A class of orthotropic and transversely isotropic hyperelastic constitutive models based on a polyconvex strain energy function

2004 ◽  
Vol 41 (14) ◽  
pp. 3833-3848 ◽  
Author(s):  
Mikhail Itskov ◽  
Nuri Aksel
Keyword(s):  
Energy Function ◽  
Strain Energy ◽  
Constitutive Models ◽  
Strain Energy Function ◽  
Transversely Isotropic

A Simple Transversely Isotropic Hyperelastic Constitutive Model Suitable for Finite Element Analysis of Fiber Reinforced Elastomers

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Leslee W. Brown ◽  
Lorenzo M. Smith
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Material Model ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Material Tests

A transversely isotropic fiber reinforced elastomer’s hyperelasticity is characterized using a series of constitutive tests (uniaxial tension, uniaxial compression, simple shear, and constrained compression test). A suitable transversely isotropic hyperelastic invariant based strain energy function is proposed and methods for determining the material coefficients are shown. This material model is implemented in a finite element analysis by creating a user subroutine for a commercial finite element code and then used to analyze the material tests. A useful set of constitutive material data for multiple modes of deformation is given. The proposed strain energy function fits the experimental data reasonably well over the strain region of interest. Finite element analysis of the material tests reveals further insight into the materials constitutive nature. The proposed strain energy function is suitable for finite element use by the practicing engineer for small to moderate strains. The necessary material coefficients can be determined from a few simple laboratory tests.

On the Constitutive Equations of Biological Materials

1975 ◽  
Vol 42 (1) ◽  
pp. 242-243 ◽  
Author(s):  
H. Demiray
Keyword(s):  
Energy Function ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Biological Materials ◽  
Biological Tissues

This paper deals with a simple possible form of the strain-energy function for biological tissues which are assumed to be transversely isotropic. Also the solution of a problem is studied and the result is compared with experiments.

New Strain Energy Function for Acoustoelastic Analysis of Dilatational Waves in Nearly Incompressible, Hyper-Elastic Materials

2005 ◽  
Vol 72 (6) ◽  
pp. 843-851 ◽  
Author(s):  
H. Kobayashi ◽  
R. Vanderby
Keyword(s):  
Wave Propagation ◽  
Energy Function ◽  
Strain Energy ◽  
Constitutive Models ◽  
Strain Energy Function ◽  
Deformation Tensor ◽  
Energy Functions ◽  
Dilatational Wave ◽  
Hyper Elastic ◽  
Strain Energy Functions

Acoustoelastic analysis has usually been applied to compressible engineering materials. Many materials (e.g., rubber and biologic materials) are “nearly” incompressible and often assumed incompressible in their constitutive equations. These material models do not admit dilatational waves for acoustoelastic analysis. Other constitutive models (for these materials) admit compressibility but still do not model dilatational waves with fidelity (shown herein). In this article a new strain energy function is formulated to model dilatational wave propagation in nearly incompressible, isotropic materials. This strain energy function requires four material constants and is a function of Cauchy–Green deformation tensor invariants. This function and existing (compressible) strain energy functions are compared based upon their ability to predict dilatational wave propagation in uniaxially prestressed rubber. Results demonstrate deficiencies in existing functions and the usefulness of our new function for acoustoelastic applications. Our results also indicate that acoustoelastic analysis has great potential for the accurate prediction of active or residual stresses in nearly incompressible materials.

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.

Wrinkling of a Fiber-Reinforced Membrane

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
E. Shmoylova ◽  
A. Dorfmann
Keyword(s):  
Boundary Conditions ◽  
Energy Function ◽  
Mechanical Response ◽  
Transverse Isotropy ◽  
Base Material ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Incompressible Material ◽  
Fiber Reinforced ◽  
Relaxed Energy

In this paper we investigate the response of fiber-reinforced cylindrical membranes subject to axisymmetric deformations. The membrane is considered as an incompressible material, and the phenomenon of wrinkling is taken into account by means of the relaxed energy function. Two cases are considered: transversely isotropic membranes, characterized by one family of fibers oriented in one direction, and orthotropic membranes, characterized by two family of fibers oriented in orthogonal directions. The strain-energy function is considered as the sum of two terms: The first term is associated with the isotropic properties of the base material, and the second term is used to introduce transverse isotropy or orthotropy in the mechanical response. We determine the mechanical response of the membrane as a function of fiber orientations for given boundary conditions. The objective is to find possible fiber orientations that make the membrane as stiff as possible for the given boundary conditions. Specifically, it is shown that for transversely isotropic membranes a unique fiber orientation exists, which does not affect the mechanical response, i.e., the overall behavior is identical to a nonreinforced membrane.

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
Sign in / Sign up

Export Citation Format

Share Document