On Formulas for the Velocity of Rayleigh Waves in Prestrained Incompressible Elastic Solids

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
Pham Chi Vinh
Keyword(s):  
Rayleigh Wave ◽  
Energy Function ◽  
Rayleigh Waves ◽  
Strain Energy ◽  
Hydrostatic Stress ◽  
Strain Energy Function ◽  
Elastic Solids ◽  
Algebraic Form ◽  
Cubic Equation ◽  
Isotropic Solids

In the present paper, formulas for the velocity of Rayleigh waves in incompressible isotropic solids subject to a general pure homogeneous prestrain are derived using the theory of cubic equation. They have simple algebraic form and hold for a general strain-energy function. The formulas are concretized for some specific forms of strain-energy function. They then become totally explicit in terms of parameters characterizing the material and the prestrains. These formulas recover the (exact) value of the dimensionless speed of Rayleigh wave in incompressible isotropic elastic materials (without prestrain). Interestingly that, for the case of hydrostatic stress, the formula for the Rayleigh wave velocity does not depend on the type of strain-energy function.

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.

Large deformation isotropic elasticity: on the correlation of theory and experiment for compressible rubberlike solids

1972 ◽  
Vol 328 (1575) ◽  
pp. 567-583 ◽  
Keyword(s):  
Energy Function ◽  
Strain Energy ◽  
Pure Shear ◽  
Density Ratio ◽  
Strain Energy Function ◽  
Elastic Solids ◽  
Simple Tension ◽  
Isotropic Elasticity ◽  
Full Discussion ◽  
Theory And Experiment

A method of approach to the correlation of theory and experiment for incompressible isotropic elastic solids under finite strain was developed in a previous paper (Ogden 1972). Here, the results of that work are extended to incorporate the effects of compressibility (under isothermal conditions). The strain-energy function constructed for incompressible materials is augmented by a function of the density ratio with the result that experimental data on the compressibility of rubberlike materials are adequately accounted for. At the same time the good fit of the strain-energy function arising in the incompressibility theory to the data in simple tension, pure shear and equibiaxial tension is maintained in the compressible theory without any change in the values of the material constants. A full discussion of inequalities which may reasonably be imposed upon the material parameters occurring in the compressible theory is included.

On interfacial waves in pre-stressed layered incompressible elastic solids

1995 ◽  
Vol 450 (1939) ◽  
pp. 319-341 ◽  
Keyword(s):  
Energy Function ◽  
High Frequency ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Bifurcation Equation ◽  
Interfacial Waves ◽  
Elastic Solids ◽  
Frequency Limit ◽  
Material Parameters ◽  
Stress And Deformation

Interfacial waves along the plane boundary between two pre-stressed incompressible elastic solids are considered. One of the solids is a half-space while the other has arbitrary uniform thickness. The principal axes of the underlying pure homogeneous deformation in the two solids are aligned, with one axis normal to the interface. For propagation along an in-plane principal axis, the dispersion equation is derived in respect of a general strain-energy function. Conditions on the pre-strain, pre-stress and material parameters that ensure the existence of a unique interfacial wavespeed at low frequencies are obtained, and it is shown that, in special circumstances, non-dispersive waves can exist at the low-frequency limit. Asymptotic results at the high-frequency limit are also obtained. For the case of equibiaxial pre-strain, more specific conditions are derived for the existence of interfacial waves at the low- and high-frequency asymptotes, and these provide information on the existence of waves for the whole frequency range. A particular feature of the structure considered is that it may act as a mechanical filter in different frequency regimes depending on the pre-strain, pre-stress and material parameters. When the wavespeed vanishes, the dispersion equation reduces to a bifurcation equation, solutions of which define states of stress and deformation which form boundaries of the region of stability of the underlying state of stress and deformation in the two materials for given material properties. The bifurcation equation is examined separately and an explicit bifurcation criterion is given for equibiaxial deformations. The results are illustrated graphically by considering several numerical examples based on a certain class of strain-energy functions, which includes the neo-Hookean strain-energy function. The results highlight low- and high-frequency features and demonstrate the influence of pre-stress and deformation on the multiplicity of propagating modes.

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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