On compressible materials capable of sustaining axisymmetric shear deformations. Part 1: Anti-plane shear of isotropic hyperelastic materials

1995 ◽  
Vol 39 (1) ◽  
pp. 75-95 ◽  
Keyword(s):  
Shear Deformations ◽  
Plane Shear ◽  
Hyperelastic Materials ◽  
Axisymmetric Shear ◽  
Compressible Materials

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.

scholarly journals A note on anti-plane shear for compressible materials in finite elastostatics

1977 ◽  
Vol 20 (1) ◽  
pp. 1-7 ◽  
Author(s):  
James K. Knowles
Keyword(s):  
Elastic Material ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Plane Shear ◽  
Isotropic Elastic Material ◽  
Necessary And Sufficient ◽  
Compressible Materials

AbstractThis note gives a necessary and sufficient condition that a compressible, isotropic elastic material should admit non-trivial states of finite anti-plane shear.

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