energy functions that are consistent with their infinitesimal counterparts, including the development of a strain energy function for the general anisotropic material that contains the general 4th order classical stiffness tensor. The generality of the single-variable strain functions sets a platform for future development of adequate specific forms of the isotropic/anisotropic strain energy function; future modellers only require to construct specific forms of the functions $$f_\alpha$$ f α and $$g_\alpha$$ g α to model their strain energy functions. The spectral invariants used in the constitutive equation have a clear physical interpretation, which is attractive, in aiding experiment design and the construction of specific forms of the strain energy. Some previous strain energy functions that appeared in the literature can be considered as special cases of the proposed generalized strain energy function. The resulting constitutive equations can be easily converted, to allow the mechanical influence of compressed fibres to be excluded or partial excluded and to model fibre dispersion in collagenous soft tissues. Implementation of the constitutive equations in Finite Element software is discussed. The suggested crude specific strain function forms are able to fit the theory well with experimental data and managed to predict several sets of experimental data.

Inflation of a Plane Circular Membrane

1967 ◽  
Vol 89 (3) ◽  
pp. 403-407 ◽  
Author(s):  
H. O. Foster
Keyword(s):  
Experimental Data ◽  
Analytical Solution ◽  
Excellent Agreement ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Circular Membrane ◽  
Radial Stretching

An analytical solution has been found for the inflation of rubber-like membranes when the deformations are assumed to be large. Radial stretching of the membrane before inflation is incorporated into the problem. Experimental data for “Dental Dam” rubber show excellent agreement with the theory over the range of validity of the neo-Hookean strain energy function employed in the analyses.

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.

Age Dependency of the Biaxial Biomechanical Behavior of Human Abdominal Aorta

2004 ◽  
Vol 126 (6) ◽  
pp. 815-822 ◽  
Author(s):  
Jonathan P. Vande Geest ◽  
Michael S. Sacks ◽  
David A. Vorp
Keyword(s):  
Experimental Data ◽  
Abdominal Aorta ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Infrarenal Aorta ◽  
Biomechanical Behavior ◽  
Age Related ◽  
Human Abdominal Aorta ◽  
Group 1

Background: The biomechanical behavior of the human abdominal aorta has been studied with great interest primarily due to its propensity to develop such maladies as atherosclerotic occlusive disease, dissections, and aneurysms. The purpose of this study was to investigate the age-related biaxial biomechanical behavior of human infrarenal aortic tissue. Methods of Approach: A total of 18 samples (13 autopsy, 5 organ donor) were harvested from patients in each of three age groups: Group 1 (<30years old, n=5), Group 2 (between 30 and 60 years old, n=7), and Group 3 (>60years old, n=6). Each specimen was tested biaxially using a tension-controlled protocol which spanned a large portion of the strain plane. Response functions fit to experimental data were used as a tool to guide the appropriate choice of the strain energy function W. Results: Under an equibiaxial tension of 120 N/m, the average peak stretch values in the circumferential direction for Groups 1, 2, and 3 were mean±SD1.46±0.07,1.15±0.07, and 1.11±0.06, respectively, while the peak stretch values in the longitudinal direction were 1.41±0.03,1.19±0.11, and 1.10±0.04, respectively. There were no significant differences between the average longitudinal and circumferential peak stretch within each group p>0.1, but both of these values were significantly less p<0.001 for Groups 2 and 3 when compared to Group 1. Patients in Group 1 were modeled using a polynomial strain energy function W, while patients in Groups 2 and 3 were modeled using an exponential form of W, suggesting an age-dependent shift in the mechanical response of this tissue. Conclusion: The biaxial tensile testing results reported here are, to our knowledge, the first given for the human infrarenal aorta and reinforce the importance of determining the functional form of W from experimental data. Such information may be useful for the clinician or researcher in identifying key changes in the biomechanical response of abdominal aorta in the presence of an aneurysm.

Modeling and Identification of Polyurethane Foam in Uniaxial Compression: Combined Elastic and Viscoelastic Response

2003 ◽  
Author(s):  
Rajani K. Ippili ◽  
Richard D. Widdle ◽  
Patricia Davies ◽  
Anil K. Bajaj
Keyword(s):  
Polyurethane Foam ◽  
Uniaxial Compression ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Integral Approach ◽  
Relaxation Kernel ◽  
Static Response ◽  
Highly Nonlinear ◽  
Hereditary Integral ◽  
Compression Data

Polyurethane foam used in automotive seating applications is a highly nonlinear and viscoelastic material. These properties are manifested even in its quasi-static response. In this paper, two different approaches to model and identify these material properties are presented. In both the approaches the viscoelastic property is assumed linear and modeled by a convolution of the input with a relaxation kernel that is a sum of exponentials (hereditary integral approach). The elastic force contribution is however assumed nonlinear and modeled by a polynomial in one approach, and by a model derived from Ogden strain energy function in the other. Uniaxial compression data from experiments is used to identify the parameters of the models. The robustness of the identification procedures and the issues associated with them are also discussed.

Sign in / Sign up

Export Citation Format

Share Document