Experimentally Tractable, Pseudo-elastic Constitutive Law for Biomembranes: I. Theory

2003 ◽  
Vol 125 (1) ◽  
pp. 94-99 ◽  
Author(s):  
John C. Criscione ◽  
Michael S. Sacks ◽  
William C. Hunter
Keyword(s):  
Stress Response ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Scalar Function ◽  
Constitutive Law ◽  
Biaxial Testing ◽  
Reference Volume ◽  
Stress Strain Relation ◽  
Work Done

Although visco-elastic in general, the stress-strain relation of biomembranes is one-to-one or pseudo-elastic when being loaded after preconditioning. This pseudo-elastic relation is hypoelastic (i.e., it is not hyperelastic), yet much of the stress response can be characterized by a scalar function Ω that represents the work done (per unit reference volume) on the specimen during loading. (Since a pseudo-strain-energy function W is optimized to fit the test data and not the work done, Ω is not equal to W in general.) The remaining part tR of the stress response does no work during loading. With biaxial testing, Ω can be definitively determined from data. Moreover, for tests with the stretch directions coaxial to the axes of anisotropy, tR can be accurately characterized by a scalar function ω that depends on the strain. This paper is part 1 of 2 with “I. Theory” and “II. Application.”

A Hyperelastic Constitutive Law for Aortic Valve Tissue

2009 ◽  
Vol 131 (8) ◽  
Author(s):  
Karen May-Newman ◽  
Charles Lam ◽  
Frank C. P. Yin
Keyword(s):  
Aortic Valve ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Material Behavior ◽  
Constitutive Law ◽  
Biaxial Testing ◽  
Strain Behavior ◽  
Wide Range ◽  
Strain Invariants

The objective of the present study was to perform biaxial testing and apply constitutive modeling to develop a strain energy function that accurately predicts the material behavior of the aortic valve leaflets. Ten leaflets from seven normal porcine aortic valves were biaxially stretched in a variety of protocols and the data combined to develop and fit a strain energy function to describe the material behavior. The results showed that the nonlinear anisotropic behavior of the aortic valve is well described by a strain energy function of two strain invariants, which uses only three coefficients to accurately predict the stress-strain behavior over a wide range of deformations. This structurally-motivated constitutive law has many applications, including computational modeling for clinical and engineering valve treatments.

A Microstructurally Based Orthotropic Hyperelastic Constitutive Law

2002 ◽  
Vol 69 (5) ◽  
pp. 570-579 ◽  
Author(s):  
J. E. Bischoff ◽  
E. A. Arruda ◽  
K. Grosh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Constitutive Model ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Entropy Change ◽  
Constitutive Law ◽  
Elastic Behavior ◽  
The Finite Element Method

A constitutive model is developed to characterize a general class of polymer and polymer-like materials that displays hyperelastic orthotropic mechanical behavior. The strain energy function is derived from the entropy change associated with the deformation of constituent macromolecules and the strain energy change associated with the deformation of a representative orthotropic unit cell. The ability of this model to predict nonlinear, orthotropic elastic behavior is examined by comparing the theory to experimental results in the literature. Simulations of more complicated boundary value problems are performed using the finite element method.

Modeling of Visco-Hyperelastic Behavior of Foams

2008 ◽  
Author(s):  
Y. Anani ◽  
M. Asghari ◽  
R. Naghdabadi
Keyword(s):  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Constitutive Law ◽  
Energy Functions ◽  
Material Constants ◽  
Maxwell Element ◽  
Rate Dependent ◽  
Dependent Behavior ◽  
Strain Energy Functions

In this paper, a new visco-hyperelastic constitutive law for describing the rate dependent behavior of foams is proposed. The proposed model was based on a phenomenological Zener model: a hyperelastic equilibrium spring, which describes the steady-state, long-term response, parallel to a Maxwell element, which captures the ratedependency. A nonlinear viscous damper connected in series to a hyperelastic intermediate spring, controls the ratedependency of the Maxwell element. Therefore, the stress is the sum of equilibrium stress on the equilibrium spring and overstress on the intermediate spring. In hyperelastic theory stress is not calculated directly as in the case of small-strain, linear elastic materials. Instead, stresses are derived from the principle of virtual work using the stored strain energy potential function. In addition, foams are compressible, therefore classic strain energy functions such as the Ogden strain energy function or the Mooney-Rivlin strain energy function are not suitable to describe hyperelastic behavior of foams. So, strain energy functions must include the effect of compressibility. That means the third principal invariant of the deformation gradient tensor F should enter in strain energy functions. For rate-dependent behavior of foams, history integral constitutive law is used. For the equilibrium spring and the intermediate spring, the same strain energy function is employed. In order to use this stain energy function in history integral equation, the kernel function of it is calculated. The effect of compressibility is considered in rate-dependent behavior of foams too. All material constants were obtained from the results of uniaxial tensile tests. Nonlinear regulation was used to find these constants. In these calculations, Average strain rate was employed to find material constants.

Mechanical power and hyperelasticity

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Mechanical Power ◽  
Elastic Materials ◽  
Cyclic Motion

This chapter covers the notion of hyperelasticity—the concept that stress is derived from a strain—energy function–by invoking an analogy between elastic materials and springs. Alternatively, it can be derived by invoking a work inequality; the notion that work is required to effect a cyclic motion of the material.

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.

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.

Viscohyperelastic Strain Energy Function

2017 ◽  
pp. 59-78 ◽  
Author(s):  
Arne Vogel ◽  
Lalao Rakotomanana ◽  
Dominique P. Pioletti
Keyword(s):  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function
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