Unloading Waves in a Plucked Hyperelastic String

1989 ◽  
Vol 56 (2) ◽  
pp. 459-465 ◽  
Author(s):  
J. L. Wegner ◽  
J. B. Haddow ◽  
R. J. Tait
Keyword(s):  
Finite Deformation ◽  
Strain Energy ◽  
Similarity Solutions ◽  
Plane Motion ◽  
Governing Equations ◽  
Energy Functions ◽  
Fixed End ◽  
Strain Energy Functions ◽  
Deformation Plane

The governing equations for the finite deformation plane motion of a hyperelastic string are obtained in conservation form. These equations and the corresponding jump relations are used to investigate the response of a symmetrically-plucked string when it is suddenly released. Similarity solutions, which are valid until the first reflection occurs at a fixed end, are obtained for two strain energy functions. Justification is given for the use of isothermal strain energy functions.

On plane deformations of incompressible isotropic elastic solids

1978 ◽  
Vol 83 (1) ◽  
pp. 127-136 ◽  
Author(s):  
R. W. Ogden
Keyword(s):  
Strain Energy ◽  
Finite Plane ◽  
Governing Equations ◽  
Field Equations ◽  
Elastic Solids ◽  
Energy Functions ◽  
Closed Form Solutions ◽  
New Formulation ◽  
Strain Energy Functions ◽  
Plane Deformations

In two recent papers (6, 10) a new formulation of the governing equations for finite plane-strain deformations of compressible isotropic elastic solids was presented. This has been used to obtaingeneral solutions to the field equations for a certain class of strain–energy functions, and then closed-form solutions to a large class of boundary-value problems.

Strain energy functions for filled elastomers

1965 ◽  
Vol 9 (7) ◽  
pp. 2565-2579 ◽  
Author(s):  
M. Shinozuka ◽  
A. M. Freudenthal
Keyword(s):  
Strain Energy ◽  
Energy Functions ◽  
Filled Elastomers ◽  
Strain Energy Functions

Transverse Impact of a Hyperelastic Stretched String

1985 ◽  
Vol 52 (1) ◽  
pp. 137-143 ◽  
Author(s):  
M. F. Beatty ◽  
J. B. Haddow
Keyword(s):  
Strain Energy Function ◽  
Similarity Solutions ◽  
Plane Motion ◽  
Governing Equations ◽  
Transverse Impact ◽  
Normal Impact ◽  
Wave Speeds ◽  
First Order ◽  
Special Case ◽  
Infinite String

Governing equations are derived for the plane motion of a stretched hyperelastic string subjected to a suddenly applied force at one end. These equations can be put in the form of a quasilinear system of first-order partial differential equations, which is totally hyperbolic for an admissible strain energy function. There are, in general, two wave speeds and two corresponding shock speeds. Special consideration is given to the jump relations across the shocks. Similarity solutions for a string moved at one end in loading or unloading are obtained for a general hyperelastic solid. The results are applicable to the familiar neo-Hookean or Mooney-Rivlin material, and the nature of the solution for another special hyperelastic material is discussed. These solutions are valid for a semi-infinite string, or until the first reflection occurs. It is shown that a special case of the similarity solution is valid for the normal impact of a stretched string by a constant speed, point application of load. Exact solution to the equations for the neo-Hookean model is derived in terms of elliptic integrals, and some numerical results are provided.

On the Development of Volumetric Strain Energy Functions

1999 ◽  
Vol 67 (1) ◽  
pp. 17-21 ◽  
Author(s):  
S. Doll ◽  
K. Schweizerhof
Keyword(s):  
Strain Energy ◽  
Volumetric Strain ◽  
Strain Energy Function ◽  
Material Behavior ◽  
Additional Material ◽  
Energy Functions ◽  
Material Parameters ◽  
Physical Conditions ◽  
Starting Point ◽  
Strain Energy Functions

To describe elastic material behavior the starting point is the isochoric-volumetric decoupling of the strain energy function. The volumetric part is the central subject of this contribution. First, some volumetric functions given in the literature are discussed with respect to physical conditions, then three new volumetric functions are developed which fulfill all imposed conditions. One proposed function which contains two material parameters in addition to the compressibility parameter is treated in detail. Some parameter fits are carried out on the basis of well-known volumetric strain energy functions and experimental data. A generalization of the proposed function permits an unlimited number of additional material parameters.  Dedicated to Professor Franz Ziegler on the occasion of his 60th birthday. [S0021-8936(00)00901-6]

Finding the Constitutive Relation for a Specific Elastomer

1993 ◽  
Vol 115 (3) ◽  
pp. 329-336 ◽  
Author(s):  
Yun Ling ◽  
Peter A. Engel ◽  
Wm. L. Brodskey ◽  
Yifan Guo
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Strain Energy ◽  
Pure Shear ◽  
Strain Energy Function ◽  
Invariant Polynomial ◽  
Energy Functions ◽  
Finite Element Program ◽  
Biaxial Extension ◽  
Strain Energy Functions

The main purpose of this study was to determine a suitable strain energy function for a specific elastomer. A survey of various strain energy functions proposed in the past was made. For natural rubber, there were some specific strain energy functions which could accurately fit the experimental data for various types of deformations. The process of determining a strain energy function for the specific elastomer was then described. The second-order invariant polynomial strain energy function (James et al., 1975) was found to give a good fit to the experimental data of uniaxial tension, uniaxial compression, equi-biaxial extension, and pure shear. A new form of strain energy function was proposed; it yielded improved results. The equi-biaxial extension experiment was done in a novel way in which the moire techniques (Pendleton, 1989) were used. The obtained strain energy functions were then utilized in a finite element program to calculate the load-deflection relation of an electrometric spring used in an electrical connector.

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