Anti-plane shear deformations for non-Gaussian isotropic, incompressible hyperelastic materials

2001 ◽  
Vol 457 (2012) ◽  
pp. 1999-2017 ◽  
Author(s):  
Cornelius O. Horgan ◽  
Giuseppe Saccomandi
Keyword(s):  
Shear Deformations ◽  
Plane Shear ◽  
Hyperelastic Materials ◽  
Non Gaussian

Large Deformations of a Rotating Solid Cylinder for Non-Gaussian Isotropic, Incompressible Hyperelastic Materials

2000 ◽  
Vol 68 (1) ◽  
pp. 115-117 ◽  
Author(s):  
C. O. Horgan ◽  
G. Saccomandi
Keyword(s):  
Angular Velocity ◽  
Strain Energy ◽  
Large Deformations ◽  
Rotating Cylinder ◽  
Solid Cylinder ◽  
Hyperelastic Materials ◽  
Steady Rotation ◽  
Non Gaussian ◽  
Limiting Value ◽  
Small Angular Velocity

The purpose of this research is to investigate the steady rotation of a solid cylinder for a class of strain-energy densities that are able to describe hardening phenomena in rubber. It is well known that use of the classic neo-Hookean strain energy gives rise to physically unrealistic response in this problem. In particular, solutions exist only for a sufficiently small angular velocity. As the velocity approaches this limiting value, the analysis predicts that the rotating cylinder collapses to a disk. It is shown here that this nonphysical behavior does not occur when generalized neo-Hookean models, which exhibit hardening at large deformations, are used.

scholarly journals Generalized shear deformations for isotropic incompressible hyperelastic materials

1977 ◽  
Vol 20 (2) ◽  
pp. 129-141 ◽  
Author(s):  
James M. Hill
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Shear Deformations ◽  
Partial Differential ◽  
Hyperelastic Materials ◽  
Restricted Form ◽  
Consistent Solution

AbstractFor isotropic incompressible hyperelastic materials the single function characterizing generalized shear deformations or as they are sometimes called anti-plane strain deformations must satisfy two distinct partial differential equations. Knowles [5] has recently given a necessary and sufficient condition for the strain–energy function of the material which if satisfied ensures that the two equations have consistent solutions. It is shown here for the general material not satisfying Knowles' criterion that the only possible consistent solution of the two partial differential equations are those which are already known to exist for all strain–energy functions. More general types of generalized shear deformations for such meterials are shown to exist only for special or restricted form ot the strain-energy function. In derving these results we also obtain an alternative derivation of Knowles' criterion.

Z-direction fiber orientation in paperboard

TAPPI Journal ◽  
2010 ◽  
Vol 9 (10) ◽  
pp. 25-32
Author(s):  
JOHN M. CONSIDINE ◽  
DAVID W. VAHEY ◽  
ROLAND GLEISNER ◽  
ALAN RUDIE ◽  
SABINE ROLLAND DU ROSCOAT ◽  
...  
Keyword(s):  
Compressive Strength ◽  
Shear Strength ◽  
Bond Strength ◽  
Fiber Orientation ◽  
Internal Bond ◽  
Internal Bond Strength ◽  
Shear Deformations ◽  
Plane Shear ◽  
Conventional Tests ◽  
Out Of Plane

This work evaluated the use of conventional tests to show beneficial attributes of z-direction fiber orientation (ZDFO) for structural paperboards. A survey of commercial linerboards indicated the presence of ZDFO in one material that had higher Taber stiffness, out-of-plane shear strength, directional dependence of Scott internal bond strength and directional brightness. Laboratory handsheets were made with a specialized procedure to produce ZDFO. Handsheets with ZDFO had higher out-of-plane shear strength than handsheets formed conventionally. Materials with high out-of-plane shear strength had greater bending stiffness and compressive strength because of their ability to resist shear deformations.

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