The Nonlinear Elastic Behavior of Open-Cell Foams

1991 ◽  
Vol 58 (2) ◽  
pp. 376-381 ◽  
Author(s):  
W. E. Warren ◽  
A. M. Kraynik
Keyword(s):  
Strain Energy ◽  
Three Dimensional ◽  
Strain Energy Function ◽  
Elastic Behavior ◽  
Dimensional Structure ◽  
Arbitrary Orientation ◽  
Tetrahedral Unit ◽  
Open Cell Foams ◽  
Nonlinear Elastic ◽  
Force Displacement

A constitutive model for the nonlinear elastic behavior of isotropic low-density opencell foams with three-dimensional structure is formulated in terms of a strain energy function. The theory is based on micromechanical analysis of an idealized tetrahedral unit cell of arbitrary orientation that contains four half-struts joining at equal angles. The force-displacement relations for each strut are expressed by compliances for bending and stretching that do not depend on the magnitude of applied force. Contributions to the strain energy from large deformation effects are assumed to depend on strut reorientation and stretching, and are determined by analyzing a pin-jointed structure. The analysis is considered to be valid for finite strains below the onset of yielding associated with strut buckling.

Nonlinear Modeling of 3D Open-Cell Foams

1999 ◽  
Author(s):  
Yu Wang ◽  
Alberto M. Cuitiño
Keyword(s):  
Strain Energy ◽  
Nonlinear Modeling ◽  
Three Dimensional ◽  
Strain Energy Function ◽  
Nonlinear Material ◽  
Open Cell ◽  
Wide Range ◽  
Open Cell Foams ◽  
Explicit Correlation ◽  
Strain Energy Functions

Abstract In this article, we present a hyperelastic model for light and compliant open cell foams with an explicit correlation between microstructure and macroscopic behavior. The model describes a large number of three dimensional structures with regular and irregular cells. The theory is based on the formulation of strain-energy function accounting for stretching which is the main deformation mechanism in this type of materials. Within the same framework, however, bending, shear and twisting energies can also be incorporated. The formulation incorporates nonlinear kinematics which traces the evolution of the structure during loading process and its effects on the constitutive behavior, including the cases where configurational transformations are present leading to non-convex strain-energy functions. Also nonlinear material effects at local or beam level are introduced to accommodate a wide range of different material behaviors. Since the micromechanical formulation presented here has explicit correlation with the foam structure, it preserves in the constitutive relation the symmetries or directional properties of the corresponding structures, including the cases of re-entrant foams which exhibit negative Poisson’s ratio effects. The model captures the central features exhibit by these materials. Predictions of the model for macroscopic uniaxial strain are presented in this article.

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.

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.

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.

The Cosserat Point Element as an Accurate and Robust Finite Element Formulation for Implicit Dynamic Simulations

2019 ◽  
Vol 17 (01) ◽  
pp. 1844006
Author(s):  
Mahmood Jabareen ◽  
Yehonatan Pestes
Keyword(s):  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Three Dimensional ◽  
Nonlinear Dynamic Analysis ◽  
Strain Energy Function ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Dynamic Simulations ◽  
Cosserat Point

The reliability of numerical simulations manifested the need for an accurate and robust finite element formulation. Therefore, in the present study, an eight node brick Cosserat point element ( CPE ) for the nonlinear dynamic analysis of three-dimensional (3D) solids including both thick and thin structures is developed. Within the present finite element formulation, a strain energy function is proposed and additively decoupled into two parts. One part is characterized by any 3D strain energy function, while the other part controls the response to inhomogeneous deformations. Several example problems are presented, which demonstrate the accuracy and the robustness of the developed CPE in modeling the dynamic response of elastic structures.

Effect of Nonlinear Elastic Behavior on Bilayer Decohesion of Thin Metal Films From Nonmetal Substrates

2002 ◽  
Vol 69 (4) ◽  
pp. 407-414 ◽  
Author(s):  
S. P. Baker ◽  
X. Wang ◽  
C.-Y. Hui
Keyword(s):  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Metal Films ◽  
Thin Metal ◽  
Elastic Behavior ◽  
Thin Metal Films ◽  
Target Layer ◽  
The Difference ◽  
Nonlinear Elastic

Nonlinear unloading behavior has been observed in thin metal films on substrates. In the present work, the effects of this nonlinear unloading behavior on the strain energy release rate in bilayer decohesion experiments, in which a highly stressed overlayer (“driver”) is used to decohere a layer (“target”) from a substrate, is modeled. Cases where either the driver or the target layer are nonlinear are considered. For particular combinations of stiffnesses and thicknesses, the difference between linear and nonlinear unloading behavior can be quite large (several hundred percent) at experimentally observed stress levels. For practical cases of CR/CU and CU/glass driver/target layer combinations, the maximum difference is about 25%.

Nonlinear Finite Element Analysis of Crack Tip of Rubber-Like Material

2007 ◽  
Vol 353-358 ◽  
pp. 1013-1016
Author(s):  
Jian Bing Sang ◽  
Su Fang Xing ◽  
Xiao Lei Li ◽  
Jie Zhang
Keyword(s):  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Elastic Behavior ◽  
Element Analysis ◽  
Finite Element Program ◽  
User Subroutine ◽  
Element Program ◽  
Notch Tip

It has been well known that rubber-like material can undergo large deformation and exhibit large nonlinear elastic behavior. Because of the geometrically nonlinear of rubber like material, it is more difficult to analyze it with finite element near the notch tip. What is more, because there are varieties of the strain energy functions, implementation of these models in a general finite element program to meet the need of industry applications can be time consuming. In order to make use of the constitutive equation of Y.C. Gao in 1997 and analyze the notch tip of rubber-like material, a framework to implement the rubber-like material model is established within the general-purpose finite element program MSC.Marc. It will be very convenient to implement this isotropic hyperelastic model into the program with a user subroutine. This paper starts with the theoretical analysis based on the strain energy function given by Y.C. Gao in 1997. A user subroutine is programmed to implement this strain energy function into the program of MSC.Marc, which offer a convenient method to analyze the stress and strain of rubber-like material with the strain energy function that is needed. Though analysis with MSC.Marc, it is found that the result with finite element is consistent with the analytical result that given by Y.C. Gao in 1997, which testify that analyzing rubber like material with this method is reasonable and convenient.

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.

Nonlinear Elastic Constitutive Relations of Auxetic Honeycombs

2009 ◽  
Author(s):  
Jaehyung Ju ◽  
Joshua D. Summers ◽  
John Ziegert ◽  
Georges Fadel
Keyword(s):  
Cell Walls ◽  
Strain Energy ◽  
Constitutive Relations ◽  
Effective Strain ◽  
Strain Energy Function ◽  
Periodic Boundary Conditions ◽  
Plane Shear ◽  
Local Cell ◽  
Nonlinear Elastic ◽  
Nonlinear Constitutive Relation

When designing a flexible structure consisting of cellular materials, it is important to find the maximum effective strain of the cellular material resulting from the deformed cellular geometry and not leading to local cell wall failure. In this paper, a finite in-plane shear deformation of auxtic honeycombs having effective negative Poisson’s ratio is investigated over the base material’s elastic range. An analytical model of the inplane plastic failure of the cell walls is refined with finite element (FE) micromechanical analysis using periodic boundary conditions. A nonlinear constitutive relation of honeycombs is obtained from the FE micromechanics simulation and is used to define the coefficients of a hyperelastic strain energy function. Auxetic honeycombs show high shear flexibility without a severe geometric nonlinearity when compared to their regular counterparts.

Antiplane Wave Scattering from a Cylindrical Void in a Pre-Stressed Incompressible Neo-Hookean Material

2012 ◽  
Vol 11 (2) ◽  
pp. 367-382 ◽  
Author(s):  
William J. Parnell ◽  
I. David Abrahams
Keyword(s):  
Wave Scattering ◽  
Small Amplitude ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Incident Field ◽  
Constitutive Behaviour ◽  
Void Size ◽  
Scattering Coefficients ◽  
Nonlinear Elastic Medium ◽  
Nonlinear Elastic

AbstractAn isolated cylindrical void is located inside an incompressible nonlinear-elastic medium whose constitutive behaviour is governed by a neo-Hookean strain energy function. In-plane hydrostatic pressure is applied in the far-field so that the void changes its radius and an inhomogeneous region of deformation arises in the vicinity of the void. We consider scattering from the void in the deformed configuration due to an incident field (of small amplitude) generated by a horizontally polarized shear (SH) line source, a distance r0 (R0) away from the centre of the void in the deformed (undeformed) configuration. We show that the scattering coefficients of this scattered field are unaffected by the pre-stress (initial deformation). In particular, they depend not on the deformed void radius a or distance r0, but instead on the original void size A and original distance R0.

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