scholarly journals A general polyconvex strain-energy function for fiber-reinforced materials

PAMM ◽  
2005 ◽  
Vol 5 (1) ◽  
pp. 245-246 ◽  
Author(s):  
Bernd Markert ◽  
Wolfgang Ehlers ◽  
Nils Karajan
Keyword(s):  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Fiber Reinforced ◽  
Fiber Reinforced Materials ◽  
Reinforced Materials

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.

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.

Fiber symmetry

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Composite Materials ◽  
Constitutive Equation ◽  
Transversely Isotropic ◽  
Fiber Reinforced ◽  
Fiber Reinforced Materials ◽  
Reinforced Materials

This chapter develops the general constitutive equation for transversely isotropic, fiber-reinforced materials. Applications include composite materials and bio-elasticity.

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.

scholarly journals The research on precise forming technology of “λ” type composite skin

2021 ◽  
Vol 30 ◽  
pp. 263498332199474
Author(s):  
Qiang Guo ◽  
Kai He ◽  
Hengyuan Xu ◽  
Youyi Wen
Keyword(s):  
Carbon Fiber ◽  
Middle Layer ◽  
Fiber Reinforced ◽  
Process Verification ◽  
Forming Technology ◽  
Fiber Reinforced Materials ◽  
New Type ◽  
Carbon Fiber Reinforced ◽  
Type Composite ◽  
Reinforced Materials

With the application of “ λ” type composite skin becoming more and more extensive and diversified, its precise forming technology is also widely concerned. This article mainly solves the quality problems of “ λ” type corner area, such as delamination dispersion and surface wrinkle, which exist in reality commonly in the manufacturing process. The prepreg is heated along the corner area of the tooling to solve the problem that prepreg is difficult to be compacted due to the large modulus of carbon fiber in “ λ” type corner area. Furthermore, two precompaction tests are creatively increased at 16 layers (middle layer) and 32 layers (last layer) for the thick structure, respectively, to ensure the compaction effect of the blank. In addition, combined with the characteristics of highly elastic rubber and carbon fiber-reinforced materials, a new type of soft mold structure with proper flexibility and good stiffness is proposed innovatively through the reasonable placement of carbon fiber-reinforced materials and the setting of exhaust holes according to the structure characteristics of “ λ” type root skin. Through further process verification, it is shown that the improved process has effectively solved the problems of wrinkles and internal delamination at the sharp corners of parts and realized zero-defect manufacturing of “ λ” type root skin for the first time.

Boundary Layers in Fiber-Reinforced Materials

1973 ◽  
Vol 40 (2) ◽  
pp. 518-522 ◽  
Author(s):  
G. C. Everstine ◽  
A. C. Pipkin
Keyword(s):  
Boundary Layers ◽  
Fiber Reinforced ◽  
Fiber Reinforced Materials ◽  
Reinforced 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.

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